Adaptive Optics for Industry and Medicine: Proceedings of the Sixth International Workshop

Adaptive Optics for

Industry and Medicine

This page intentionally left blank

Adaptive Optics for Industry and Medicine Proceedings of the Sixth International Workshop 12-15june2007 National University of Ireland, Ireland

editor

Christopher Dainty Nationat University of Ireland, Galway, Ireland b Imperial College, London, UK

Impeiral College Press

Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Re. Ltd.

5 Toh Tuck Link, Singapore 596224 USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

UK ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE

ritish Library C a t a I o ~ ~ g - i n - ~ b ~Data ~tion A catalogue record for this book is available from the British Library.

A D A ~ OPTICS I ~ FOR INDUSTRY AND MEDICINE Proceedings of the Sixth International Workshop Copyright 0 2008 by Imperial College Press All rights reserved. This book, or parts thereox may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any inforination storage and retrieval system now known or to be invented, withoat written permissionfront the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN-13 978- 1-84816-110-8 ISBN-10 1-84816-1 10-7

Printed in Singapore by World Scientific Printers (S) Re Ltd

Prefaee

The Sixth Inte~ationalWorkshop on Adaptive Optics in Industry and Medicine took place in Galway, Ireland, from June 12-15, 2007. It was attended by approximately 130 delegates from 18 countries and also had a small exhibition with 12 companies participating. This series of Workshops started in 1997, with the first meeting being held in Shatura, Russia and subsequent ones being located in Durham (UK), Albuquerque (USA), Miinster (Germany) and Beijing (China). This series is driven by grassroots activity in the field, and the relatively small size of the meetings has ensured an informal and lively occasion. The subject of adaptive optics started with the publication by Horace Babcock, in 1953, of a paper describing how atmospheric turbulence may be compensated for in Earth-based telescopes. The idea was taken up by the US military in the 1970s and by astronomers in the late 19XOs, and because of the demanding requirements for the then-available technology, adaptive optics was regarded as an expensive and sophisticated technique, to be undertaken only by big research and engineering teams. It was only in the late 1990s that people recognised that the basics of adaptive optics are not "rocket science", indeed they are very simple, and that through appropriate technological development, very highquality but low cost adaptive optics systems could be constructed. Perhaps this is most vividly illustrated by the disclosure, at the Sixth Workshop, that adaptive optics is deployed in many DVD players at a cost of approximately 60 (euro-) cents per piece, and in quantities of more than one million per month. Another indication of the growing practicality of adaptive optics was the presence of many companies at this Workshop. Organising any meeting, particularly one run at as low cost as possible, involves a significant volunteer effort. I would like to thank my colleagues on the Scientific Organising Committee for their help: Pablo Artal, John Gonglewski, Wenhan Jiang, Satoshi Kawata, Alexis Kudryashov, Gordon Love, Scot Olivier, Sergio Restaino, Robert Tyson, Ulrich Wittrock and Zhang Yudong. Local assistance was also provided by many people in the Applied Optics Group in Galway, with particular thanks to Emer McHugh and Una Murphy for administrative support. The Workshop was co-sponsored by The European Optical Society and by The Optical Society of America. Finally, the Workshop could not have been held without the financial support of many companies and organisations: Advanced Medical Optics, Andor Technologies, Bausch & Lomb Ireland, Boston Micromachine Corporation, CILAS, Fraunhofer Institut Photonische Mikrosysteme, Hamamatsu, Holoeye, Imagine Optics and Imagine Eyes, IrisAO, Night-N, O K 0 Flexible Optics, Optos, Phasics, Scimeasure, IDA Ireland, Enterprise Ireland, Fhilte Ireland and Science Foundation Ireland. V

vi

The Seventh International Workshop on Adaptive Optics in Industry and hMedicine is due to be held in Russia in 2009, and I hope that many people reading this Proceedings will be able to attend that event. Galway, October 2007

Chris Dainty

Contents Preface

V

Part 1 Wavefront Correctors and Control

Liquid crystal lenses for correction of presbyopia (Invited Paper) Guoqiang Li and Nasser Peyghambarian

3

Converging and diverging liquid crystal lenses (Oral Paper) Andrew X Kirby, Philip J. FK Hands, and Gordon D. Love

9

Liquid lens technology for miniature imaging systems: status of the technology, performance of existing products and future trends (Invited Paper) Bruno Berge

14

Carbon fiber reinforced polymer deformable mirrors for high energy laser applications (Oral Paper) S.R. Restaino, J.R. Andrews, R. Martin, T. Martinez, R. Romeo, C.C. Wilcox

17

Tiny multilayer deformable mirrors (Oral Paper) Tatiana Cherezova,Alexander So bolev, Alexander Alexandrov, Alexey Kudryashov, and Vadim Samarkin

23

Performance analysis of piezoelectric deformable mirrors (Oral Paper) Oleg Soloviev, Mikhail Loktev and Gleb Vdovin

29

Deformable membrane mirror with high actuator density and distributed control (Oral Paper) Roger Hamelinck, Nick Rosielle, Maarten Steinbuch, Rogier Ellenbroek, Michel Verhaegen and Niek Doelman

35

Characterization and closed-loop demonstration of a novel electrostatic membrane mirror using COTS membranes (Oral Paper) David Dayton, Justin Mansell, Bob and John Gonglewski

41

vii

viii

Electrostatic micro-deformable mirror based on polymer materials (Oral Paper) Frederic Zamkotsian, Patrick Lanzoni, Veronique Conedera and Norbert Fabre

47

Recent progress in CMOS integrated MEMS A 0 mirror development (Oral Paper) A. Gehner, J. U.Schmidt, M Wildenhain,J. Knobbe and M Wagner

53

Compact large-stroke piston-tip-tilt actuator and mirror (Oral Paper) W. Noell, A. Hugi, T. Overstolz, , S. Waldis,R. Stanley and N. F. de Rooij

59

MEMS deformable mirrors for high performance A 0 applications (Oral Paper) Paul Bierden, Thomas Bifano and Steven Cornelissen

65

A versatile interferometrictest-rig for the investigation and evaluation of ophthalmic A 0 systems (Poster Paper) Steve Gruppetta,Jiang Jian Zhong and Luis Diaz-Santana

I1

Woofer-tweeter adaptive optics (Poster Paper) Thomas Farrell and Chris Dainty

77

Deformable mirrors based on transversal piezoeffect (Poster Paper) Gleb Vdovin, Mikhail Loktev and Oleg Soloviev

83

Low-cost spatial light modulators for ophthalmic applications (Poster Paper) VicenteDurdn, Vicent Climent, Enrique Tajahuerce,Jesus Lancis, Zbigniew Jaroszewicz, Just0 Arines, Jorge Ares, and Salvador Bard

89

Latest MEMS DM developments and the path ahead at Iris A 0 (Poster Paper) Michael A. Helmbrecht, Nathan Doble, Carl Kempf and Min He

95

Electrostatic push pull mirror improvernents in visual optics (Poster Paper) S. Bonora and L. Poletto

101

25cm bimorph mirror for petawatt laser S. Bonora, C J Hooker, S. J. Hawkes, J. L. Collier and C. Spindloe

106

ix

Hysteresis compensation for piezo deformable mirror (Poster Paper) H. Song, R. Fraanje, G. Schitter, M Verhaegen and G. Vdovin

112

Static and dynamic responses of an adaptive optics ferrofluidic mirror (Poster Paper) A. Seaman, CJ Cookson, J.B. Macpherson, E.F. Borra, A.M Ritcey, D. Asselin, H, Jerominek, S. Thibault and M.C. W. Campbell

118

New HDTV (1920 x 1080) phase-only SLM (Poster Paper) Stefan Osten and Sven Krueger

124

Monomorph large aperture deformable mirror for laser applications (Poster Paper) J-C Sinquin, J-MLurCon, C Guillemard

130

Low cost, high speed for adaptive optics control (Oral Paper) Christopher D. Saunter and Gordon D. Love

136

Open loop woofer-tweeter adaptive control on the LAO multi-conjugate adaptive optics testbed (Oral Paper) Edward Laag, Don Gavel and Mark Ammons

143

Part 2 Wavefront Sensors Wave front sensorless adaptive optics for imaging and microscopy (Invited Paper) Martin J Booth, Delphine Debarre and Tony Wilson

151

A fimdamental limit for wavefront sensing (Oral Paper) Carl Paterson

157

Coherent fibre-bundle wavefront sensor (Oral Paper) Brian Vohnsen,I. Iglesias and Pablo Artal

163

M a x i m ~ - l i ~ e l i h o methods od in wave-front sensing: nuisance parameters (Oral Paper) David Lara, Harrison H. Barrett, and Chris Dainty

169

Real-time wavefront sensing for ultrafast high-power laser beams (Oral Paper) Juan M Bueno, Brian Vohnsen,Pedro M Prieto, Luis Roso and Pablo Artal

175

X

Wavefront sensing using a random phase screen (Oral Paper) M Loktev, G. Vdovin and 0.Soloviev

182

Quadri-Wave Lateral Shearing Interferometry: a new mature technique for wave front sensing in adaptive optics (Oral Paper) Benoit Wattellier,Ivan Doudet, Sabrina Velghe and Jkr6me Primot

188

In vivo measurement of ocular aberrations with a distorted grating wavefront sensor (Oral Paper) P Harrison, DM Cuevas, GRG E r y , P Fournier, L Diaz-Santana and C Torti

193

Position-sensitive detector designed with unusual CMOS layout strategies for a Hartman-Shack wavefront sensor (Oral Paper) Davies W. de Lima Monteiro, Luciana P. Salles, Pedro Retes, Andrk S. 0.Furtado and Gleb Vdovin

200

Adaptive Optics system to compensate complex-shaped wavefronts (Oral Paper) Miguel Ares, and Santiago Roy0

206

A kind of novel linear phase retrieval wavefront sensor and its application in close-loop adaptive optics system (Oral Paper) Xinyang Li, Min Li, Bo Chen, WenhanJiang

212

Ophthalmic Shack-Hatmann wavefront sensor applications (Oral Paper) Daniel R. Neal

219

Wave front sensing of an optical vortex and its correction with the help of bimorph mirror (Poster Paper) F.A. Starikov, G.G. Kochemasov, S.M. Kulikov, A.N. Manachins~, A. V. Ogorodnikov,S.A.Sukharev, V.P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. Atuchin and I. Soldatenkov

227

Recent advances in laser metrology and correction of high numerical aperture laser beams using quadri-wave lateral shearing-interferometry (Poster Paper) Benoit Wattellier,Ivan Doudet and William Boucher

234

Thin filmoptical metrology using principles of wavefront sensing and interference (Poster Paper) D.M. Faichnie, A.H. Greenaway and I. Bain

237

xi

Direct diffractive image simulation (Poster Paper) A.P. Maryasov, N.P. Maryasov, A.P. L a y b

243

High speed smart CMOS sensor for adaptive optics (Poster Paper) T.D. Raymond, D.R. Neal, A. Whitehead,and G. Wirth

248

Traceable astigmatism measurements for wavefront sensors (Poster Paper) S R G Hall, S D Knox, R F Stevens

254

art 3 A~aptiveOptics in Vision Science Dual-conjugate adaptive optics i n s t ~ e nfor t wide-field retinal imaging (Oral Paper) Jorgen Thaung, Mette-Owner Petersen and Zoran Popovic

263

Visual simulation using electromagnetic adaptive-optics (Oral Paper) Laurent Vabre, Fabrice Harms, Nicolas Chateau,Karolinne Maia Rocha, Ronald Krueger

269

High-resolution field-of-view widening in human eye retina imaging (Oral Paper) Alexander l? Dubinin, Tatyana Yu. Cherezova, Alexis l? Kudryashov

275

Psychophysical experiments on visual performance with an ocular adaptive optics system (Oral Paper) E. Dalimier, J.C. Dainty and J. Barbur

28 1

Does the accommodative mechanism of the eye calibrate itself using aberration dynamics? (Oral Paper) K. M Hampson, S. S. Chin and E. A. H. Mallen

287

A study of field aberrations in the human eye (Oral Paper) Alexander l? Goncharov, Maciej Nowakowski, Euginie Dalimier, Matt Sheehan, and Chris Dainty

293

Dual wavefront corrector ophthalmic adaptive optics: design and alignment (Oral Paper) A&-edoDubra and David Williams

299

xii

High speed simultaneous SLO/OCT imaging of the human retina with adaptive optics (Oral Paper) M Pircher, R.J. Zawadzki, J. W. Evans, J.S. Werner and C.K. Hitzenberger

304

Characterization of an AO-OCT system (Oral Paper) Julia W. Evans, Robert J. Zawadzki, Steve Jones, Scot Oliver, John S. Werner

310

Adaptive optics optical coherence tomography for retina imaging (Oral Paper) Guohua Shi, Zhihua Ding, Yun Dai, Xunjun Rao, Yudong Zhang

316

Development, calibration and performance of an electromagnetic-mirrorbased adaptive optics system for visual optics (Oral Paper) Enrique Gambra, Lucie Sawides, Carlos Dorronsoro, Lourdes Llorente and Susana Marcos

322

Adaptive eye model (Poster Paper) Sergey 0. Galetskzy and Alexty V. Kudryashov

329

Adaptive optics system for retinal imaging based on a pyramid vvavefiont sensor (Poster Paper) Sabine Chiesa, Elizabeth Daly, Chris Dainty and S.R. Chamot

336

Modeling of non-stationary dynamic ocular aberrations (Poster Paper) Conor Leahy and Chris Dainty

342

High-order aberrations and accommodation of human eye (Poster Paper) Lixia Xue, Yun Dai, Xuejun Rao, Cheng Wang, Yiyun Hu, Qian Liu and WenhanJiang

348

Electromagnetic deformable mirror: experimental assessment and first ophthalmic applications (Poster Paper) L. Vabre, E.J. Fernandez, F. Harms, J. Charton, B. Hermann, A. Unterhuber,B. Povaiay, N. Chateau and W. Drexler

354

Correcting ocular aberrations in optical coherence tomography (Poster Paper) Simon Tuohy, Adrian Bradu, Adrian Gh. Podoleanu, Nicolas Chateau and Chris Dainty

359

xiii

Part 4 Adaptive Optics in Optical Storage and Microscopy The application of liquid crystal aberration compensator for the optical disc systems (Invited Paper) Masakazu Ogasawara

369

Commercialization of the adaptive scanning optical microscope (ASOM) (Oral Paper) Benjamin Potsaid, John T. Wen, Scott Barry and Alex Cable

376

A practical implementation of adaptive optics for aberration compensation in optical microscopy (Oral Paper) A J Wright, S P Poland, J Vijverberg,J M Girkin

382

Active focus locking in an optically sectioning microscope using adaptive optics (Poster Paper) S Poland, A J Wright,J M Girkin

388

Towards four dimensional particle tracking for biological applications Heather I. Campbell, Paul A. Dalgarno, Aurelie Putoud, Robert Lambert, Carola C. Diez, Alan Baird, Scott G. Aitken, David P. Towers, RichardJ. Warburton and Alan H. Greenaway

394

Adaptive optics for microscopy (Poster Paper) Xavier Levecq

400

art 5 Adaptiv~Optics in Lasers

Improved Beam Quality of a High Power Yb:YAG Laser (Oral Paper) Dennis G. Harris, FaIgun D. Patel, Charles E. Turner, Jr. and Michael M Johnson

407

Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser (Oral Paper) Petra We@, Ulrich Wittrock

413

New results in high power lasers beam correction (Oral Paper) Alexis Kudryashov, Alex Alexandrov, Vadim Samarkin, Valentina Zavalova Alexey Rukosuev,

419

xiv

Adaptive Optical Systems for the Shenguang-III Prototype Facility (Oral Paper) Zeping Yang, Chunlin Guan, Mingwu Ao, Ende Li, Muwen Fan, Ningping Shi, Yudong Zhang, Wenhan Jiang

426

Adaptive optics control of solid-state lasers (Poster Paper) WalterLubeigt, David Burns, Mike Gr@th and Leslie Laycock

433

Gerchberg-Saxton algorithm for multimode beam reshaping (Poster Paper) Inna l? Ilyina, Tatyana Yu. Cherezova

439

New algorithm of combining for spatial coherent beams (Poster Paper) RuoJir Yang ,Xiaojun Zhang, Feng Shen and Wenhan Jiang

445

Intracavity mode control of a solid-state laser using a 19-element deformable mirror (Poster Paper) Ping Yang, Wei Yang, Yuan Liu, Mingwu Ao, Shijie Hu, Bing Xu, WenhanJiang

45 1

art 6 Adaptive Optics in Communication and At~ospheric Compensation Fourier image sharpness sensor for laser communications (Oral Paper) Kristin N. Walker and Robert K. Tyson

459

Fast closed-loop adaptive optics system for imaging through strong turbulence layers (Oral Paper) Ivo Buske and WorfgangRiede

465

Correction of wavefront aberrations and optical communication using aperture synthesis (Oral Paper) R.J. Eastwood, A.M Johnson, C. Kolper andA.H. Greenaway

47 1

Adaptive optics system for a small telescope (Oral Paper) G. Vdovin, M Loktev and 0.Soloviev

477

Fast correction of atmospheric turbulence using a membrane deformable mirror (Poster Paper) Ivan Capraro, Stefan0 Bonora, Paolo Villoresi

483

xv

Atmospheric turbulence measurements over a 3km horizontal path with a S h a c ~ - H wavefront a ~ ~ sensor (Poster Paper) Ruth Mackey, K Murphy and Chris Dainty

489

Field-oriented wavefront sensor for laser guide stars (Poster Paper) Lidija Bolbasova, Alexander Goncharov and VEadimirLukin

495

This page intentionally left blank

Part 1

Wavefront Correctors and Control

This page intentionally left blank

LIQUID CRYSTAL LENSES FOR CORRECTION OF P ~ S ~ Y O P GUOQIANG LI and N. PEYGHAMBARIAN College of Optical Sciences, University of Arizona, Tucson, A 2 85721,USA Email: [email protected]~ii~.e~i~

Correction of presbyopia has been increasingly important. An electro-active lens allows voltage controlled change of the focusing power across the entire aperture. Such a lens must have high light efficiency, relatively large aperture, fast switching time, low driving voltage, and power-failure-safe configuration. New switchable, flat, thin liquid crystal diffractive lenses that meet the above requirements will be presented. The operation principle is based on electrical tuning of the refractive index of a 5 p-thick layer of nematic liquid crystal using a circular array of photolithographic~ydefined transparent electrodes. The effects of the gaps between the ring electrodes and the fringing field on the lens performance will be analyzed. Lenses with three different designs will he demonstrated: (1) All the ring electrodes for modulating the multi-level phase profile are patterned in one layer with a lpm gap between the neighboring electrodes. (2) In order to avoid the lateral gaps between the electrodes, a preliminary experiment with interleaved electrode pattern has been performed for a 4-level lens. (3) A robust design is given with three-layer electrode pattern and two-layer via structures for flexible interconnection and no-gap pattern. Designs 1 and 3 allow any even-numbered phase levels greater than 4 and provides the capability of correction for near-, intermediate-, and distance-vision. Such a lens has potential of revolutionizingthe field of presbyopia correction.

1. Introduction Presbyopia is a condition of vision that the eye’s ability to focus is diminished with aging, mainly due to the loss of elasticity of the crystalline lens. For example, a normal eye typically has an accommodation of 10 diopters at age 25 and at age 60, the accommodation is reduced to only about 1 diopter. For those with no refractive error, they usually have good distance vision but have difficulty in near vision such as reading and intermediate vision such as walking down steps. The first symptoms usually occur at mid-forties. The conventional bifocal and trifocal lenses for this correction have been around for more than 200 years and they have some drawbacks. They have a limited field of view for each vision task, requiring user to gaze down to accomplish near vision and in some cases causing dizziness and discomfort. Some users need three different eyewears for reading, computer, and driving. Our goal is to develop electroactive lenses1-2 that allow voltage controlled change of the focusing power across the entire aperture. Such a lens must have high light efficiency, relatively large aperture, fast switching time, low driving voltage, and power-failure-safe configuration3. New switchable, flat, thin liquid cr stal (LC) diffractive lenses that meet the above requirements will be presented3 - 7.

2. Design and results The LC lens structure is shown in Fig. 1 (a). A nematic LC layer is sandwiched between a ground electrode substrate and a patterned electrode substrate. The 3

4

ground electrode substrate contains a uniform conductive indium-tin-oxide (ITO) layer and the patterned electrodes are fabricated by photolithographic processing. For higher diffraction efficiency and ease of control, the patterned electrodes

3 -

Fig. 1 LC lens with patterned electrodes. (a) Hat lens structure; (b) Top view of one-layer electrode pattern; (c) Cross section of the two-layer electrode pattern, where odd- and even-numbered electrodes are interleaved into two layers.

have a ring shape defined by diffractive optics. The center wavelength is the peak of the human photopic response, 555 nm. The initial orientation of the molecules is parallel to the polarization of the incident beam, which is an extraordinary beam and its effective refractive index can be changed in the range from n, to no due to the reorientation of the LC molecule when a voltage is applied. The material has a positive dielectric anisotropy (>0.2), which provides enough phase modulation for the visible wavelength with a 5 ym-thick cell. If all the ring electrodes for tailoring the refractive index are patterned in one layer, there must be gaps between neighboring electrodes (Fig. l(b)). In order to eliminate the gaps between the electrodes, the odd- and even-numbered electrodes can be interleaved into two layers which are separated by a SiO2 insulator layer (Fig. l(c)). The effects of the gaps between the ring electrodes and the fringing field on the lens performance have been analyzed. Here, we just show an example. Assume the focal length is lm, and the diameter of the lens is 10mm. Figure 2 (a) depicts the normalized intensity distribution around the main focal point for no gap and gaps of various values. When the aperture of the lens is large, the gaps distort the phase profile and hence reduce the diffraction efficiency. The gaps should be kept small. Figure 2 (b) illustrates the deviation of the phase profile of one zone from the ideal case caused by the fringing field effect. Type B transition reduces the diffraction efficiency too.

5

Fig. 2 Effects of the gaps between the neighboring ring electrodes and the fringing field. (a) Intensity distribution at the focal plane for no gap and gaps of various values. (b) Illustration of the phase profile caused by the fringing field. Dashed line, the ideal phase profile.

Lenses with three different designs have been demonstrated: (1) All the ring electrodes for modulating the multi-level phase profile are patterned in one layer with a 1pm gap between the neighboring electrodes3. Over the patterned ITO, an electrically insulating layer of SiOz is sputtered and into which small via openings (conducting holes for vertical interconnections) were etched. An electrically conductive layer of IT0 is subsequently sputtered over the insulating layer to fill the vias and contact the electrodes and patterned to form independent electrical bus bars. Lenses with eight phase levels, 10 mm diameters and focal lengths of 1 m and 0.5 m (+1.0 diopter and +2 diopter of add power, respectively) have been demonstrated.

(2) In order to avoid the lateral gaps between the electrodes and allow high diffraction efficiency, the odd- and even-numbered ring electrodes are separated

6

in two layers4. A preliminary experiment with interleaved electrode pattern has been performed for a 4-level, 15 mm-aperture, 2-diopter lens with the expected performance. (3) A robust design is given with three-layer electrode pattern and two-layer via structures for flexible interconnection and no-gap pattern5. The microfabricated transparent concentric ring electrodes are distributed in two layers and different voltages are applied to each electrode through bus lines in another layer. Connection between the electrodes and the bus lines is achieved by vias in the third dimension. This design makes it easier to fabricate lenses with higher-level phase steps and larger aperture and overcome the shorts between the electrodes. This method can be used for design of LC lens of any phase levels. It should be noted that, unlike the conventional binary optics, in this design the increase of the phase levels (e.g., to 16 levels) in each zone does not increase the fabrication steps. For vision correction of presbyopic eyes, polarization insensitive switchable lenses are needed. As homogeneously aligned nematic LC is polarization sensitive, two lenses with orthogonal buffing directions were integrated as a single polarization insensitive lens. A method for active alignment of the two lenses has been described'. To test the imaging properties of the lens, a model human eye was constructed and a double lens element was placed in front of the model eye to provide near vision correction. For demonstration, a lens is first tuned with a focal length of 50 cm (2-diopter add power), 4-level phase modulation, diffraction efficiency of 78% and then reconfigured to operate as a l-diopter &level lens with a diffraction efficiency of above 91%. The lens operates with low voltages (c 2 V ~ S ) fast . response (-130 ms), small aberrations (the RMS value of the higher-order aberrations is about O.O393L), and a power-failure-safe configuration. Figure 3 shows correction of a model eye using the switchable lens. The object is initially in the reading distance. When the LC lens is off, the model eye has insufficient power to form a sharp image (Fig. 3(a)). But by switching on the diffractive lens with 2-diopter add power, the image is brought into focus with excellent contrast (Fig. 3(b)). Figure 3(c) illustrates the number of the phase steps of the lens is tuned from 4-level to 8level and correspondingly the focal length is adjusted from f to 2f. In this case, the object is moved to a farther distance. Dependence of the diffraction efficiency on the incidence angle is related to the field of view effect for normal use of the spectacle lenses. The diffraction efficiency decreases monotonically as the increase of the incidence angle. It drops about 4% when the lens is tilted 20' and it is acceptable for real application. This decrease results from the change of the phase profile for normal incidence light compared with light coming at an oblique angle. Such a lens provides the capability of correction for near-, intermediate-, and distance-vision.

7

Fig. 3 Hybrid imaging using the van-focal LC lens for demonstration of vision correction. The LC lens is (a) OFF and @) activated with 2-diopter power. (c) The lens is reconfigured from 4-level 1diopter to 8-level 1-diopter case. (d) Hybrid imaging with the 1-diopter power.

3. Discussions and conclusions The approach demonstrated here can be extended to the design of lenses with multiple digital focal lengths while keeping the same diffraction efficiency. This provides more powerful ability in accommodating near-, intermediate-, and distance-vision. Individually addressable electrodes (subzones) would allow this capability. The focal length can be adjusted by controlling the zone period using individually addressed ring pattern. Assume the geometry of the electrode pattern is designed for an elementary focal length f with L-level phase modulation in each zone. If the zone period r: is increased to 2 rt by grouping every two neighboring subzones into one, i.e., applying the same voltage to the two neighboring electrodes, the focal length is changed to 2f with the same Llevel phase modulation. Similarly, with the fixed electrode pattern, the focal length can be varied to kf (k is an integer) by increasing the zone period to k q2 . This technique may also be applied to provide the capability of quasicontinuously changing the focal length, allowing correction for all the subjects with different accommodation requirements by using individually addressed ring pattern. For each desired focal length, a number of rings are grouped together to form each subzone. With current fabrication technology, the array of ring electrodes with a small feature size (less than 5 pm) can be made. For a lens of 15mm in diameter, the focal length can be continuously changed from 30 cm to

8

infinity. The proposed structure is easier to control than the spatial light modulator. The diffractive lens has opposite chromatic aberration as to the human eye, so they can cancel each other to some extent. The chromatic aberration of the diffractive lens can be reduced by using the concept of multi-order diffractive lens, where the phase jump at the zone boundaries is p2n (p>l, integer) for the design wavelength5. Assuming the brain is adapted to a certain degree of chromatic aberration, balancing the dispersion of the diffractive lens and the eye is less desirable. On the other hand, the brain can handle both balanced and imbalanced chromatic aberrations. Negative focusing powers can also be achieved with the same lenses by changing the sign of the slope of the applied voltages. Usually correction of presbyopia needs an add power less than 3 diopters. With the state-of-the-art facilities, it is feasible to make such lenses. For correcting a residual refractive error for myopia or hyperopia, a curved substrate can be used or the lens can be used together with a contact lens for eyes that need minor correction for distance vision. The other concern is the temperature dependence of the lens performance. The refractive indices of the LC change due to the temperature variation (n, has a larger change than no). A temperature sensor and a variable voltage circuit are needed for compensation. These results represent significant advance in the state-of-the-art in liquid crystal diffractive lenses for vision care and other applications. They have the potential of revolutionizing the field of presbyopia correction when it is combined with autofocus function. The authors thank J. McGinn, J. Haddock, M. Giridhar, D. Mathine, P. Valley, P. Ayras, J. Schwiegerling, G. Meredith, S . Honkanen, and B. Kippelen for help in this work. References 1. C.W. Fowler and E.S. Pateras, Liquid crystal lens review, Ophthal. Physiol. Opt. 10,186 (1990). 2. W. N. Chman, Candiffractive liquid crystal lenses aid presbyopes? Ophthal. Physiol- Opt. 13,427 (1993). 3. G. Li et al., Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications, Proc. Natl. Acad. Sci. USA 103, 6100 (2006). 4. G. Li, P. Valley, M. S. Giridhar, D. Mathine, G. Meredith, J. Haddock, B. Kippelen, N. Peyghambarian, Large-aperture switchable thin diffractive lens with interleaved electrode pattern, Appl. Phys. Lett. 89, 141120 (2006). 5 . G. Li, P. Valley, P. Ayrtis, D. Mathine, S. Honkanen, and N. Peyghambarian, Highefficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures, Appl. Phys. Lett. 90, 11 1105 (2007).

CONVERGING AND DIVERGING LIQUID CRYSTAL LENSES A. K. KIRBY, P. J. W. HANDS, G. D. LOVE Durham University, Dept. of Physics, Duhrham, DHI 3LE, UK We report on recent work on the application of liquid ctystals to variable lenses. We demonstrate the construction and operation of a novel and simple form of modal LC lens which offers both converging and diverging modes of operation, as well as tipkilt and astigmatism.

1. Introduction Considerable work has been carried out in the field of electronically variable lenses (see, e.g. [l-31 and these proceedings). We have reported previously on the design and production of modal liquid crystal (LC) lenses [4-51 and their use as adaptive focus elements. We have recently developed a new LC device which overcomes some of the limitations of the modal LC lens;

*

*

The fabrication of the modal LC lens is complicated by the requirement for a high-resistance electrode, which is normally achieved by depositing an extremely thin layer of Indium Tin Oxide (ITO) onto a glass substrate. Producing the required thickness with good uniformity is problematic, and the deposition process typically has a low yield. The new LC device has a simple construction and requires only medium-resistance IT0 coated glass substrates, which are rather easier to manufacture. A normal modal LC lens can be driven to provide a positive (converging) lens of variable power. The new device can also be driven to provide a lens which can be varied from positive to negative optical powers. The effective optical throw of the lens, for a given cell thickness, is doubled compared to the modal lens. Correspondingly the relaxation time, for a given lens throw, is reduced by a factor of approximately 4. The optical power of the device along x- and y-axes can be controlled independently, allowing tip, tilt and limited astigmatic correction. 9

10

2. ~ o ~ t r u c t i oand n operation The basic principle of operation of the device is illustrated in figures 1 and 2. One substrate of the device is grounded (lower electrode, as shown), and tirnevarying voltages (Vl, V2) are applied to the opposite sides of the other (upper) electrode. If the V1 & V2 are out of phase (4 = 180') then the RMS of the field between the upper and lower electrodes takes on the form illustrated by the dashed line in figure 2. The solid line indicates the equivalent optical phase shift.

LC

Glass substrate

- - - - - - - - - - - - - - - - -/ -I \

-

-

Electrode

Figure 1. 1-D schematic and 3D illustration of Lc device

5

4

3

-2

-1

0

1

2

3

4

5

Nrn Figure 2. Phase (solid) and voltage (dashed) profiles for A & J ~ . v=lSOo ~

By altering the relative phase and voltages of V1 and V2 (#) and by the addition of a bias-voltage term the shape and scale of the voltage profile, and hence the phase profile, can be adjusted - particularly the 'plateau' in the centre of the phase profile can be eliminated.

11

All liquid crystals exhibit an inversion of the dielectric anisotropy at some driving field frequency. For most materials this ‘crossover frequency’ is impractically high to be of use - typically several MHz, at which frequency dielectric losses in the material cause heating and usually melting, taking the material out of the liquid crystal phase. There do exist some materials, collectively known as dual-frequency liquid crystals, which have a low crossover frequency, typically a few kHz. Using on of these materials (Niopik LClOOl), we can produce a negative (diverging lens). The effect of driving with a field frequency above it’s crossover frequency is that the LC molecules will tend to realign normal to the applied field, i.e. in the plane of the cell, whereas in the more conventional case of driving with a field frequency below the crossover frequency, the molecules tend to align with the applied field. In other words, driving with a low frequency causes the cell to switch ‘on’ and driving with a high frequency causes the cell to switch ‘off. This mechanism is normally used to improve switching times of cells; however it can be used to produce a negative-lens form. If both high and low frequency fields are applied simultaneously, the LC molecules respond essentially to the difference in the torques and settle at an equilibrium position. If the cell is biased using a low-frequency drive voltage with no inter-electrode phase difference (4 = 0), and a high-frequency drive voltage with @=180’ are applied simultaneously, then the voltage difference profile, VLF-V~p,and the corresponding optical phase profile, take on the form shown in figure 3. 12 10 0

-Vlf-Vhf g

>

6

c z I

- - Optical

4

2 0 0

2

x(mm)

a

lo

Figure 3. Production of negative (diverging) lens, using dual-frequency LC materials. Solid line represents the difference between the low frequency bias voltage and the high-frequency structure voltage. The dashed trace represents the corresponding optical phase profile.

12

3, Results

Figures 4-6 show interferograms and unwrapped phase profiles for converging lens operation with varying drive voltages.

Figure 4. Interferogram and unwrapped x- and y- phase profiles for Vm(x,y) = 5.65V, Vm(bias) = 2.12V, (b = 180'

Figure 5 . Interferogram and unwrapped x- and y- phase profiles for Vm(x.y) = 5.65V, Vm(bias) = 2.82V, (b = 180'

Figure 6 . Interferogram and unwrapped x- and y- phase profiles for Vm(x,y) = 4.60V, Vm(bias) = 3.54V, = 180'

13

Both the positive and negative (converging and diverging) lens operation of the device and independent control of x- and y- axes is demonstrated in Figure 7, which shows the production of astigmatism.

Figure 7. Interferogram and unwrapped x- and y- phase profile using drive voltages of V x ~ ~ z 5 . rm, 6 5 VxLF-bias=2.12Vrm. & =4=180°, V p z 6 . 7 v,, V y ~ ~ 2 . vr, 35

Acknowledgments

The original idea of this method of addressing LCs was proposed by Dr. Alexander Naumov. His help and enthusiasm for LC adaptive optics is gratefully acknowledged. This work was funded by the EPSRC and the EU Eurocores SONS programme.

eferences 1. S. Kuiper and H.H.W. Hendricks, ”Variable-focus liquid lens for miniature cameras”. Appl. Phys. Lett. 85(7):1128-1130(2004) 2. A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast scanning,” Opt. Lett. 26( 14):1078-1080(2001) 3. L.G. Commander, S.E. Day, and D.R. Selviah,, “Variable focal length microlenses,” Optics Comms. 177:157-170(2000) 4. A.F. Naumov, G.D. Love, M.Yu. Loktev and F.L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Optics Express 4(9):344-352(1999) 5 . P.J.W. Hands, S.A.Tatarkova, A.K.Kirby, G.D.Love. “Modal liquid crystal devices in optical tweezing: 3D control and oscillating potential wells.” Opt. Express 144525-4537 (2006)

LIQUID LENS TECHNOLOGY FOR MINIATURE IMAGING SYSTEMS: PERFORMANCE OF PRODUCTS AND OF EXISTING EXIST FUTURE TRENDS * B. BERGE Varioptic, 24B rue Jean Baldassini, 69007 Lyon, France. On leave from Ecole Normale Supkrieure de Lyon, 46 allke d’ltalie, 69007 Lyon, France.

s

Summary The miniaturization of optical systems and in particular of digital cameras, has made manufacturers turn to technologies, very different to those used in recent decades. This article presents variable focal length lenses without moving parts, developed by the company Varioptic to meet this demand. To realize functions such as zoom and auto focus traditional mechanical technologies rely on the precise translation of lenses relative to each other. These technologies function correctly in cameras and video cameras, but they remain expensive: it is estimated that one half of the manufacturing costs of a digital camera is linked to the optical assembly. In addition, it is difficult to miniaturize them because the tolerances required for the maintenance of the optical quality become incompatible with the friction introduced by the mechanical guides. Over approximately the last six years, a range of miniature cameras have appeared in mobile telephones, introduced by the manufacturers of CMOS and CCD image sensors. Initially of poor quality, these cameras are now tending to compete with the entry level of the range of digital cameras with captors of more than IMP, with a flash and sometimes a focus adjustment and a zoom.

14

15

The solution introduced by the company Varioptic rests on a new technology of variable focal length lenses without moving parts, based on an encapsulated liquid technology, where the optical surface is modulated by an electrical voltage. For over a year, these lenses have been tested by the major mobile telephone manufacturers (the mobile telephone market is one of the most demanding in terms of reliability) and are now available on the market, for mobile telephones and also for a multitude of other applications. The liquid lens technology is characterized by a very wide range of focal length variation, linked to a high optical quality and a “reasonably” rapid response, of the order of 20-50 milliseconds. An enclosure contains two non miscible liquids of the same density, which rest

against a metallic mechanical part protected by a thin insulating hydrophobic film. One of the two liquids is a conductor (water) and the other is an insulator (oil). The assembly is subjected to an electrical voltage applied between an electrode in contact with the liquid conductor and the insulated metallic part with a conical shape. Two products have been introduced thus far an the chart below presents their performance. Liquid lens

ARCTIC 320

ARCTIC 416

Usable diameter (mm) 3

Optical power variation (dioptries or m-’1 Wave front curvature Optical quality (wave front error ms) Hvsteresis Response time (ms) Temperature

Shocks

> 20

> 35

>50A

>30A

< 0,5 A 100 -20°C to 60°C -40°C to 85°C

> 20 shocks OK

50 -20°C to 60°C -40°C to 85°C > 20 shocks OK

functional storage

Free fall 1,8m on a hard concrete floor

16

The figure below presents the optical response for an Arctic 416 lens. 7-

--

20

E

15

O

10

L

-

optical quelhy statistics

25

u)

2

5

L

0 . 0

.-0

9 L Q)

3

-5

-10

-15

0

11 -20

-

$

E

-25

O 0

Voltage (V at 1 kHz)

100 maximumwsvefmntermrrms (nm)

Figure 1: On the left, the optical response as a function of the command voltage and optical quality of the Arctic 416 lens: on the right a histogram of the optical quality of production batches. The command voltage is 60V at 1kHz. As the effect of the focal length variation is obtained by an electrostatic effect based on the presence of electrical charges stored in a capacitor, the electrical energy dissipation is minimal, less than 1mW in the lens. Figure I , also shows the performance in terms of optical quality of the lens, measured as the maximum error of the wave front, across all the focal length curve. As a conclusion, the status of current technology has been shown to approach the optical quality of glass or plastic lenses with the additional ability of power variations. Applications in cameras, security, bar code reading, endoscopy, web cams, etc. and future trends will be discussed during the communication.

Carbon Fiber Reinforced Polymer Deformable Mirrors for High Energy Laser Applications S.R. RESTAINO, J. R. ANDREWS, T. MARTINEZ, C. C. WILCOX Remote Sensing Division, Code 7216, Naval Research Laboratory 3550 Aberdeen SE Albuquerque, NM 87117 USA

R. ROMEO, R. MARTIN Composite Mirror Applications, Inc. 100 Research Loop Tucson AZ, 85710 USA

The Naval Research Laboratory has been involved in developing Carbon Fiber Reinforced Polymer (CFRP) optical and structural components for the upgrade of the Naval Prototype Optical Interferometer. In this program we have developed a first 16" prototype telescope all in CFRP and are now developing a 1.4 meter telescope also composed entirely of CFRP. Within this framework we have started investigating the development of deformable mirrors using this material. In this paper we will present some background information on CFRP material for optical applications, and especially results on our CFRP telescope development efforts. We also present results on the deformable mirror development. Experimental results on energy density threshold tests will be presented. The overall status of the program is discussed and immediate future developments are explored.

1. Introduction The Naval Prototype Optical Interferometer (NPOI) is the world's only long baseline optical interferometer operating in the visible region, i.e. wavelengths below 0.8 pm. It is also the only optical interferometer capable of recombining up to six beams, from different apertures, simultaneously. Currently the NPOI uses Siderostuts, i.e. flat mirror that track the object in the sky and redirect its light into the beam relay system. The collection aperture is limited to only 12 cm to avoid atmospheric turbulence problems. Thus the overall sensitivity of the instrument is limited to objects with a visual magnitude of 6. Recent investigation has aimed at increasing the sensitivity of the interferometer by implementing larger apertures for light collection [ 11. When coupled with adaptive optics [2], the NPOI hopes to acquire visual magnitude 12 objects. However, building dozens of meter class telescopes for array population is too costly, and building several telescopes that can be moved from station to station is impractical 17

18

considering the weight of traditional telescopes. Therefore, the use of Carbon Fiber Reinforced Polymer (CFRP) materials was explored for telescope construction [ 11. There are several advantages to using CFRP for telescope construction, including an order of magnitude decrease in weight, allowing easier transportation from station to station on the array. As all components of the telescope, including optics, are constructed from composite materials having a low Coefficient of Thermal Expansion (CTE), dimensional changes due to temperature variations can be minimized. Also, since all optical components are made from a single high precision tool, duplicate components can be manufactured for much less than traditional steel and glass telescopes [3]. In figure 1 is shown the almost completed 1.4 meter telescope without the mount that will also be in C M .

Figure 1. Picture of the 1.4meter CFRP telescope.

There are several reasons why this technology is under investigation. As the manufacturing process relies on replication technology, there is a possibility of

19

substantial cost savings for the production of multiple items. The light-weight characteristics are very appealing since this maximizes transportability of the telescope which is essential for optical interferometry. Furthermore, the relatively small mass of CFRP telescopes allows completely different approaches for the driving motors and any other ancillary aspects. Finally, as the entire telescope structure and optics are composed of the same material, and hence the same CTE, thermally induced aberrations are easily predicted and controlled.

2. Optical Quality The outmost important aspect of this program is the production of high optical quality CFRP mirrors. Since this is a replication technique one of the crucial steps is the polishing and testing of the mandrel. It is a well known problem that the testing of convex surfaces is much harder than concave ones which seems to be one of the major reasons why such technology, which has been in use for decades in many areas, has not yet been exploited for the manufacturing of optical components. In Table I we compare some physical properties of many common materials used for optical mirror substrates and applications.

Table I

SiC(CVD) Be A1

CFRP

3.2 1.85 2.7 1.761.87

466 300 70

0.21 0.08 0.33

35--700

0.35

440 240 310 270-6oo

2.2 11 23

- 1.3 -50

0.05 0.05 2.5

190 210 170

730 1900 890

70--530

The most interesting result summarized in Table I is that most of the physical parameters for CFRP have a range instead of a single value. This is one of the characteristics that allows the material to have such a great potential, especially in

20

the area of deformable mirrors for high energy applications. The reason for the variability of values is that the physical parameters are determined by the carbon fiber matrix orientation of the plies, number of plies, ply thickness and ply material. Different orientations, thicknesses, etc will yield different values ranging from negative to positive and can be made zero in some cases. This “tunability” of the material opens the door for a vast variety of new approaches. The number of possible combinations and how these can affect the final product in terms of optical quality and performance is almost limitless. Our current effort is to produce high quality mirrors in the meter class. In Figure 2 we show a wavefront map obtained with a commercial wavefront sensor of one of the 16” parabolic mirrors produced for our program.

Figure 2. Wavefront map of a 16” CFRP mirror obtained using a commercial wavefront sensor.

The next step in our program was to determine if this material and approach lend itself to an active control.

21

3. Active Control CFRP mirror phase-plates require metallic inserts in order to attach actuators, if a push-pull actuation is needed. Our first step was to develop a twelve inches phaseplate with nineteen passive actuators. The phase plate with the actuators is shown in Figure 3. The key point of this first step was to insure that no optical imprints were detected by introducing these metal inserts into the mirror substrate.

Figure 3. The 12 inches phase plate with the 19 passive actuators attached to the metal inserts.

All tests performed have shown no detectable optical imprints when this type of actuators are pushed or pulled. We are now in the process of determining the best type of actuators and the best geometry for the disposition. Given the flexibility of many parameters of this material, in specific stiffness and thickness, several actuation schemes are possible prompting our ongoing research. The other aspect that we are analyzing is the heat dissipation capabilities of this material, this specifically related to high energy laser application. The first experimental verification was to use a conventional 16 inches CFRP mirror with a commercial propane torch. The experiment consisted in monitoring the surface of the mirror through a Ronchi grating while using the propane torch. The torch was rated with an output of roughly 3 KWatts. The Ronchigram shows no detectable changes of the mirror figure while being heated by the torch compared to when the torch is off. A battery of more quantitative tests is need in order to assess the

22

capabilities of CFRP to quickly thermalize under the presence of a considerable power load like the case of high energy laser applications.

4. Conclusions In this paper we have presented some aspect of the Naval Research Laboratory program in CFRP optics demonstration. The bulk of this program is aimed at the development of large light-weight telescopes, with diameters of 1.4 meter, for long baseline optical interferometry applications and other imaging applications. Part of this ongoing program is also the control of the CFRP optics for both Active and Adaptive Optics applications. Within this framework we are also investigating the use of this technology for the production of deformable mirrors specifically geared towards high energy laser applications. The preliminary analysis and experimental results are very promising but more investigation is needed in order to attain the stated goals.

References 1. S. R. Restaino, J. R. Andrews, C. C. Wilcox, T. Martinez, D. M. Payne, “Ultra-

light weight telescope with portable A 0 system for laser communications applications,” Proc. SPIE Vol. 6105, (2006) 2. J.W. Hardy, “Adaptive Optics for Astronomical Telescopes”. Oxford Press, New York (1998). 3. J.R. Andrews, F.E. Penado, S.T. Broome, C.C. Wilcox, S.R. Restaino, T. Martinez, S.W. Teare, F. Santiago, “Characterization of the lightweight telescope developed for the JWOI”, Proc. SPZE Vol. 6267, (2006).

TINYMULTILAYERDEFORMABLEMIRRORS T.W. CHEREZOVA*,A. S. SOBOLEV", A. G . ALEXANDROV, A.V. KUDRYASHOV, V. V. SAMARKIN Night N (opt) Ltd., Sudostroitelnaya Str. 18, Bld.5, Moscow I IS407 Russia samarkin Bniphtn. ru

* Moscow State University, Laser Beam Diagnostics Lab., Vorobievy Gory, Moscow, Russia

-

Abstract Formation of the given laser beam intensity and phase is an important practical and scientific problem. Bimorph flexible mirror is one of the most widely used devices for this purpose. We present a new approach of multilayer bimorph mirrors and a numerical model to simulate them, based on the finite elements method. The multilayer mirror consists of a substrate and a number of PZX layers.

Keywords: bimorph corrector, laser beam control, wavefront aberrations

. Introduction In modern laser technologies, in particular in nano technologies, it is often necessary to form and control a specific intensity distribution on the surface being treated. One of the simplest ways to achieve the best beam focusability and profile control is to use the systems of adaptive optics. Such systems consist of the wavefront corrector, sensor and some electronics to control of the corrector's surface. Main element of any adaptive system is the corrector which determines the properties and ability of the system. It is very well known that conventional bimorph corrector (or mirror) is intended to reproduce and thus correct for low order aberrations of the wavefront [I]. Traditional bimorph mirrors have the diameter of more than 30 cm, but a large number of industrial and scientific applications need a noticeably smaller diameter. The use of beam expanders (reducers) is not the perfect way to fit small beams to large aperture mirror. We developed the new type of corrector - a small aperture (tiny) deformable multilayer mirror. Such mirrors could be easily integrated into flexible programmable machines or laser robots and they allow optical systems to be more compact and reliable. 23

24

A conventional semipassive bimorph mirror consists of passive substrate made of glass, silicon or copper and active PZT disk firmly glued to substrate. There is a grid of electrodes placed on the outer surface of PZT disk to reproduce the main aberrations. When we apply voltage to control electrodes, transverse piezoelectrical effect induces stress in PZT and the mirror bends. In this paper we will consider circular mirrors with segment-shaped control electrodes (for example, fig. la). This grid design can be completely described by setting sectioning radii and angular sectioning of the electrodes.

2. Finite elements method for bimorph mirror modeling One of the most important characteristics of the bimorph mirror is a set of the response functions of its electrodes. Some models of the bimorph mirror have already been studied, but as we have shown previously [2] it is more practical to use numerical methods, in particular, variation approach of the finite element method. This approach is a very powerful and effective method for treating thin plate bending. The multilayer plate is assumed as a unity of a large number of finite elements of simple form (triangular in our simulations). Actually these elements are prisms with the thickness that equal to the mirror in the element location. But the thin plate approach deals with flat elements. The properties of each of these simplified elements are determined by the properties of the corresponding prism element. Different parameters of the layers constituting the prism, including presence and absence of PZT are taken into account. Thus here is the way to consider different radii of PZT and substrate layers and difference in their Poisson coefficients. The next step is to simplify all volume forces (caused by neighborhood elements and piezoelectric tension) acting upon the element to the system of nine nodal forces and nodal moments. The elements are, by assumption, parts of the thin plate, so one can easily derive the relation between extended nodal forces (forces and moments) and element deformation. Each element deformation can be determined by nine extended nodal displacements (displacement itself and two orthogonal tilts, every in each of the three nodes) by treating it as a sum of 9 polynomials of the third order. Assuming the Huke (linear) law of mirror deformation the relation between extended nodal forces and displacements can be brought to the form of linear system of nine equations. The equation of mirror equilibrium states that forces in each node should be balanced, thus one acquires a system of linear equations with extended nodal displacements as unknowns, extended nodal forces as a right side column and elements of the square matrix determined by each element configuration. Each

25

element interacts only with a few neighborhood elements, so the matrix of the system is sparse. Boundary conditions are determined by the type of mirror clamping and give a number of additional equations for extended displacements in boundary nodes, which override that, derived from mirror equilibrium condition. As the mirror type that we consider usually has almost free clamping to increase peak-to-valley deformation, we simply leave equations, which state equilibrium in boundary nodes. All this stuff has been embodied in the MATLAB program. Calculated mirror deformation well corresponds to experimentally measured one. It is demonstrated in fig. 1, which shows: b- calculated response function profile, c - measured one. Electrode location is shown in fig.lb with solid line. Relative root-mean square deviation of these profiles is 6%. This value fits common accuracy of measurement with Shack-Hartmann wavefront sensor, thus proving quality of our bimorph mirror modeling.

Fig. 1. (a) segment-shaped electrode grid response function of one of the middle ring electrodes calculated (b); experimentally measured (c).

3. ~ x p e r i ~ e n tsample al of the tiny mirror A laser beam often has significant number of low order aberrations, and mirror should have large stroke while reproducing them. Simultaneously, there are higher order aberrations, that have smaller amplitude, but quality of their reproducing is more crucial. It is very difficult to achieve simultaneously good quality and large amplitude with the use of only one PZT layer. The first step to solve this problem is the use of additional PZT layer with one large electrode, which occupies the whole PZT surface. Its response function is parabolic and this electrode is often stated as focuddefocus electrode. Light modifications of our software for mirror modeling allow treating of such mirrors: we only have to add piezoelectric forces coming from the second PZT disk. While trying to determine electrode spacing one have faced a problem: different aberrations require different electrode spacing (it is obvious), and moreover different radii and angles of sectioning to be reproduced. That is why

26

the number of electrodes increases rapidly, though every aberration itself requires a small number of electrodes. The idea is the following: let us use the second layer (reproducing only defocus) to reproduce one more aberration, say astigmatism. The outer layer is to reproduce, for example, spherical aberration. This mirror has been manufactured and it is one of our first examples of the tiny bimorph mirrors (fig. 2). The mirror parameters are following: substrate thickness 1.5 mm, its diameter: 20 mm, each PZT layer thickness: 0.35 mm, PZT radius: 15 mm, the mirror has two PZT layers, the control electrode grid (outer surface) and another electrode grid are shown in fig.2a. If we simultaneously apply the same voltage to all electrodes of the outer layer from fig.2a, then it would act as a defocus electrode. If we apply voltage of equal absolute value, but of the different signs to the electrodes of the inner PZT layer, we will reproduce astigmatism. The electrode grid on the outer PZT layer, presented in fig.2a, is common for reproducing spherical aberration. Radius sectioning is 0.38 and 0.73 times PZT radius.

Fig. 2. Experimental sampte of the tiny corrector: (a) electrode grids of the mirror; (b) half finished mirror; ( c )photo of the mirror in the holder.

Simulated mirror astigmatic surface is presented in fig. 3a. The good fact about the simulations is that maximum of mirror deformation is not near the mirror edge, but 4.4 millimeters from it. It is very good in applications because usually the real beam illuminates central part of the mirror, which is 3 or 4 millimeters smaller, than mirror diameter. Let us consider the outer layer. Electrode sectioning radii are 2.9 millimeters and 5.5 millimeters. Mirror deformation when reproducing spherical aberration versus normalized on PZT radius coordinate (“1” corresponds to the FZT edge) is shown in fig. 3b. There are experimental surface of the mirror in microns and ideal spherical aberration derived numerically, approximation error is 15%.

27

Fig. 3. Simulated astigmatism (a); spherical aberration, reproduced by outer layer: (a) theoretical simulation; (b) experimentallyreproduced.

4. Multimorph mirrors The most advanced mirrors have 2 layers of PZT with the electrode grid, designed to reproduce low order aberrations. Let us add one (and later even more) active layer. Negative effect is the increase of mirror thickness: it greatly reduces mirror sensitivity. The previously considered mirror could reproduce only three aberrations, but coma is also very common in optical systems. Adding a new layer allows us to use electrode grid for this aberration.

I

Fig. 4. Principal design of the multimorph mirror. 3 layers of control electrodes, 4 FZT layers.

One of the most important parameters, which determines PZT layer sensitivity, is its distance from median line (plane). Median line is a surface where material deformations are absent, when the plate itself bends. If median line is situated in the middle of PZT layer, then applying voltage to this layer doesn't cause any mirror deformation. Let us numerically illustrate this dependence. We will consider 2 mirrors, the first one has a median line 1, which is situated directly between the layers, and second one has a median line

28

situating in the middle of the PZT layer. Table 1 shows reproducing of defocus in microns by these 2 mirrors. Electrode layers are numbered starting from the outer one. Note, that the sensitivity of the last electrode layer for second mirror is neglectable, change of mirror thickness on 0.2 millimeters had a devastating effect on this electrode. The effect is the reduction of layer sensitivity, when the number of PZT layers increase. Table 1. Defocus reproduction by FTX layers in different mirrors

Number of electrode layer Mirror 1, p Mirror 2, p

1 6.8 5.1

2 5.3 5.0

3 1.5 0.1

5. Conclusion We have numerically investigated a new generation of the bimorph mirrors and showed how their design follows the previous development of the bimorph mirrors. The results are very promising, we can use mirrors with a multiple number of active layers to independently compensate for different aberrations. As we have shown, small variation in mirror thickness can significantly influence the mirror performance.

efere~~es

1. A. V. Kudryashov, V. I. Shmalhausen, Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications. Opt. Eng. 35(1 l), pp. 3064-3073 (1996). 2. A. S. Sobolev, T. Yu. Cherezova, A. V. Kudryashov, Analytical and numerical models of a bimorph mirror. Optiku utmosfery i okeunu, 18(3), pp. 277-281 (2005).

PERFORMANCE ANALYSIS OF PIE~OELECTRIC ~ E ~ O R ~ A B MIRRORS L E OLEG SOLOVIEV*, MIKHAIL LOKTEV, and GLEB VDOVIN

Flexible Optical B. V., Rijntgenweg 1, 2624 B D Delft, the Netherlands *E-mail: olegOokotech. com We investigate the performance of piezoelectric deformable mirrors (PDM) in general with the novel 109-channel 50mm O K 0 PDM taken as an example. The mirror performance in forming and fast correction of large high-order aberrations is presented.

Keywords: Deformable mirrors, high-order optical aberrations.

1. Piezoelectric Deformable Mirrors Piezoelectric deformable mirrors (PDMs) with column piezoelectrical actuators based on transversal effect are fabricated by Flexible Optical B.V. (OKO) since 2004; they have been covered in a number of publications (see, for instance, Refs. 1-3). These mirrors represent an array of actuators fixed to a thick stable mirror base and a thin flexible mirror plate bonded to them (see Fig. 1). The shape of the faceplate is controlled by the voltages applied to the actuators which can push and pull the reflective plate. There are two parameters that are important when the amplitude of response is described: maximum stroke of a free actuator and maximum difference between the neighbor actuators (interactuator stroke). The deformable plate is bonded only to actuators and has a free edge; thus when all actuators move together, the plate is translated without any deformation. The range of translation is equal to the maximum stroke of a free actuator. Due to the finite stiffness of the actuators, the maximum interactuator stroke is defined not only by the maximum free actuator stroke, but also by the ratio of the actuator rigidity to that of the reflective plate 29

30

and by the actuator pitch. At present, O K 0 PDM can be fabricated with minimum pitch of about 4.3 mm and maximum free actuator stroke of 8 pm; depending on the stiffness of the reflective plate, the inter-actuator stroke can reach 3 pm. Since the amplitude of local response of a piezoelectric mirror depends only on the stiffness of the plate and the actuators, PDMs can be scaled to very large numbers of control channels. Piezoelectric mirrors demonstrate hysteresis of 7 to 15%. This property limits their applicability for feedfo~urdcontrol; for the feedback-based applications, fast correction of low and high-order aberrations with large amplitude is possible. The performance of the PDMs can be good approximated by thin-plates theory;* it was investigated for a general case and compared with the performance of membrane mirrors in Ref. 5. However, the paper does not consider some limitations imposed by the real applications and mirror design, such as limited voltage range, finite thickness of the plate and actuators. Flexible faceplate

Fig. 1. Simplified scheme of a piezoelectrical deformable mirror (PDM)

2. 109-channel PDM

In this paper, we focus on the practical results of using of the PDMs for generating of and compensating of optical aberrations. For this purpose, we took one of the recent PDMs fabricated by O K 0 - 50mm PDM with 109 actuators, shown in Fig. 2, and tested it in a A 0 setup with a closed feedback loop analogous to that described in Ref. 6 , Chapter 7; the mirror was driven by three 40-channel high-voltage amplifier units controlled by three 40-channel USB DAC units (for technical parameters of the driving electronics, please refer to the Ref. 7, section “Electronics”). Because the mirror we used had initially slightly deformed spherical surface (see Table l), caused by the stress in the mirror coating, we used a concave mirror with a matched curvature as a reference mirror.

31

Fig. 2. Typical front view of a 109-channel piezoelectric deformable mirror and the geometry of mirror actuators with its correspondence to the mirror connectors (view from the mirror side). See Table 1 for the technical parameters of the mirror. Table 1. Technical parameters of the mirror. Parameter

Value

Size/weight Aperture shape Mirror coating Actuator voltages Number of electrodes Actuator capacitance C, Actuator hysteresis Main initial aberration Initial RMS deviation from reference sphere Requency range

100 x 100 x 60 mm3 / 650g circular 50mm in diameter A1 0 400V (with respect t o the ground electrode) 109 (see Fig. 2) N 5nF better than 10% sphere with R M lOOm less than 2pm

Maximum free/interactuator stroke Actuator pitch

8pm at +400V 4.3mm

+

0.. .2kHz mirror itself, 0.. lkHz mirror with standard HV amplifier

.

2pm

2.1. Initial figure and active flattening of the mirror Due to the stress introduced by the coating and free-edge mounting of the reflective plate, the initial figure of a PDM is seldom flat. Coated unbonded plates are most often spherical; when fixed to the actuator array, they develop some random shape. This surface can be actively flattened with respect to a plane or a reference sphere by applying some biasing voltages to the actuators. This reduces the dynamical range of the mirror; usually, the mirror considered to be acceptable if the decrease is less than 20%.

32

Initial and flattened figures of the 109-channel PDM under test are shown in Fig. 3. The mirror surface was flattened from 5 X peak-to-value, 1 X RMS surface to 0.5 X peak-to-value, 0.05 X RMS, as shown in Fig. 3 at the cost of 15% of the voltage diapason.

Fig. 3. Shape of the mirror plate before and after active flattening shown as interferograms and as 3-D plots. The z-axis of 3-D plots is in wavelengths (A = 638 nm).

2.2. Aberration generation

First, we tested the mirror in generation of static aberrations; the results obtained are shown in Fig. 4. The mirror was actively flattened with the respect to the reference sphere with a RMS error of better than X/20. Due to the hexagonal actuator geometry, the mirror was also good in generating low-order and high order aberrations with rotational symmetry of the 2nd and the 3rd orders. To check the mirror dynamicd performance, we tested the mirror in generating of random high order aberrations as shown in Fig. 5 (each of the actuators was set either to its minimum or maximurn position) with the frequency of M 1 kHz during more than 10 minutes. The mirror successfully

33

Fig. 4. Test of the mirror: piston, defocus, astigmatism, spherical aberration, trefoil, and quatrefoil generated. Note reduced range of the quatrefoil because of rotational symmetry of 4th order. Interferograms were formed by He-Ne laser with X=638nm.

survived this hard test.

Fig. 5 . Random aberration generated during the dynamic mirror test

34

3. Conclusions

We have tested 109-channel 50 mm piezoelectric deformable mirror in generation of and compensation for static and dynamic aberrations. Our conclusion is that the 109-ch 50 mm piezoelectric O K 0 mirror is suitable for fast dynamic correction of large low- and high-order optical aberrations such as defocus, astigmatism, coma, etc, in lasers, telescopes, ophthalmology, displays, and general imaging optics.

eferences 1. S. R. Chamot, C. Dainty and S. Esposito, Optics Express 14, 518 (2006). 2. E. Dalimier and C. Dainty, Optics Express 13, 4275 (2005). 3. G. Vdovin, M. Loktev, A. Simonov, V. Kijko and S. Volkov, Optics Letters 30, 795 (2005). 4. S. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells (McGraw-Hill, 1953). 5. M. Loktev, D. W. De Lima Monteiro and G. Vdovin, Optics Communications 192, 91 (2001). 6. M. Loktev, 0. Soloviev and G. Vdovin (eds.), Adaptive Optics Product Guide, November 2006 edn. (OK0 Technologies, 2006). 7. http://www.okotech.com.

DEFORMABLE MEMBRANE MIRROR WITH HIGH ACTUATOR DENSITY AND DISTRIBUTED CONTROL* ROGER HAMELINCK", NICK ROSIELLE, MAAR'IEN STEINBUCH Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, Eindhoven, 5600 MB, The Netherlands ROGIER ELLENBROEK, MICHEL VERHAEGEN DCSC, De'l University of Technology, Mekelweg 2 De&, 2628 CD, The Netherlands NIEK DOELMAN TNO Science and Industry, Stieltjesweg I , Delft. 2628 CK,The Netherlands Progress on the construction of a deformable mirror with 427 actuators is presented. The mirror consists of a thin continuous membrane on which actuators impose the out-ofplane displacements. Low voltage electro-magnetical push-pull actuators are used. The actuators are arranged in 7 hexagonal modules. Each module consists of 61 actuators and has its own 61 channel, 16 bits driving electronics. The actuators and electronics are designed for low power dissipation. A multi-drop LVDS connection provides up to 16 modules with a 1 kHz update rate. The dynamic response of the actuators is tested. The results are in good agreement. The 427 channel prototype is to be implemented on a breadboard with a wavefront emulator, sensor and a distributed control algorithm.

1. IntrQductiQn The mirror consists of a thin continuous membrane on which actuators impose the out-of-plane displacements. Low voltage electro-magnetical push pull actuators are used. Figure 1 shows the actuator layout and connection to the reflective deformable membrane. In figure 2 a single actuator is shown. Each actuator consists of a closed magnetic circuit in which a strong permanent magnet provides a static magnetic force on a ferromagnetic core which is suspended in a membrane. The force is influenced by applying a current through a coil that is situated around the magnet to provide movement of the core. * T h i s work is partially funded by the Dutch Innovative Research Program Precision Engineering

35

36

This movement is transferred via a rod imposing the out-of-plane displacements in the reflective deformable membrane. The stiffness is determined by the suspension of the ferromagnetic core and the negative stiffness from the magnetic circuit. The resulting stiffness of the actuator is chosen high enough to avoid mechanical resonances below 1 kHZ and to avoid large coupling, but still low enough to be called a soft actuator and to limit the power dissipation to a few mWs per actuator.

Reflective defonnable

/

/

Base date

’ d la narc oil

Figure 1 . Schematic of the base plate with three actuators and the connection via rods with the reflective membrane surface.

Figure 2. Single actuator.

37

2. The standard 61 actuator module The actuators are arranged in 7 hexagonal grid modules of 61 actuators. With a pitch of 6 mm, this results in a 48 mm wide hexagonal plate. Figure 3 and figure 4 show the different mechanical and electrical components needed for the module. The figures illustrate the layer based design.

Figure 3. The mauufactured components, from left to right: the 25pm thick membrane suspension and the baseplate as seen from the front and backside.

Each grid has its own 61 channel, 16 bits driving electronics. The drive electronics are designed for low power dissipation and make use of Pulse Width Modulation. A multi-drop LVDS connection provides up to 16 modules with a 1 kHz update rate. Both communication and power is provided through this single cable.

Figure 4. The flex foil to connect the coils to the PCB, the coils and the PCB.

38

Figure 5 shows one of the assembly steps and the fully assembled module.

Figure 5. Baseplate assembly with the membrane suspension (left), and the fully assembled actuator module (right).

-

3. The 427 actuator prototype In the prototype 7 of the modules are placed on a stable and stiff reference support structure. The modular design makes it possible to extend the mirror to very large numbers of actuators. Figure 6 shows the assembly of one grid and its placement on the prototype base.

Figure 6. The module placed on the prototype base.

39

. Testing The dynamic response of the actuators is tested. Transfer functions of the actuators are measured using white noise input current with various dc-offsets (figure 7). I

I

I

Figure 7. Bode-diagrams of act. #11 with various dcofi&. (-0.025 < DC,fia< 0.025V).

Figure 8. Measured and predicted current/ohmk losses of act. #11 over its stroke.

40

A mass-spring system is fit on these transfer functions. Characteristics such as resonance frequencies, force, stiffness, motor constant, current, dissipation and efficiency - all as function of the position of the actuator - have been determined. These experimental results are compared with the theoretic predictions. Part of the result is shown in figure 8. The results are in good agreement.

5. Future work The 427-channel prototype is to be implemented in the existing breadboard setup at TNO Science and Industry together with a wavefront emulator, wavefront sensor and distributed control algorithm. Control of a mirror with many actuators normally yields a very high computational complexity for a real-time system. To overcome this, an efficient distributed control algorithm is designed in a companion project of which some results will be shown [l]. By design, the deformable mirror has local influence functions, suiting the use of a distributed control algorithm. The bottle-neck in a distributed control design is the wavefront reconstruction step. This can be overcome by the use of a specific distributed parameterization of a spatiotemporal turbulence model. This is a dynamical filter that is identified from Shack-Hartmann measurement data of an A 0 breadboard set-up. The obtained reconstruction error is shown to be small even when local controllers communicate to a very limited set of neighbours.

eference 1. R. Ellenbroek, M. Verhaegen, R. Hamelinck, N. Rosielle, M. Steinbuch, N. Doelman, “Modeling and distributed control design for a new deformable mirror”, SPIE proc. Vol. 6272,2006.

CHARACTERIZATION AND CLOSED-LOOP DEMONSTRATION OF A NOVEL ELECTRO-STATIC MEMBRANE MIRROR USING COTS MEMBRANES DAVID DAYTON Applied TechnologyAssociates, 1300 Britt SE Albuquerque, NM 87123 USA JUSTIN MANSELL Active Optical Systems, 2021 Girard Blvd. Albuquerque, NM 81106 USA JOHN GONGLEWSKI Air Force Research Laboratory, 3550 Aberdeen SE Kirtland AFB, NM 871 17 USA Electro-static membrane mirrors have been in use for over ten years in active and adaptive optics apptications in industrial, academic, and research systems. We introduce a deformable membrane mirror produced from commercial off the shelf (COTS) pelticle membranes. This geatly reduces production costs of the device. Devices can be fabricated in up to 3 inch formats without large static aberrations. The mirror is capable of closed loop bandwidth in excess of several hundred Hz. Measurements of the device influence functions are presented along with results of closed loop real time control performance measurements.

1. ~ntroduction Although fabrication and experimentation with membrane mirrors has taken place for several years, it is only recently that the manufacturing process to produce micro-machined devices has evolved enough to meet the needs of the adaptive optics community. Several bulk micro-machined deformable mirrors have been developed as a compact low-cost adaptive optics.’’2 Typically these devices consist of a silicon chip mounted over an array of electrostatic pads for actuation. The chip contains a thin section with a reflective coating that forms the mirror. When a potential difference is applied between the mirror and a pad, an electrostatic force is produced on the portion of the membrane above the 41

42

electrode inducing mirror deformation. In recent paper^^*^*^ we demonstrated closed loop control of one such membrane mirror. We introduce and characterize a new micro-machined deformable mirror architecture that survives electrostatic snap-down well and has small static aberrations. The mirror is produced using COTS pellicles for the membrane. We describe the mirror attributes and the results from a high-speed laboratory closed-loop adaptive optics control experiment.

1.1. D e f o ~ a b l Mirror e Architecture and Fab~cation The deformable mirror used in this experiment is a 1” diameter low-cost polymer membrane deformable mirror created by Active Optical Systems, LLC (AOS). Figure 1.1 shows a schematic of the AOS membrane mirror along with pictures of the fabricated device. The device is created by bonding a commercially available pellicle to an array of electrostatic pads on a printed circuit board. The 5-micron thick nitro-cellulose pellicle is coated with aluminum to provide both reflectivity and an electrical connection to the membrane. Recessed Front Surface

Silicon Wafer Support Electrodes

I -

Figure 1.1 a) Schematic of Conventional Membrane Mirror.

Figure 1.1 b) Schematic of AOS Membrane Mirror.

Figure 1.1 c) Picture of AOS Membrane Mirror.

The electrostatic pads for the mirror described here were segmented annular regions. Figure 1.2 shows the actuator pattern on the deformable mirror. Each ring of actuators is 1.65 mm thick separated by 0.25 mm. The outer radius of

43

this actuator pattern is 9.3 mm, which leaves the outer region of the membrane to provide some degree of freedom for the edge of the actuated region. Although AOS has demonstrated up to 40-pm of throw from these polymer membrane deformable mirrors, this mirror was created using a large gap between the membrane and the electrostatic pads to avoid electrostatic snap-down. The electronics used in this experiment had a maximum voltage of 280V, which was 93% of the maximum design value.

Figure 1.2 Layout of electrodes.

The operational bandwidth of a membrane mirror is often limited by the first resonant frequency. We have measured the resonant frequency to be a little greater than 500 Hz. 2.

L a b o r a Characterization ~~

In this section we discuss laboratory measurements made on the AOS device in preparation for the development of a closed loop control algorithm. A Zygo interferometer with a Phase Shift Technologies front end is used to produce plots of the mirror surface. Figure 2.1 a) shows the mirror surface with no applied voltage. In this unbiased condition, the mirror has about 1.14 wave P-V mechanical deviation from a flat surface. Next figure 2.1 b) shows the effect of applying a 280-volt bias to each of the mirror electrodes. The figure shows the mirror surface with the static aberrations of 2.1 a) removed. This results in 7 waves P-V deformation and is the maximum throw of the device in our experiments.

44

b) Mirror Surface 280 V to all Actuators Static Aberrations Removed 7 Waves P-V

a) Static Aberrations Un-Biased Membrane Mirror I. 14 Waves P-V

Figure 2.1 Measurements of static minor surface.

The influence functions for a membrane mirror can be calculated by solving the second order equation for the surface of a stretched membrane with fixed circular boundary conditions'

where S is the surface displacement, V is the electrode voltage, T is membrane tension, and d is the separation between the membrane and the electrodes. Figure 2.2 compares cross-section cuts through the surface influence functions along one radial. Figure 2.2 a) shows measured influence functions, while 2.2 b) shows the calculated functions. The figures show that the measured mirror influence functions closely match the calculated values except for the outer actuator. 1.0

1.0

*

3 ;

gi? 0.5

0.5

(

0

0.5 Relative Aperture

1.0

0.5 Relative Aperture

1

Figure 2.2 Cross-sectionsof measured and calculated influence functions along a radial.

45

3. Closed Loop P @ ~ o r ~ a n c @ A MEMS A 0 test bed has been set up at the Air Force Research Laboratory. The test bed uses a wave-front sensor which runs at 1 KHz. A real time control algorithm was run on a Pentium based PC with a loop time of 1.0 milli-second. The test bed uses a circular rotating phase plate, produced by Lexitek, to generate dynamic wave front disturbances to test the device temporally as well as spatially. The phase plate can be rotated at different speeds to simulate different Greenwood frequencies.

U

Figure 3.1 Tilt disturbance rejection.

streh1=0.20 (0.25)

Strehl=O.15 (0.16)

Strehl=.O5 Predicted Strehl eQ

n

m w

m

pn

n

o

a

m

n

r

40 Hz

r

x

60 Hz

Open Loop

Figure 3.2 Long exposure closed loop Strehl ratio with different dynamic disturbances.

46

The 3dB closed loop tilt rejection bandwidth of the membrane mirror control system was measured to be about 60 Hz by driving a tip-tilt mirror at different sinusoidal frequencies and measuring tip-tilt rejection. The closed loop bandwidth is primarily limited by the mirror resonance at 500 Hz. A plot of the tilt disturbance rejection is shown in figure 3.1 and indicates a 3dB closed loop bandwidth of about 60 Hz. Figure 3.2 shows long exposure point spread functions and associated Strehl ratios produced by the closed loop system when run with different dynamic disturbances produced by the Lexitek spinning phase plate. We simulated Greenwood frequencies from 10 to 60 Hz producing closed loop Strehl ratios between .15 and .28. These Strehl ratios were slightly less than values predicted most likely due to limitations in the throw of the device. 4.

Concl~ions

We characterized a new type membrane deformable mirror manufactured using commercial off-the-shelf pellicle membranes suspended above an array of electrostatic actuator pads. The primary advantage of this device over conventional membrane mirrors is that the production costs are greatly reduced by using COTS membranes. Different configurations can be rapidly and cheaply proto-typed. In addition, the pellicle membranes are sturdier than many etched membranes allowing for complex multi-layer coatings to be applied to the front surface. We measured the influence functions and found that slight fabrication variations produced variations in the mirror response to applied voltages. Closed-loop control experiments indicated that the mirror has a 3dB bandwidth of about 60 Hz. We ran the control loop for dynamic disturbances using a Lexitek spinning phase plate and measured Strehl ratios for different Ckeenwood frequencies. Static aberrations of the mirror surface limited performance somewhat.

References 1. 2. 3. 4. 5. 6.

G. Vdovin, Opts. Comm., 115, (1995). J. Mansell, and R. L. Byer. SPIE Vol. 3353 (1998). D. Dayton, S . Restaino, J. Gonglewski, et.al., Opts. Comm., 176, (2000). D. Dayton, J. Gonglewski ,SPIE Vol. 3760 (1999). D. Dayton, 3. Gonglewski, SPIE Vol. 3866 (1999). R. Noll, JOSA 66, 3 (1976).

ELECTROSTATIC MICRO-DEFORMABLE MIRROR

BASED ON POLYMER MATERIALS FREDERIC ZAMKOTSIAN, PATRICK LANZONI Laboratoire dxstrophysique de Marseille, 2, place Le Verrier, 13248 Marseille Cedex 4, France

VERONIQUE CONEDERA, NORBERT FABRE LAAS-CNRS, 7 avenue du colonel Roche, 31077 Toulouse cedex, France MOEMS-based electrostatic micro-deformable mirrors (MDM) are promising for future AO systems. Original complete polymer mirrors have been designed for low driving voltage and high stroke, and first prototypes have been realized. Specific controlcommand strategy for the linearization of electrostatic actuation is presented and tested. Electrostatic MDM are well-suited for open-loop operation.

1. I ~ t r o d ~ c t i o ~ Future adaptive optics (AO) systems require deformable mirrors with very challenging parameters, including very large number of actuators and small inter-actuator spacing (c lmm). New technologies based on micro-opto-electromechanical systems (MOEMS) are promising for the development of a complete generation of new deformable mirrors. The major advantages of the microdeformable mirrors (MDM) are their compactness, scalability, and specific task customization using elementary building blocks. However this technology has also some limitation in terms of maximal size of the mirrors (8 inches wafers) and limited strokes. New A 0 architectures are under investigation to avoid these limitations. [ 11 Among all A 0 systems, Multi-Object Adaptive Optics (MOAO) is a concept enabling the correction of a large number of small fields scattered in a wide field of view (up to 10-20 arcmin) by means of independent wave front sensor on guide stars and correction “buttons” in open-loop on the studied objects. The collected Iight, corrected partially from the atmosphericat perturbations, permits optimal feeding of a spectrograph. This concept has been introduced recently in the FALCON project [2], and is now widely studied and known as MOAO systems. For open-loop operation, a deformable mirror must 47

48

exhibit a very good behaviour in terms of stability and reproducibility. Electrostatic mirrors are very good candidates as we demonstrated it on polymerbased actuators [3]. We present in this paper the development of polymer-based microdeformable mirrors, and open-loop operation strategy of electrostatic MDM. 2. ~lectro$tat~c polymer ~ c r o - d ~ f o r ~mirror ble Micro-deformable mirrors (MDM) are based on the MOEMS technology, closely linked to the micro-electronics fabrication process. A great level of sophistication in the micro-electronics technology ensures excellent tolerances on layer thickness and patterning precision. Most devices are based on the electrostatic motion. Main parameters of these components are the actuator stroke, the inter-actuator spacing, the inter-actuator coupling, the actuator bandwidth, the driving voltage, and the continuous mirror quality. Three main MDM architectures are under study in different laboratories: the bulk micromachined continuous-membrane deformable mirror, the segmented deformable mirror, and the surface micro-machined continuous-membrane deformable mirror. The third concept is certainly the most promising architecture, but it shows limited strokes for large driving voltages 141. All these devices are based on silicon or polysilicon materials. Our electrostatic MDM design is based on three elementary buildings blocks (Fig. 1). From top to bottom, the mirror surface has to be continuous and with the highest optical quality in order to minimize straylight and diffraction effects. Mirror material without stress and perfect planarization are the main goals; the actuation mechani$m is electrostatic force. Low driving voltage and large stroke are two key parameters; the driving e~ectro~ic$ has to underlie the deformable mirror structure and must be integrated in the substrate when the number of actuators becomes large. The processes to build the electronics and the optical architecture have to be compatible. In addition, the driving voltage has to be small enough, a few tens volts, for generation by an integrated electronics. Anchoring post Mirror surface Actuation mechanism Driving eiectronics

Figure 1. Schematic view of our Micro-Deformable Mirror (MDM).

49

In collaboration with LAAS-CNRS, we have chosen to develop an original process based on polymer materials. We propose to use SUX material as the structural layer of active piston actuators based on the electrostatic force; this polymer exhibits a low Young modulus (E = 6GPa) compared to typical polysilicon structures (E = 158GPa), allowing large strokes and low driving voltages. The same material is also well suited for the continuous mirror realization, leading to a complete MOEMS device made with SU8 material. The process used for the realization of the polymer-based actuators and efficient planarization capabilities have been demonstrated. The architecture of the actuators is typically based on a 580pm plate supported by 4 spring arms. Active actuators have been realized (Fig. 2) and exhibit a piston motion of 2pm for 30V. Using our dedicated characterization bench [5], we have measured a 6.5kHz resonance frequency, above the requirements for A 0 applications [3].

Figure 2. Polymer actuator with a 5 8 0 p plate.

The first realization of a complete electrostatic polymer-based MDM has been completed. Both actuator and mirror structural layers are SU8 polymers, and the sacrificial layer materials are SiOz for the actuator step and sol-gel for the mirror step. The first l0pm thick SU8 actuator structural layer is deposited on a lOpm thick SiOz sacrificial layer. The architecture of the actuators array is then defined by photolithography (Fig. 2), and the structural layer is polymerized. A second 6pm thick SU8 structural layer is deposited on a 6pm thick sol-gel sacrificial layer, forming the continuous mirror. After polymerization, a final polishing step by CMP is added for removing the remaining print-through patterns, before mirror coating. Wet etching of the sacrificial layers and supercritical COz cleaning release the structural layers in a free standing structure. SEM picture of a 3x3 array is shown in Fig. 3. The surface quality is very smooth, but remaining stress in the mirror layer induces a

50

slight bending of the whole surface. A Wyko white-light interferometer measurement of the mirror surface before release shows that flatness below 82nm peak-to-valley is obtained. However, after etching of the sacrificial layers, the released mirror shows a low order bending of the surface of 1.8,um peak-tovalley. A flat surface might be obtained after release, by decreasing the residual stress in the structure. Further developments in that direction are under way.

Figure 3. Complete polymer-basedMDM.

3. Open-loop operation A 0 systems are based on linear matrices operations. The requirement on the linearity of the deformable mirrors is usually below 10%. In the case of deformable mirrors driven by electrostatic forces, the actuation is highly nonlinear, with a V2 first order non linearity and higher order terms due to the gap diminution. Then, in order to "linearize" the actuation of the deformable mirror, we have developed a dedicated 14-bit electronics. After calibrating the behavior of the actuator and fitting the curve by a polynomial, the coefficients of the polynomial are loaded into the electronics which delivers linearized outputs. The order of the polynomial is adjustable according to the level of non-linearity of the device. For this study, we have designed a first MDM prototype with the architecture described above and realized it at Memscap foundry in the USA, with polysilicon material. The mirror has nine 200*2O0pm2 piston actuators. After linearization, the mismatch on the central actuator between the actual motion and the command is as low as 3.5nmrms (Fig. 4a). We have then defined an influence function a, calculated by averaging the motion maps normalized by the calibration function measured at the centre of the actuator.

51

The motion of any point on the mirror is determined by the equation:

where a is the influence function of the actuator (Fig. 4b) and k, a scalar determined during the calibration process. 'Using this equation, the residual error over the whole array for all voltages is below 5nm rms.

Figure 4.(a) Linearization of the central actuator; (b) Influence function a.

Last elements to be studied are the cross non-linearities between actuators. We have chosen to test our strategy on a 37 actuators MMDM made by OKO. Following the same procedure, we demonstrate that the motion is now determined by:

where a is the influence function of the actuator, k related to the voltage of the studied actuator, and the scalar h related to the neighbours actuator voltages. Using Eq. 2, the residual error measured in the vicinity of the studied actuator (approximately the size of the actuator footprint) is below 5nm r m for all actuators (Fig. 5). A generalization of this strategy is under development in order to take into account all possible location of the neighbours.

52

Figure 5. Cross non linearities evaluation.

The description of the motion of this mirror is applicable to all electrostatically-drivenactuators.

eferences 1. F. Zamkotsian, K. Dohlen, "Prospects for MOEMS-based adaptive optical systems on extremely large telescopes", in Proceedings of the conference Beyond conventional Adaptive Optics, Venice, Italy (2001) 2. F. Hammer, M. Puech, F. Assemat, E. Gendron, F. Sayede, P. Laporte, M. Marteaud, A. Liotard, F. Zamkotsian, "FALCON: a concept to extend adaptive optics corrections to cosmological fields", in Proceedings of Second Buckuskog Workshop on Extremely h r g e Telescopes, S P E 5382, Backaskog, Sweden (2003) 3. F. Zamkotsian, A. Liotard, P. Lanzoni, V. Conedera, N. Fabre, H. Camon, "Electrostatic micro deformable mirror for adaptive optics", in Proceedings of the SPIE conference on Astronomical Instrumentation 2006, Proc. SPIE 6272, Orlando, USA (2006) 4. T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein and D. A. Castanon, "Continuous-membrane surfacemicromachined silicon deformable mirror", Opt. Eng., 36 (5), 1354-1360 (1997) 5. A. Liotard, S. Muratet, F. Zamkotsian, J.Y. Fourniols, "Static and dynamic MOEMS characterization by phase-shifting and time-averaged inteferometry", SPIE conference MOEMS 2005, Proc. 5716, San Jose, USA (2005)

RECENT PROGRESS IN CMOS INTEGRATED

EMS A 0 MIRROR DEVELOPMENT

A. GEHNER, J. U. SCHMIDT, M. WILDENHAIN, J. KNOBBE, M.WAGNER Fraunhofer Institute for Photonic Microsystems Maria-Reiche-Str. 2, 01109 Dresden, Germany

For high-resolution optical phase control the Fraunhofer IPMS has developed a CMOSintegrated MEMS micro mirror array including 240 x 200 independently deflectable piston mirror elements of 40,um pixel size. To further improve the actual mirror performance, amorphous T i A has been successfully implemented as a novel CMOS-integrable actuator material providing a virtually drift-free deflection. In addition, first two-level designs with separated mirrors and hinges have been realized offering the potential of increased mechanical stroke at improved optical fill factor. Finally, the high wavefront correction capability of the IPMS mirror device has been demonstrated within an A 0 testhed.

IN9

IN2

IN.24

IN25

IN26

IN 48

Figure 1,CMOS integrated 240 x 200 piston micro mirror array.

1. M ~ M A S 0 Technology Platform As a core component the Fraunhofer IPMS has developed a fine segmented MicroElectro-Mechanical-System (MEMS) micro mirror array together with an integrated active-matrix CMOS address circuitry [l].The device provides 240 x 200 pistontype mirror elements with 40 ,um pixel size. Each of them can be independently addressed and electrostatically deflected according to the analog voltage levels programmed into the underlying storage cells. Employing so far a one-level architecture with hinges and mirrors formed within the same structural layer the 53

54

Figure 2. MEMS Phase Former Kit with software interface for user PC.

elements have been designed to offer a vertical analog deflection of up to 0.5pm corresponding to a phase shift of 2.5 a in the visible. Fig. 1shows a schematic view, a SEM photograph of an array portion, and the packaged chip. To enable full user programmability and control the mirror device is offered as a complete spatial light modulator (SLM) system, in terms of a so-called MEMS Phase Former Kit 121 as shown in Fig. 2. It also comprises an electronic driving board and a comfortable driver software for Windows XP@based PCs. Besides a Graphical User Interface (GUI) for autonomous operation with pre-defined data patterns also an open ActiveX@ programming interface is provided allowing an implementation of all necessary SLM control functionalities into the user‘s own software environment for a completely automated data processing. Thereby, the used high-speed IEEE1394a FireWire interface supports frame rates up to 500 Hi. 2. TIAI Mirrors with Improved Mechanical Drift Stability During recent work emphasize has been put on a continuous improvement of the actual MEMS mirror technology. A major challenge for the large-scale integration of micro mirrors lies in the development of a CMOS-compatible fabrication process, which has to enable both high-quality optical surfaces as well as a true analog deflection capability. Main impediments are given by the limited choice of suitable materials and the applicable temperature regime. In particular, most commonly used metals like Al or near-Al alloys may exhibit unwanted mechanical creep effects. Such drift or creep especially occures for low-melting metals with a face centered cubic cristalline structure as a result of stress relaxation processes caused by dislocation movement or grain boundary sliding when set under mechanical strain.

55 lntenslty [a u ]

Refledvtty ph]

2000

1600

1200 800

4w

20

30

40

60

50

70 80 2 Theta [deg]

200

400

600

800

1000 1200 1400 Wavelength [nmj

Figure 3. X-ray diffractogram of TiAl and an Al-alloy (left); reflectivity curves of bare and Al-coated TiAl (right),

Those effects can be virtually avoided by amorphous TiAl films. For that reason, low-temperature sputter deposited TiAl has been investigated at IPMS as a novel actuator material 131. As revealed by the x-ray diffractograms in Fig. 3, there is only a single broad band for TiAl indicating an amorphous film structure compared to the sharp reflexes of a polycristalline Al-alloy. For first evaluations of the process technology and the mechanical performance single-level mirrors of 40 pm pixel size have been fabricated using three types of structural layers: 200 nm pure TiAl, a 25/300/25nm AlRiAI/Al layer stack, and a 400 nm near-Al alloy. The symmetric AlRiAl/Al layer stack has been incorporated to improve the reflectivity of bare TiAl layers (see Fig. 3) and to compensate for thermal expansion mismatch, respectively. The mirrors were characterized by white light interferometery using a Veeco NT 2000. Fig. 4 shows the resulting deflection vs. voltage characteristic. The obtained 500 nm stroke fits Deflection z [nm]

0

5

Deflection z [nm]

10

15

20 25 Address Voltage U M

0

5

10

Time [min]

Figure 4. Deflection vs. voltage (left) and deflection vs. time (right) for the various actuator layers.

56 Deflection z [nm]

0

5

10

15

20

25

30 35 40 45 Address Voltage U M

Figure 5. SEM photographs of two-level micro mirrors with various hinge designs (left), z(U)-characteristic (upper right), and checkerboard deflection profile (bottom right)

well into the 27V address voltage range of current IPMS CMOS backplanes. Furthermore, the mechanical drift-stability has been investigated by applying a constant address voltage during a time interval of 10 min at an initial deflection of about 500 nm near maximum load. As revealed by the deflection vs. time curves in Fig. 4, the TiAl-based actuators offer a significant improvement yielding only a small residual drift of 15 nm compared to 115 nm for the near-Al alloy. In addition, the Ti41 actuators instantly deflect back to zero upon voltage turn-off, whereas the Al alloy actuators still show some residual deflection, which diminishes after a certain time period in the order of minutes.

3. Two-Level Mirror Actuators In a further approach, two-level "hidden hinge" mirrors of various designs have been realized employing a sacrificial polyimide and an Al-alloy as structural layer. Fig. 5 shows SEM photographs of three examples including their deflection characteristics derived from checkerboard deflection patterns as also depicted in the Figure. As can

57

MTF 10

09

08 07

06 05 04

03

02 01

n I.o_

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Normalized Spatial Frequency Figure 6. A 0 demonstration system and measured MTF curves (left) for the undisturbed, disturbed, and corrected system employing the depicted water ripple like aberration; USAF 1952 test chart images without and with mirror correction for the same aberration (right).

be seen from the curves, the diagonal hinges turned out to be comparatively stiff. They could be weakened by introducing additional diagonal spring elements leading to comparable results as with the investigated orthogonal hinge design. Furthermore, after a non-linear rise deflection saturates, that is when the mirrors come to rest upon the underlying hinge posts. Note, that the corresponding gap is defined by the thickness difference between the second sacrificial layer and the hinges, thus yielding an increased deflection of up to 550 nm for the 100 nm thinner hinges (hollow symbols in Fig. 5). So far, these designs have not yet been optimized and there is still the potential to reach mechanical strokes of 0.8 - 1.0 p m for 40pm pixel sizes or even up to 3.0 p m for 80 p m mirror elements.

4. A 0 Perfor~anceC~aracte~zation For presentation purposes as well as for a more quantitative performance analysis of the IPMS mirror devices a complete Adaptive Optics (AO) demonstration system has been developed [4]. The system as shown in Fig. 6 has been designed to enable

58

an imaging and an adaptive-optical correction of extended objects under polychromatic incoherent illumination. Wavefront errors of different severeness and complexity can be introduced by means of fixed or rotating phase plates. The optics has been realized within a commercially available Linos tube system yielding a very compact and transportable set-up with a footprint of only 450 x 600 mm'. For a quantitative evaluation of the mirrors' wavefront correction capabilities modulation transfer function (MTF) measurements have been performed. For that purpose sinusoidal gray-tone gratings with various spatial frequencies have been employed as image objects. The diagram in Fig. 6 shows the measured MTF curves for the non-disturbed, disturbed and corrected system, respectively, employing the depicted higher order "water-ripple"-like aberration. The fact, that with correction the contrast ratio of the undisturbed MTF is reproduced up to 95% impressively demonstrates the high correction capability of the IPMS mirror array especially for complex waveforms. For the same aberration Fig. 6 also includes USAF 1952 test chart images without and with applied mirror correction, where feature sizes of a similar MTF contrast of 50% have been marked for comparison. 5. Conclusion§

Besides the successfull characterization of the IPMS mirror arrays within an A 0 testbed, two important steps for the monolithic integration of high-quality MEMS mirrors onto CMOS have been accomplished, i.e. the realization of creep-resistant TiAl actuators as well as first two-level mirror designs. To exploit the full technological potential future activities will focus on a combination of both approaches, a strain- and hence drift-minimizing hinge design as well as a modified sacrificial layer technology for a further increased mechanical stroke.

eference§ 1. Gehner A., Wildenhain M., Neumann H., Knobbe J., Komenda O., ~ ~ analog light processing - an enabling technology for adaptive optical phase control, Proc. SPIE, Vol. 6113 (2006). phase-former-kit-e.pdf. 2. http:ll~.ipms.fraunhofer.dele~productslSLMl 3. Schmidt J. U., Knobbe J., Gehner A., Lakner H., CMOS integrable micro mirrors with highly improved drift-stability, Proc. SPIE, Vol. 6 4. Wildenhain M., Knobbe J., Gehner A., Wagner M., Lakner H., A 0 SLM Demonstration System and Test Bed, Proc. SPIE, Vol. 6467 (2007).

M

S

COMPACT LARGE-STROKE

PISTON TIP-TILT ACTUATOR AND MIRROR

w. NOELL', A. HUG?, T. OVERSTOLZ~,s.WALDIS', R. STANLEY~, N. F. DE ROOIJ' University of Neuchdtel, Institute of h4icrotechnology,Ih4T 2002 Neuchatel, Switzerland Centre Suisse d'Electronique et de Microtechnique SA, CSEM, 2002 Neuchatel, Switzerland

1. Introduction Many applications in optics require very flat and accurately displaceable micromirrors. Typically, devices are tunable cavity systems (interferometers, lasers, filters, etc) and beam manipulating devices, e.g. deformable mirrors for adaptive optics. Recent optical MEMS developments have shown that siliconon-insulator (SOI) based devices provide excellent flatness even when operating in resonance [l]. However, S I devices are subject to bow due to the residual stress in the SO1 substrate induced by the buried oxide [2]. In the case of gimbal based systems, the device may suffer from stress which could yield to buckling [3,4]. Additional mechanical stress can be introduced to the device by packaging and thermal mismatch effects. We have designed and fabricated a compact accurately controlled piston tip-tilt micromirror, where the residual stress is locally released and compensated by a curved-beam device suspension resulting in optically flat micromirrors (Fig. 1). Deflectable mirror membranes used in adaptive optics require fast and small actuators underneath the thin mirror membranes. The devices proposed above can also be used as simple actuators. Due to their compact design, large stroke, and the integrated technology they are based on, these actuators have the potentiai to be used over large arrays as a bases for an actuator array for deformable mirrors.

9.

59

60

2. Concept

2.1. Device Cons~erations Three symmetrically arranged C-shaped suspension beams are wound around a central micromirror. Unlike torsion bars in gimbaled devices forming a straight axis where stress can propagate, the suspension with three beams arranged in 120" segments avoids stress propagation and buckling of the beams and mirror, respectively. The result is an optically flat and stress-released mirror of 1.5 mm edge length with highly increased (in-plane) stability. The C-shape of the beams allows them to be folded around the mirror and the vertical comb electrodes resulting in a very compact device. The beam height is reduced over the device height to increase the vertical flexibility of the suspension. At the same time the lateral stability is maintained to avoid lateral snap-in of the asymmetric vertical comb-drive actuators.

Figure 1 Left Device Concept. Tunable cavity devices such as interferencefilters and tunable lasers can suffer from non-parallel cavity errors due to dust inclusion from the packaging process. The piston tip-tilt MEMS actuator provides integrated asymmetric comb drives, stress-compensating suspension beams, and an optically flat micromirror surface. The mirror itself can also be used as independent device, e.g. as an actuator base for an adaptive mirror membrane. Right: Actuator and Suspension Concept: Exploded view of the concept of the micromirror device. The device is fabricated with SO1 and DRIE technology. The central micromirror is suspended by three C-shaped beams, that are vertically soft but provide in-plane stability for the three aspmetric vertical comb drive actuators. The design is very compact and due to its integrated electrodes allows for independent driving and array arrangements.

61

Figure 3. Design and details on the microfabricated microminors. a) The triangular minor is the most compact design for C-shaped beams. b) The zoom-in shows the to height Ievefs of 12 and I 5 pm, respectively.

The micromirror itself is open on both sides and suitable for transmission devices. At the same time the in-plane stress of the SO1 substrate is compensated in order to avoid buckling and static mirror deformation.

3. Results - Devices and Experiments 3.1.1. Single Triangular Mirror The device is based on bulk micromachining of SO1 substrate with thicknesses of 50/2/350 pm (Fig. 3). We used a self aligned delay mask process to thin down the suspension beams and the moveable combs to a height of 1 2 p m (Fig. 3b) [5]. The different height levels of the static and the moveable comb electrodes and their initial offset position allow a vertical actuation of the mirror. By applying a potential the offset position tends to be equalized by lifting up the moveable combs and thus the mirror until a symmetrical configuration is achieved. The piston tip-tilt mirror is characterized by an accurate vertical displacement of more than 18 pm @ 80 V and a tip-tilt of up to 2 mrad @ 50 V. Pure vertical displacement is achieved by applying the same potential to all three static comb electrodes, whereas a tip-tilt results by applying a different potential to at least one of the three electrodes. Fig. 4 shows the measurements performed with a white-light interferometer. The stress and curvature of the chip and mirror frame is clearly visible (Fig. 4a). The zoom-in on the central area of the mirror in operation shows the extremely low roughness and high flatness (Fig. 4b) of the device. The mirror remains optically flat. Hence the stress from the substrate was not propagated to the mirror. In dynamic measurement the mirror could be displaced by 4pm at 250Hz and 30V. There actuation remained stable.

62

0

0

500

1000

1500

2000

2500

3000

3500

4000

4500

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750

4914

839

Figure 4.White-light interferometer measurements of the fabricated micromirror of Fig. 3. The mirror edge length is about 1.5 mm and the length of the chip about 5 mm. a) In the non-actuated state the bow of the frame is clearly visible. The rectangle of central area of the mirror is measured in subsequent measurements b). The optically flatness of the mirror is maintained even in operation. The peak-to-peak deformation was less than 13nm. This is due to the stress compensation of the curved beams that release their stress in a vertical movement.

3.1.2. Vertical Actuator for Deformable Mirror Applications

In the previous configuration the mirror and actuator are one integrated device. The large stroke of the actuator, however, could be used as driving component for deformable mirrors. The technological approach allows to fabricate the actuators as large arrays that would be addressed by a second wafer or printed circuit board (PCB) providing the wiring.

63

Deformable mirror membrane

Figure 5 . In an more advanced configuration,mirror and actuator are two separated sub-components of the device. The actuators are arranged in arrays and drive a deformable mirror membrane.

The vertical comb-drive actuator shown above works only upwards. Inverting the layout of the electrodes, the actuator could also be used to pull down, doubling the range of a single actuation component. Figure 6 shows the electrode configuration and the technological pre-study of such a device, which is currently under testing. Two sets of two vertical actuators are arranged around a central piston. One set pulls the piston upwards, while the other set can pull the piston downwards. Addressing just one single actuator, i.e. one quadrant, would additionally allow small tilt angles.

Figure 6 . Piston actuator for membrane deformation. a) The vertical asymmetric comb-drive can be arranged in two ways to create a bi-direction up-down actuator. b) Arrays and c) single actuators show the results of a pre-study, which demonstrates the feasibility of the of the fabrication process. The pitch between the piston centers is 1 mm.

64

4. Conclusion We have presented a device in which the arrangement and the shape of three curved suspension beams transforms stress exerted onto the beams in a lateral displacement which is compensated by the symmetrical structure. The curved shape and the arrangement of the beams allow a high vertical displacement and excellent lateral stability of the mirror. The result is an optically flat mirror that can be lifted up individually at one, two or three sides, making the device suitable for tunable Fabry-Perot cavities or applications in adaptive optics. The integrated vertical electrodes allow a true 3D positioning of the mirrorlplatform with-in the mechanical limitations. Due to the large stroke of the actuator design, arrays of them could be used as a base for deformable mirror membranes. At technological pre-study demonstrated the feasibility of the technology.

Ac~o~ledgement This work was carried out within a project that is founded by the Swiss Center for Electronics and Microtechnology, Inc. The founding is greatly acknowledged.

eferences 1. H. Urey, “Torsional MEMS scanner design for high-resolution display systems”, Proceedings of SPIE, Seattle, Washington, Vol. 4773, July 2002, pp. 27 - 37. 2. A. Tiberj, B. Fraisse, C. Blanc, S. Contreras, J. Camassel, “Process-induced strain in silicon-on-insulator materials”, Journal of Physics: Condensed Matter, Vol. 14,2002, pp. 13411 - 13416. 3. K. Isamoto, K. Kato, A. Morosawa, C. Chong, H. Fujita, H. Toshiyoshi, “A 5-V Operated MEiMS Variable Optical Attenuator by SO1 Bulk Micromachining”, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 10, No. 3, May/June 2004, pp. 570 - 578. 4. 0. Tsuboi, Y. Mizuno, N. Koma, H. Soneda, H. Okuda, S. Ueda, I. Sawaki, F. Yamagishi, “A Rotational Comb-driven Micromirror with a Large Deflection Angle and Low Drive Voltage”, Proceedings of the IEEE MEMS Conference, Las Vegas, Nevada, 2002, pp. 532 - 535. 5. S. Kwon, V. Milanovic, L. P. Lee, “Large-Displacement Vertical Microlens Scanner With Low Driving Voltage”, IEEE Photonics Letters, Vol. 14, No. 11, November 2002, pp. 1572 - 1574.

MEMS Deformable Mirrors for High P erformance AO Applications PAUL BIERDEN

Boston Micromachines Corporation 108 Water St. Watertown, MA 02472 USA pab @bostonmicromachines.com THOMAS BIFANO AND STEVEN CORNELISSEN

Boston Micromachines Corporation 108 Water St. Watertown, MA 02472 USA

1. Summary Boston Micromachines’ MEMS deformable mirrors are based on the surfacemicromachined, poly-silicon double cantilever actuator architecture pioneered at Boston University[l], illustrated in figure 1. The device structure consists of actuator electrodes underneath a double cantilever flexure, the actuator, which is electrically isolated from the electrodes and maintained at a ground potential. The actuators are arranged in a square grid, on a pitch of 300-400pm, and the flexible mirror surface is connected to the center of each actuator through a small attachment post that translated the actuator motion to a mirror surface deformation. his MEMS DM architecture allows for local deformation of the mirror membrane with an influence function between 20-40% on its nearest neighbor, depending on the specific device design (see figure 2).

Figure 1 . Cross-section of 1x3 electro-statically actuated MEMS deformable mirror.

65

66

Figure 2. Surface measurement of a single deflected actuator of a 144 element DM (left) and the resulting minor surface figure of the MEMS continuous face sheet.. The influence of the single element (-35% on device shown) deflection only affects its immediate neighbors leaving the rest of the mirror surface unchanged.

2. MEMS Mirror Development 2.1. Large Actuator Count DM's A 4096 element, continuous facesheet MEMS deformable mirror is currently under development for the Gemini Planet Imager (GPI) instrument. In an experimental “Extreme Adaptive Optics” testbed a 1024 element h4EMS deformable mirror was characterized to determine if the technology is suitable for this application. The testbed showed that the h4EMS DM could be flattened to less than lnm RMS within controllable ~i~~ 3. packaging for 4096 element MEMS spatial frequencies over an aperture of deformable mirror.

67

9.2mm with an average long term stability of less than 0.18nm RMS phase[2], thereby demonstrating that the MEMS DM is a feasible wavefront compensator for high contrast imaging. The target specifications for this 64 x 64 square actuator array include 2-3 pm of stroke and a 10 nm RMS surface quality. Although each of these capabilities has been demonstrated within various Boston Micromachines DMs, they have not been achieved on the same device. Table 1 describes the requirements for the 4096 actuator DM prototype.

/

Table 1: Requirements for the 4096 Actuator Deformable Mirror Pixel count 4096 (64x64 array) Square Pitch 300 to 400 pm Stroke 2-3 pm Fill Factor 99% 19.2 mrn (48 actuator diameter @ 400pm pitch) Active Aperture size Pixel surface finish (RMS)
The 4096 DM is based on a legacy design. While the actuator array is scalable, a new wire routing design is required to individually address 4096 actuators through wire traces. A buried wire process has been developed which sandwiches the conductive polysilicon wire traces between two silicon nitride dielectric layers. The design of the 4096 actuator DM poses challenges and tradeoffs between stroke, bandwidth, and surface finish. Increasing stroke requires reducing actuator stiffness. Reducing actuator stiffness reduces the maximum speed of the DM. Reducing stiffness also affects optical quality, since the small perforations in the actuator that modify stiffness translate up to the mirror surface. To test the 4096 actuator prototype, a sample of devices from the fabrication run has been evaluated based on actuator stroke and surface finish. The final manufacturing process will be determined based on testing the sample devices. The maximum stroke on most devices was measured to be greater than 4 pm. After flattening, the stroke will meet the 2-3 pm specification. Interactuator stroke was measured to be greater than 1 pm. The surface figure for two new actuator designs is shown in figure 4 to be less than 10 nm RMS. Although the actuator perforations print-through to the mirror surface, the magnitude has been reduced by adjusting their size to minimize dishing effects from the CMP.

68

Figure 4. Surface figure measurements of two DMs with modified actuator design. The actuator perforations have reduced from approximately 20nm RMS (left) the surface figure to below 10 nm -_ RMS (right).

2.2. High Speed MD's The need for high-speed control of wavefront has presented itself in a number of applications, specifically long range laser communication. A 1024 element MEMS segmented deformable mirror with corresponding control electronics was designed to address this Figure 5. Rise and fall time measurements for MEMS issue. The mirror was defonnable mirror. an extension on BMC's heritage devices and demonstrated rise time (10-90%) of <20ps. The corresponding control electronics are currently under development and are designed for a 20kHz frame rate with a 15ps latency.

2.3. Long Stroke D~~ Biological imaging has been the driving factor for increasing stroke of deformable mirrors. As imaging-depth capabilities increase, the amplitudes of wavefront aberrations increase. The maximum achievable stroke for a double cantilever actuator is dependant on a number of variables. The most significant factors are:

69

.,

-

the gap, g , between the flexure and the fixed electrode, the applied voltage, V, to the electrode the mechanical stiffness of the flexure

The 12x12 actuator array with a pitch of 450 pm and aperture of approximately 5 mm were fabricated with an increased gap, g, in order to achieve a stroke of 6 pm. Increased stroke requires an increase in voltage, but higher voltages risk the likelihood actuator snap-down. To decrease the risk of snap-down at 6 ym of deflection a split-electrode configuration was employed - eliminating electrostatic attractive force directly beneath the area of the actuator membrane that reaches closest to the electrode. In addition, a decrease in mechanical stiffness was achieved with small perforations in the actuator, thus reducing voltage demands. Devices have been fabricated, and the completed dies were attached to a ceramic package and wirebonded. Voltage versus deflection was tested using a whitelight interferometer. The results are shown for two different actuator designs. Strokes of up to 6.3 pm were measured on the devices. The maximum stroke of these actuators, at the maximum applied voltage, was within 15% of the stroke predicted by the finite element model. The difference between the measured and predicted values is mainly due to variations in the actuator gap size. Long Stroke Actuator Performance Measured and Predicted Results 8

7 6

s5 z 3

I

I

25

50

I

I

275

300

2 1 0

0

75

100

I25

150

175

200

225

250

325

Voltage, V

Figure 6. Predicted and measured voltage vs. deflection performance results for two different actuator designs. Each achieve greater than 6pm. The inset image shows a deflected actuator measured with a white-light interferometer.

70

3. Conclusion

Boston Micromachines is developing wavefront correctors for the ever increasing demands of adaptive optics in biological imaging, ophthalmic instrumentation and laser communication.

~c~owledg~en~ This work was supported in part by the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement AST 98-76783.

eferenees 1. Perreault, J. A., Bifano, T. G., Levine, B.M., and Horentein, M., “Adaptive optic correction using microelectromechanical deformable mirrors,” Opt. Eng. [41]5, pp. 561-566,2002. 2. Morzinski, K. M., Harpsoe, K., Gavel, D. T., and Ammons, S . M., The openloop control of MEMS: Modeling and experimental results, S P E 6467, 2007.

A VERSATILE INTERFEROMETRIC TEST-RIG FOR THE INVESTIGATION AND EVALUATION OF OPHTHALMIC AO SYSTEMS S. GRUPPETTA*, J. J. ZHONG AND L. DIAZ-SANTANA Department of Optometry and Visual Scieiace, City University Northampton Square, London, ECl V OHB, UK *E-mail: s t e v e . g ~ p p e t t a ~ c ~ t y . a c . u k www.city. ac.uk An interferometric test-rig is presented to test ophthalmic A 0 systems and monitor their performance. The interferometric monitoring branch is not coupled to the A 0 system, thus giving a fair and unbiased representation of the performance of the A 0 system. This is compared with the common scenario in ophthalmic A 0 systems of using the Shack-Hartmann (SH) sensor t o monitor the system’s performance. The advantages of the independent interferometric system are highlighted through qualitative and quantitative comparisons with the output of the SH sensor. Keywords: Ophthalmic Adaptive Optics

1. ~ n t r o d u c t i o n

Adaptive Optics (AO) systems for ophthalmic applications differ from their astronomical counterparts in a number of ways; these differences include cost, nature and magnitude of aberrations to be corrected and experimental conditions.’ In particular, current A 0 control algorithms are based on least-squares reconstruction algorithms primarily because of the limited knowledge on the statistics of ocular aberrations. We present a robust and versatile interferometric set-up to evaluate independently and in a quantitative manner the performance of A 0 systems for ophthalmic use. In ophthalmic applications of AO, the performance of the system is often quantified through the reconstructed wavefronts from the Shack-Hartmann (SH) sensor used in the A 0 system. This is a convenient measure of the system’s performance but its limitations need to be thoroughly understood, namely its low sampling (as typically used in ophthalmic applications) and its intrinsic coupling to the A 0 system which can lead to erroneous inter71

72

pretation and quantification of the system performance, as we will show.

St

Laser Fig. 1. Schematic representation of set-up which includes an A 0 system (SH sensor with 8x8 spot pattern, O K 0 19-element deformable mirror DM) an interferometric branch with CCD t o record interferograrns, mirrors M1 and M2 t o provide separate references for the interferometer and the SH sensor, and relay optics.

2. Experimental set-up

Recently Booth et aL2 and Horsley et aL3 have presented interferometeric methods to characterise deformable mirrors. Booth et al. used an interferometer to measure the influence functions of deformable mirrors and generate their control matrix without using a wavefront sensor. Horsley et al. measured the deformable mirror surfaces interferometrically while openloop mirror deformations were generated. In this work we take the interferometric methodology further by coupling an A 0 system to a Twyman-Green (TG) interferometer using a double reference mirror configuration (Fig. 1). This enables continuous and non-intrusive monitoring of the A 0 system’s performance in real time during closed-loop operation. The wavefront sen-

73

sor used is a SH sensor and the wavefront corrector is a deformable mirror (DM). Data from the interferometer offers a number of distinct advantages: (1) It gives an immediate real-time qualitative feedback to the investigators about the optical performance of the system at any stage during open- or closed-loop performance. It is possible to make a quick judgement about the quality of the DM or system performance directly from the shape and number of fringes in the interferogram, prior t o any data post-processing. (2) In an A 0 system the DM and SH are inherently coupled. If there is any bias or other type of systematic noise present in the SH, it will be propagated through the control system to the DM degrading the optical performance of the system. By having an independent interferometric branch we can assess the impact of some of the issues associated with this SH-DM coupling. (3) The SN data often shows near perfect correction in a stable, wellconditioned closed-loop when in fact some aberrations are present but they are not seen by the SH sensor, and hence cannot be corrected by the A 0 system. The interferogram clearly shows such residual aberrations unseen by the SH sensor. Additionally, the data from the interferometer is not limited by the bias and cross-talk between modes imposed by the finite sampling of the ~ e n s o r . ~ (4) The interferogram data can also provide quantitative information off-line by using it to retrieve the phase of the wavefront with numerical methods. The phase-retrieval algorithm we use is considerably more accurate than the least square reconstruction technique for the SH sensor. Thus a more accurate assessment of the systems performance can be made, and without the problems associated with the SH-DM coupling. ( 5 ) Finally, it i s possible to estimate the error introduced by the coupling between the SH and DM. In this manner the SH sensor can be used independently to monitor the system’s performance and with an understanding of the limitations of the methodology.

3. Qualitative and Quantitative monitoring of the A 0 system In order to highlight the mis-representations that can arise from the coupling of the SH sensor with the DM, we have run the A 0 system while introducing an artificial bias in the SH sensor through directional illumination from above the set-up (obtained by leaving the lights in the laboratory switched on.) Figure 2 (left) shows a reconstructed interferogram

74

Fig. 2. Left, optical quality as perceived by SH sensor (interferogram reconstructed from SH data) and right, actual interferogram recorded on interferometer. See text for details.

Fig. 3. Top row shows 2 interferograms as measured by the interferometer branch and the bottom row shows the interferograms obtained from the retrieved wavefronts using the phase-retrieval algorithm. The accuracy of the phase-retrieval algorithm was better than X/25.

from the SH sensor during an A 0 closed-loop. This seems to indicate a fairly flat wavefront. However, the directional illumination from above the set-up was introducing a bias in the vertical direction to the centroiding of the SH spots. The system interpreted this as tilt in the direction of the bias and overcorrected for it with the DM, thus explaining the “flat” wavefront preceived by the SH sensor. The corresponding TG interferogram (Figure 2 (right)) clearly shows this tilt, since it is independent of the A 0 system. A phase-retrieval algorithm based on the Takeda method5 was used to

75

I

Step 0

RMS error: 0.66pm RMS error: 0.63p.m R.esidiin1 RMS error: 0.17um

Step 1

RMS error: 0.32pm RMS error: 0.27p.m Residual RMS error: 0 . 1 3 ~ m

Step 2

RMS error: 0.20pm RMS error: 0.16pm Rssidiinl RMS error: 0.15um

Step 3

RMS error: 0.15pm RMS error: O.lOpm Residual RMS error: 0.13pm

Fig. 4. Top to bottom: First 4 steps of a closed-loop starting from no correction in Step 0. Left t o right: (Column 1) T G interferogram, (2) wavefront (WF) retrieved from interferogram, (3) W F reconstructed from SH sensor, and (4) interferogram calculated from W F in (3). Residual RMS is the RMS error of the difference of the WFs in columns 2 and 3.

76

retrieve the wavefront from the TG interferogram. Figure 2 illustrates the accuracy of this method. The SH reconstruction could now be compared quantitatively with the interferogram. Figure 4 shows the first 4 steps of a closed-loop correction comparing the optical quality as seen by the interferometer (first 2 columns) and by the SH sensor (last 2 columns). This provides both a qualitative and a quantitative measure of the approximations incurred by the SN sensor at a sampling of the order commonly used in ophthalmic applications (8x8 spot pattern in this test-rig.) The loss of resolution in the SH reconstructions can be appreciated when compared with the retirieved wavefronts. In particular, the retrieved wavefronts at best correction show the location of the 19 actuators as small local bulges in the wavefront - these feature are completely absent from the SH wavefronts. The RMS error values from the SH sensor also underestimate the residual aberrations when compared to the ones obtained from the wavefronts retrieved from the interferograms. 4. Conclusion

We have described an interferometric A 0 test-rig to monitor the performance of ophthalmic A 0 systems. The importance of using a monitoring system which is decoupled from the A 0 system is highlighted through qualitative and quantitative examples comparing the system’s performance as observed by the independent interferometric branch and by the SH sensor, which is inherently coupled to the A 0 system.

References 1. J. Porter, H. Queener, J. Lin, K. Thorn and A. Awwal (eds.), Adaptive Optics for Vision Science (Wiley, 2006). 2. M. Booth, T. Wilson, H.-B. Sun, T. Ota and S. Kawata, Applied Optics 44, 5131 (2005). 3. D. A. Horsley, H. K. Park, S . P. Laut and J. S. Werner, Characterization for vision science applications of a bimorph deformablemirror usin Phase-Shifting Interferometry, in Proc. SPIE, Proc. SPIE 56882005. 4. H. Li and C. Rao, Journal of Physics 48, 952 (2006). 5. M. Takeda, H. lna and S. Kobayashi, J . Opt. Soc. Am. 72,156 (1982).

Woofer-Tweeter Adaptive Optics T.D. Farrell* and 3.C. Dainty Applied Optics Group, Dept. of Experimental Physics, N. U.I. Galway, Galway, Ireland *E-mail: thomas. [email protected] An optical bench experiment has been assembled t o demonstrate the concept of woofer-tweeter adaptive optics for astronomical applications. The system includes an O K 0 37 actuator woofer deformable mirror combined with a Boston Micromachines 140 actuator tweeter. The goal of such a system is to achieve a higher degree of wavefront correction not currently possible due t o the limitations of deformable mirror technology and cost. Keywords: Adaptive Optics,Atmospheric correction.

1. Introductio~

The next generation of Extremely Large Telescopes (ELT) with apertures upwards of thirty metres diameter will all require Adaptive Optics(A0) if they are to realise their high resolution capabilities. Given the science case for these instruments and the corresponding A 0 requirmentsl there is an immediate problem in sourcing a Deformable Mirror (DM) that can fulfill both the mirror stroke and actuator density requirements. Current technology can provide DMs that have sufficient stroke (> 20pm)but are of limited spacial order whilst the higher order mirrors (> 1000 actuators) are limited by actuator stroke. It would be foolhardy to expect that future improvements in DM design will provide a solution to this problem although it may be a distinct possibility. In the meantime another approach is needed to ensure the success of these multimillion euro telescope projects. A possible solution is to combine two such mirrors in a woofer-tweeter configuration.2 This technique can be extended to any A 0 application that requires high stroke/high order DM correction or if such correction needs to be performed at a cost point. Already such A 0 systems have been used to correct for ocular abberations where the use of a MEMS DM was limiting low order c ~ r r e c t i o n . ~ 77

78 Boston Micromachines 144actuator DM SH wavefront sensor

He-Ne laser source

Schematic of woofer-tweeter A 0 demonstrator. A point source (He-Ne laser) is propagated through an atmospheric section and is corrected by dual DMs. A wavefront sensing arm provides the wavefront information whilst an imaging camera measures the image PSF. Fig. 1.

2. Laboratory Demonstrator

The aim of the laboratory demonstrator (Fig. 1,Fig. 2) is to show the feasibility of using a woofer-tweeter architecture in closed loop A 0 and to refine the control algorithms used. The system is a scaled model of an 8 metre class telescope operating in the K band. In reality the light source used is a He-Ne fibre laser which emits monochromatic light at 632.8nm. There is the possibility to include a more realistic white light source but this approach can leave the system short of photons and there are also difficulties in keeping the source point like. Etched phase screens are used to represent atmospheric turbulence and these have been found to obey Komolgorov statistics. By using various combinations of plates the strength of turbulence can be varied to ensure saturation of the tweeter. Initial low-order correction is made by an O K 0 37 actuator PZT mirror which has up to 8 p m of available stroke. Secondary correction is performed by a Boston Micromachines 140 actuator tweeter mirror which has a limiting stroke of 3.5pm. As the Boston is a MEMS mirror it is necessary to operate it from a bias position to allow positive and negative actuation. The non-linear ef-

79

fects(Fig. 3) of the mirror are taken account for in the A 0 loop ensuring that command signals are converted into the appropriate actuator voltages. Both mirrors are conjugated to the ground layer which contains the phase screen(s). The dynamic effects of turbulence can be incorporated in the experiment but operation is currently restricted to a frozen or slowly varying atmosphere. All hardware interfacing and software control is operated by a desktop PC using NI Labview.

s...... .

.*....

.

I

.

*

.

........ I

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

,

. * . ." . . . . * * ,

............ Fig. 2. WTAO optical bench

The performance gains expected from using dual mirrors is dependant on the strength of abberation, actuator geometries and the overall stroke of both mirrors. Fig. 4 gives an indication of the potential imaging gains when using a low stroke mirror like the Boston. A mirror with the actuator geometry of the Boston and 2 p m of stroke can increase imaging Strehl ratio from 0.2pm to 0.45prn at turbulence strengths of D/ro = 12. A previous study4 has shown that two mirrors can only approach the performance of a stroke unlimited tweeter. These simulations where however for a particular set of mirrors and might not be true for different setups. It is possible that the use of two mirrors with their different actuator patterns might reduce the fitting error over and above that of the tweeter. 3. Woofer-tweeter control

There are a number of possible methods with which to control two mirrors which are conjugated to the same pupil. The control method used has a

80

Actuator Voltage

Fig. 3. PeaklValley wavefront (unit normalised) as a function of voltage for a single actuator on the Boston. Note the saturation effect at 0-20V and 130V and above. The bias position for this mirror is at 94V with actuator command voltages calculated using the roots of the polynomial fit.

large effect on final imaging performance and its important t o ensure the best possible approach is found. A good control algorithm will ensure that both mirrors are complementing each other with the shapes they produce. In a zonal A 0 regime each actuators influence on WFS spot deviations is recorded in an interaction matrix.

s

=L:

DtweeterC

(2)

The corresponding controls found t o minimise some detected wavefront error Smeasured are found by least squares SVD inversion. Cwoofer

Ctweeter

= Dwoofer*Smeasured

(3)

Dwoofer*Smeasured

(4)

=I:

Individually each mirror can be used independently to perform standard

A 0 using the formulae above. If we were t o apply standard A 0 corrections

81

6

8

10

12

14

16

18

20

22

Dir,

Fig. 4. Effect of maximum mirror stroke on Strehl ratio using the actuator geornetry of the Boston. This indicates the potential gains of using a woofer DM by allowing the tweeter to operate in an unlimited stroke regime.

for both woofer and tweeter their would be reduced performance as both mirrors would counteract the others correction. Some orthogonality of correction needs t o be kept between each mirror and this can be achieved by deprojecting the woofer mirror modes from the tweeter and vice versa. __ high CLN-oofer - K d e p r o j e c t C w o o f e r

(5)

- low - KdeprojectCtweeter

(6)

Ckeeter

K dhzgh e p r o j e c t = I - QCTR-

....- C c u t o f f C : u t o f f R

(7)

Here R is the actuator cross talk matrix given by and q is the pure command for mirror mode i . Problems may arise if the mirror modes of one mirror cannot be reproduced in the other. There are other control approaches and these are planned for this experiment as part of the feasibility study. A modal approach using a Zernike basis might be a more appropriate choice3 than the mirror specific zonal methods outlined above. Another method already used in ocular adaptive

82

optics5 involves the multiplexing of adaptive optics between the woofer and tweeter. There are number of issues with this control strategy that would need t o be addressed before use in an astronomical adaptive optics system. The closed loop dynamics of switching between two mirrors could lead t o instability in the system if the loop speed is too slow t o account for the evolving turbulence. 4. Conclusions

An experimental A 0 system has been described which aims to show phase correction using dual woofer-tweeter DMs. A woofer DM has been chosen which is capable of correcting large amplitude lower order abberations whilst a high spatial resolution correcting device is used as a tweeter. As imaging performance is largely dictated by the control algorithms a comparison will be carried out between a number of different control schemes. The system is fully constructed with all the necessary interfacing and coding performed through NI Labview. An imaging camera is t o be added soon t o enable imaging performance t o be determined. Single mirror A 0 has been attempted and work is ongoing on having both mirrors correct in a closed loop.

5. Acknowledgments This work has been funded through Science Foundation Ireland and through the 1.R.C.S.E.T postgraduate scholarship scheme. My thanks also t o Dr. Alexander Goncharov and t o Dr. Nicholas Devaney for their input and guidance on this study.

References 1. R. G. Dekany, M. C. Britton, D. T. Gavel, B. L. Ellerbroek, G. Herriot, C. E. Max and J.-P. Veran, Adaptive optics requirements definition for TMT, in Proceedings of the SPIE, 2004. 2. 0. Keskin, P. Hampton, R. Conan, C. Bradley, A. Hilton and C. Blain, ahs 0 , 74 (2006). 3. R. Conan, C. Bradley, P. Hampton, 0. Keskin, A. Hilton and C . Blain, Appl. Opt. 46, 4329 (2007). 4. S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu and W. Jiang, Appl. Opt. 45, 2638 (2006). 5. S. M. Jones, S. Olivier, D. Chen, S. Joeres, S. Sadda, R. J. Zawadzki, J. S. Werner and D. T. Miller, Adaptive optics ophthalmologic systems using dual deformable mirrors, in Proceedings of the SPIE, 2007.

~EFORMABLEMIRRORS BASED ON TRANS~ERSAL PIEZOEFFECT GLEB VDOVIN, MIKHAIL LOKTEV and OLEG SOLOVIEV Flexible Optical B. V., Rontgenweg 1, 2624 BD Delft, the Netherlands *E-mail: [email protected] This article reports on the recent progress in the technology of low-cost piezoelectric deformable mirrors with actuators based on transversal piezo effect. Keywords: Piezoelectric actuator, deformable mirror, wavefront corrector, adaptive optics.

1. Piezoelectric actuators

Piezoelectric actuators are traditionally used in deformable mirrors. Piezoelectric materials have a unique combination of mechanical strength, stiffness and stability, making them very suitable for applications in precision movement control and adaptive optics. To produce a piezoelectric actuator, the piezoelectric ceramics should be poled by applying an external electric field at high temperature. Significant polarization POremains in the material after poling is finished. To produce a mechanical actuation, the external field E applied to the piezoactuator should be parallel to the vector of internal polarization Po. The actuator size changes under the action of the external field. The actuator dimensions change not only along the field, but also in the orthogonal to the field direction - the so-called transversal piezoeffect. The relative deformation E = Al/l in any direction is given by a relation: E

= dE

+a/Y,

(1) where d - the modulus of the piezoelectric coefficient, €3 is the field, Y is the Young modulus and CT is the stress. For the deformation along the field one has to take d = d33, for the transversal piezoeffect - d = d31. The field E should not exceed some 83

84

maximum value Ec to avoid the de-polarization of the actuator followed by loss of piezoelectric properties. Let us derive the main parameters of a piezo actuator. Multiplying both parts of 1 by I , we obtain:

A1 = d33V - f /k,

(2)

where V is the applied voltage, 5 = SYII i s the actuator s t i h e s s ( S is the cross section area) and f is the force applied to the actuator, f = -as. If no control voltage is applied, the actuator is equivalent to a elastic rod with stiffness k. The elongation of unloaded actuator is equal to:

A1 = d33V.

(3)

If the actuator is loaded, the elongation is always smaller than defined by (Eq. (3)). The sensitivity of the actuator to the external control voltage AllV does not depend on the actuator length and depends only on its piezo module d33. Take for example the value of d33 = 150 . for material Pz24. Maximum displacement is proportional to the actuator length:

Alma, ld33Ec. (4) For E, = lo6 V/m we obtain A1 = 1.5. 10-41. This means that to obtain a displacement of 1 pm, we need t o use actuator with a length of 6.66 mm and the control voltage will be of the order of 6666 V. High control voltage is a serious drawback of piezoelectric actuators. To reduce the control voltage, a piezoelectric stacks are used - see Fig. 1. In this case, A1 = nd33V, where n is the number of layers. This type of piezoceramic actuator can have a very high stiffness, as the layers can have large area. In case we need a sensitive actuator, transversal piezoelectric effect can be used. In this case, in place of 2 we have: =T:

A1 = Vd31llh - f / k ,

(5)

where V = Eh, h is the thickness of the element (for instance, the thickness of the tube wall in the case of tubular actuator) and 1 is the length of the actuator. Although d31 is usually only a half of d33, much larger elongations can be achieved because of large ratio l l h which can easily reach 30 ...50. Maximum displacement is given by Alma, = d311Ec.These actuators demonstrate relatively low stiffness, compared to the stacked actuators. Actuators based on the transversal effect are usually made in the form of cylinders or crosses. In the case of a cylinder, the voltage is applied between the internal and external surfaces.

85

44 Piezoelectric stack

Fig. 1. Two multi-layer piezoelectric configurations.

Even more sensitive actuators can be made using bimorph construction - see Fig. 1. The actuator consists of two stacked piezoelectric plates, connected in such a way that the sign of transversal piezoelectric elongation is opposite. The displacement of the free end of a planar bimorph actuator is given by:

Ay = 3d31V(Z/h)2, (6) while for the actuator made in the form of a bimorph disk with clamped edges, the displacement of the disk center is given by:

Ay = 0.75d31V(D/h)2. (7) In the case of a semi-passive bimorph actuator, formed by one plate of piezo-material and one plate of passive material, the displacement will be a half of given by (6) and (7). Stacking of the actuators leads to relatively high capacitance of the actuator - it can reach several pF - that can be charged and discharged with a frequency f of several kHz. The peak current I, is defined by:

I, = 27rfCV, and the power consumption is thus:

(8)

(9) Typically, an amplifier with output power of 1to 50 W is needed to drive a piezoelectric actuator with a frequency of several kHz and amplitude of several micrometers. Ppeak

= fiVmazIp+

2. Stack actuators vs transversal-effect actuators

Piezoelectric stack actuators based on direct piezoeffect, traditionally used in continuous faceplate deformable mirrors,l have high stiffness, high capacitance and relatively high price. The capacitance of several pF results

86

in a high power dissipation in the driver electronics. The high stiffness of the stack actuators increases the risk of a destruction of the mirror flexible faceplate at full actuator stroke. Authors of Ref. 2 used monolithic piezoelectric tubes based on the transversal piezoeffect, as a low-cost low-capacitance replacement for the stacked actuators. The capacitance of each tube is 15 nF and the elongation can reach 10 pm at driving voltage of 500 V at a piece price in the range of $30 to $100. N

N

3. Deformable mirrors with actuators based on the

transversal piezo effect To further reduce the actuator cost, we have developed a deformable mirror with beam actuators. The beam is made of a piezo-material poled across its thickness T , with two electrodes deposited on the beam sides. Fig. 2 shows typical geometries of tube and beam actuators. Voltage V applied to the beam results in its contaction AL = $d31V, where L is the beam length and d31 is the transversal piezoelectric coefficient of the material. To achieve a high AL, the actuator should have a high d31 and a high ratio of L / T . For instance, actuators fabricated from a soft ceramic with d ~ 1= -320 m/V, T =0.5 mm and LIT = 80, demonstrate AL of -10 pm at V=400 V. In practice, the ratio LIT is limited by the buckling stability of the actuator. We found that in most cases the condition should be satisfied: LIT < 100. It is also very important to have the correct ratio between the stiffness of the faceplate and the stiffness of the actuator. Beam actuators can be fabricated with matched stiffness, so that the faceplate is not destroyed at any combination of the actuator voltages. We tested beam actuators produced from a soft piezoelectric material with high d31, obtained from three different manufacturers from USA (Morgan), Germany (PI) and Russia. We found that the deviations of the mechanical elongation did not exceed 20%, while the hysteresis values were quite different: 9% (Germany, see Fig. 2), 9%(USA) and 16% (Russia). Deformable mirrors with column actuators utilizing the transversal piezoeffect can be fabricated for relatively low price. O K 0 piezoelectric mirrors feature free edge, 8 pm full stroke with the first resonant frequency in the kHz range. These mirrors can be coated with HR coatings for operation of up to 10kW/cm2. As of spring 2007, O K 0 fabricates piezoelectric mirrors with 19 to 109 actuators with apertures in the range from 30 to 100mm, complete with

-

87

Applied voltage, V

Fig. 2. Tube and beam piezoelectric actuators (left) and typical hysteresis curve of a transversal piezoelectric actuator (right).

Fig. 3. Interferogram of the flattened surface of the 109-ch piezoelectric deformable mirror (left); coma aberration formed by a 109-ch deformable mirror (right).

high-voltage amplifiers (0 ... 300 V, 700 Hz) driven via USB and PCI interfaces from a PC running either Windows or Linux operating systems. These mirrors can be closed-loop controlled via Front Surfer wavefront analysis and A 0 feedback system. For applications with high aspect ratio beams and for ultrafast pulse compre~sion,~ O K 0 has developed a special linear piezoelectric deformable mirror with 10x50 mm clear light aperture - see Fig. 4. The mirror is controlled by two rows of actuators, each row having 10 actuators. The mirror can be controlled either in a linear feedback loop, using Frontsurfer WF sensor, or in an optimization loop running either genetic or simplex algorithm. For instance, Fig. 4 shows the eigenmodes of an adaptive optical system operating the linear deformable mirror. At present, the main application of O K 0 piezoelectric mirrors is in high-

88

Fig. 4. Linear deformable mirror for beams with large width to height ratio and for ultrafast pulse compression (left), 20 eigenmodes of a 20-ch AOS operating with the linear deformable mirror(right).

power laser optics; other applications include medicine, astronomy, ultrafast optics and imaging.

References 1. R.H. Freeman and J.E. Pearson, ”Deformable mirrors for all seasons and

reasons” Applied Optics 21, 4, pp. 580 - 588, (1982) 2. R. Winsor, A. Sivaramakrishnan and R.B. Makidon ”Low-cost membranetype deformable mirror with high-density actuator spacing” Proc. SPIE 4007 ”Adaptive optical Systems Technology” pp 563-572, (2000) 3. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, ” Pulse compression by use of deformable mirrors,” Opt. Lett. 24, 493-495 (1999)

LOW-COST SPATIAL LIGHT MODULATORS FOR OPHTHALMIC APPLICATIONS VICENTE DURAN, VICENT CLIMENT, ENRIQUE TAJAHUERCE, JESUS LANCIS Departament de Fisica, Universitat Jaume I, I2080 CasteEl6, Spain ZBIGNIEW JAROSZEWICZ Institute of Applied Optics, Kamionkowska 18, 03-805 Warsaw, Poland and National Institute of Telecommunications, Szachowa I , 04-894 Warsaw, Poland JUST0 ARINES, JORGE ARES Area de bptica, Departamento de Fisica Aplicada, Facultad de Ciencias, Universidad de Zuragoza, Zuragoza, Spain SALVADOR BARA Departamento de Fisica Aplicada, Facultade de Fisica, Universidade de Santiago de Compostela, 15782 Compostela, Galiza, Spain We would like to point out the advantages in the field of the Adaptive Optics (AO), which offer low cost spatial light modulators (SLMs), e.g., like commercial twisted nematic liquid crystal displays (TNLCDs) commonly applied in video projection devices. Application of a proper polarimetric arrangement allows us to obtain almost phase-only modulation of SLMs, what in turn enables to implement four-level phase encoding scheme. This system is used for implementing the microlens array of a Hartmann-Shack wavefront sensor as well as for compensating of optical aberrations as those typically found in human eyes. Consequently, we are demonstrating that it is possible to use these easily available SLMs in A 0 systems, where they act as a single element to both measure and compensate optical aberrations.

1. Introduction Wavefront sensing and compensation becomes nowadays an important practical tool in biomedical optics. As a consequence there can be observed a continuous trend towards the development of reliable, low-cost and easy-to-use devices for their transfer to clinical practice. Eye aberration compensation has been successfully demonstrated using deformable mirrors”2, spatial light modulator^^-^ (SLM) and/or static phase plates’. 89

90

In the present communication we focus our attention on commonly used TNLCDs. These devices represent an attractively-pricedalternative for other A 0 devices and therefore can find an application in everyday ophtalmological practice for human eye's aberration measurement and obtaining high-resolution imaging of the eye's interior. We propose here a complete A 0 system consisting of single TNLCD, which works alternately as a Hartmann-Shack sensor unit and as a compensation unit.

2. TNLCD phase only working mode First step which needs to be executed in order to apply TNLCDs in A 0 is to achieve their phase only modulation, what will enable to implement multiplelevel phase encoding scheme. In order to perform TNLCD phase modulation response with a small residual intensity variation, we have used a polarimetric arrangement that includes retarder plates and linear polarizers, whose detailed configuration is described elsewhere"' (see figure 1). In our experiments we used a TNLCD Sony Model LCX016AL, with an effective area of 26.6 x 21 mm' and composed of 832 x 624 pixels (of effective size 26.7 x 21.3 pn' each) arranged in a square array with center-to-center spacing of 32 pm.

Y

Fig. I: Experimental setup for achieving phase-only modulation. P denotes a polarizer; QWP, a quarter-wave plate; and LCD,the sample display. In the above diagram, the x-axis coincides with the input molecular director of the liquid crystal cell. PI and P2 are, respectively, the orientation of the polarizer and the analyzer. L1 and LQ are the angles of the slow axis of the quarter-wave plates with respect to x-axis. In the optimal confignration, PI= -25", LI= -28", LQ = 17", PZ= -51".

91

3. TNLCD as a compensation unit in A 0 systems In the second step the calibrated TNLCD is applied as a phase compensating unit. The optimization procedure described above enabled us to implement fourlevel phase encoding scheme for compensating of optical aberrations as those typically found in human eyes9-'* (see figures 2, 3 and 4). Consequently, it allows for application of these easily accessible SLM's in A 0 systems, where the eyes aberrations measurement is performed by a separate unit, usually a Hartmann-Shack wavefront sensor.

Fig. 2: Aberrated PSF produced by an artificial eye including a refractive phase plate encoding a typical aberration pattern of a human eye.

Fig. 3: PSF produced by the TNLCD when encoding the four-level compensatingphase conjugate to that in Fig. 2.

Fig. 4 PSF of the aherrated artificial eye after compensationusing the TNLCD.

92

4. TNLCD as a complete A 0 system In contrast to origins of adaptive optics, i.e., when a compensation of atmospheric turbulences decreasing the seeing conditions in astronomy was sought-after, there can be found a significant class of problems, where the frequency of aberrations measurements does not need to be so high. One of possible applications of low frequency A 0 systems can be found in the area of ophthalmology. It permits the third step of our proposal: when the TNLCD is applied both as a wavefront measurement unit and phase compensating unit. First the TNLCD serves as a Hartmann-Shack wavefront sensor by displaying on it an array of diffractive microlenses (figure 5 left). Next, the obtained information is used for implementing the compensating phase distribution on the same TNLCD (figure 5 right), building in this way a single TNLCD A 0 system11,12, whose block diagram is shown in figure 6.

Fig. 5: Grayscale representation of the four-level TNLCD patterns: (left) for generating a 9 x 9 diffractive microlens array; (right) for compensating the aberration produced hy an artificial eye.

A

B

Fig. 6: Block diagram of the single TNLCD A 0 system. A: aberrated beam, B: corrected beam; 1: A 0 TNLCD block, 2: entrance pupil, 3: input relay system for projecting the aberrated wavefront with the suitable scale, 4 heamsplitter, 5: CCD sensor, 6: system control block, 7: output relay system, 8: exit pupil.

93

The following sequence of images obtained with the CCD shows the process of measurement and correction of the wave front’s aberration obtained with this single TNLCD A 0 system. Figure 7 presents an image of the microlenses array foci taken during the aberration measurement step. Figure 8 shows the compensating phase function found from measurement of microlens array foci displacements and encoded on TNLCD. Finally, figure 9 contains the PSFs of aberrated and compensated wavefronts.

Fig. 7: Focal pattern of the Hartmann-Shack sensor microlenses m a y encoded on TNLCD and illuminated with a wavefront containing a typical aberration pattern of a human eye.

Fig. 8: Fringe pattern corresponding to the phase encoded on TNLCD, which compensates the measured aberration pattern.

94

Fig. 9: PSF of a human moderately aberrated eye before and after the compensation realized by the single TNLCD A 0 system.

Acknowledgmen~ This work has been supported by the Spanish Ministerio de Educacicin y Ciencia, grants FIS2005-05020-C03-03 and FX32004-02404, by the Polish Ministerstwo Nauki i Informatyzacji under Contract Number 4 T07D 003 29 169l/TO7/2005/29 and European Regional Development Fund.

eferences 1. E. J. Femitndez, I Iglesias and P. Artal, Opt. Lett. 26,746 (2001). 2. L. Diaz-Santana, C . Torti, I. Munro, P. Gasson and C. Dainty, Opt. Express 11,2597 (2003). 3. T. Shirai,Appl. Opt. 41,4013 (2002). 4. P. M. Prieto, E. J. Femitndez, S . Manzanera and P. Artal, Opt. Express 12, 4059 (2004). 5. R. Navarro, E. Moreno-Barriuso, S. Bar6 and T. Mancebo, Opt. Lett. 25, 236 (2000). 6. V. Duritn, J. Lancis, E. Tajahuerce and Z. Jaroszewicz, J. Appl. Phys. 97, 043101 (2005). 7. V. Duran, J. Lancis, E. Tajahuerce and Z. Jaroszewicz, J. Appl. Phys. 99 113101 (2006). 8. V. Duritn, J. Lancis, E. Tajahuerce and M. Fernitndez-Alonso, Opt. Express 14,5607 (2006). 9. E. Tajahuerce, V. Climent, J. Lancis, S. Barit, J. Arines and 2. Jaroszewicz, Spanish patent application P 2006 01631 presented on 16th of June 2006. 10. V. Duritn, V. Climent, E, Tajahuerce, 2. Jaroszewicz, J. Arines and S . Bar6, J. Biomed. Opt. 12,014037 (2007). 11. V. Climent, E. Tajahuerce, V. Duritn, J. Lancis, S. Barit, J. Ares, J. Arines, and Z. Jaroszewicz, Spanish patent application P200700870 presented on 28th of March 2007. 12. J. Arines, V. Duritn, Z. Jaroszewicz, J. Ares, E. Tajahuerce, P. Prado, J. Lancis, S. Bar6 and V. Climent, Opt. Express (sent to Editor).

M. A. HELMBRECHT", N. DOBLE, C. J. KEMPF, M. HE Iris AO, Inc. 2680 Bancroft Way, Berkeley CA 94704, USA Iris A 0 currently fabricates 37-segment DMs with 5 ~ m stroke, 3.5 mm inscribed aperture, and 2.3 kHz roll off frequency. The DMs are positioned with simple piston/tip/tilt commands rather than nonlinear voltages by using a Calibrated position controller and calibrated drive electronics. Open-loop positioning errors of less than 30 nm rms have been shown over the majority of the operating space using the calibrated controller. This paper will present an update of development at Iris A 0 on segmented deformable mirrors (DM), compact drive electronics, and control techniques for the DM. It will also describe current research directions geared towards making MEMS DMs easier to use and increasing performance while reducing cost.

eformable-Mirror Background Iris A 0 has been developing compact, easy-to-use, robust microelectromechanical systems (MEMS) segmented deformable mirrors (DM) since 2002. As a spin-off company evolving from research funded by the Center for Adaptive Optics (CfAO), the DMs commercialized by Iris A 0 were originally geared towards satisfying performance requirements of both atmospheric correction and retinal imaging applications. At the outset, a DM fabrication process and design that could achieve high stroke, a fast temporal response, and could be scaled to thousands of degrees of freedom was necessary. Because MEMS fabricationprocess development is intensive and very costly, a DM architecture was conceived that would be able to satisfy atmospheric and biological aberration correction with changes in design instead changes in the fabrication process. Once the fabrication process is developed, modifying the DM to be suitable for applications with requirements outside of those targeted by the astronomy and vision-science communities is a much simpler endeavor. A segmented approach was chosen because it scales well to large numbers of actuators. Figure 1 shows a schematic drawing of one segment of the resulting DM design. Each DM segment consists of a surface-micromachined actuator * [email protected], +1-510-849-2375, www.irisao.com

95

96

platform that is elevated above the substrate because of residual stresses in three bimorph flexures. Three underlying electrodes position the DM segment in a piston fashion when energized equally or tilt the segment when energized differentially. Not shown in the schematic is a dedicated wiring layer beneath the electrodes.

Flexurn Figure I. Schematic diagram of one segment of the Iris A 0 37-segment DM.

Actuators with different gaps can be designed by simply changing the length of the top bimorph material. Making the flexures wider stiffens them, resulting in faster temporal response. Thus, within the constraints of the drive electronics and material properties, a high-stroke DM (10-20 pm) for slower applications or a faster DM (> 2 kHz) with 5 p m of stroke can be designed with the same manufact~ingprocess. The thin (2.25 pm) polycrystalline silicon (polysilicon) used for the actuator platform and flexures does not provide a high-quality optical surface because of print through effects that remain after polishing and strain gradients in the material. The moments introduced by the connection at the tips of the flexures further distort the actuator platforms. Additionally, the fill factor of the actuator platforms is too low (~95%)for A 0 applications. To overcome these hurdles, thick (currently 20 pm) single-crystal silicon mirror segments are assembled onto the actuator platforms using a thermo-compression bonding process. This results in segments that are flat over a range of 6-20 nm rms with 1 0 0 ~ 1 0 0 0 ~ Ti/Au optical coatings and an array with more than 98.5% fill factor. The DM segments also remain flat over large temperature ranges (peak-to-valley bow of 0.56 nmlOC).

97

With present designs, the bimorph flexures provide sufficient restorative spring forces such that the frequency response of the DM is slightly underdamped at 2.3 H z . Despite the mass of the thick segment, 2040% rise and fall times are only 120 and 140 ps respectively as seen in Figure 2 El]. Segmentheight variations across the array due to temperature excursions are less than 0.8 nm rmsPC. Present DMs provide 5 pm of stroke and are capable of over +4 mrad tilt on each axis. Actuator prototypes currently under development have shown up to 12 pm of stroke. These higher-stroke actuators have the same footprint as those of the DM shown here, allowing for an easy drop-in upgrade to higher stroke devices when they become available. = 36V

.,FSC37-01-05-1217, Segment 6 Step Response Plat, Vp, 20j'O

,20)6

I

I

I

II

4 Time (s)

x lo"

Figure 2. Step response of an S37-5 DM. The vertical scaling is 100's of nanometers and the horizontal scaling is milliseconds. For a 1.63 pm step (driven by 36V), the rise times are 120 and 170 ps for the 20-80% and 10-90% bounds respectively. Fall times are 140 ps and 200 p s for the 20-80% and 10-90% bounds respectively. The small signal frequency response for this DM segment is slightly under-damped (Q=-2) at a frequency of 2.3 kHz.

. ~aseofuse Iris A 0 has strived to make the DM easy to use by providing a precision openloop position controller. The controller positions the DM segments using intuitive piston/tip/tilt position commands (pm, mrad, mrad) rather than requiring the user to understand the complicated nonlinear relationship between DM position and electrode voltage. It is calibrated for each segment, and therefore accounts for all manufacturing variations across the DM array. The

98

DM controller also limits DM positioning to within the safe operating region, also referred to as the reachable space, of the DM segments. Experimental verification has shown that the controller maintains surface figure errors to better than 30 nm rms over nearly all of the operating space 121. Figure 3 shows examples of Zernike modes placed on the segmented DM.

2.5

2

15

1

Q.5

05

1

15

2

Zf

Flat

Y Tilt

Astigmatism

Focus

3

35

I!

-,

Figure 3. Pseudo fringe plots of low order Zernike profiles placed onto the S37-5 DM with the openloop controller. Each fringe corresponds to 600 nm in surface height variation. The global tilt and focus profiles show fringe patterns with discontinuities.These correspond to segments that are at the limits of the reachable space. Axis scales are in millimeters.

Any arbitrary shape can be placed onto the DM as long as the positions are within the reachable space of the segments. If the position is outside of the reachable space, the PTT DM controller sends the segment to the reachable position closest to the desired position. The ability to precisely flatten the DM to better than ?J20 (30 nm rms) without feedback from a wavefront sensor simplifies assembly and alignment of

99

A 0 systems because the A 0 control loop does not need to be closed in order to flatten the mirror for fine alignment. Precision open-loop positioning also enables the use of segmented DMs in A 0 loops sensed with Shack-Hartmann wavefront sensors. Typically, these types of wavefront sensors cannot detect the piston position of segments. Without good position control, the segments could drift because the piston position is not detected. On the contrary, DMs with good open-loop positioning capabilities will not drift as long as the A 0 controller implements the cophasing. A simple technique to ensure cophasing is to send modal shapes to the DM. Stable closedloop control of the segmented DM using a Zernike-based controller has been shown on a test bench [3] and in an AO-equipped confocal scanning laser ophthalmoscope [4] using the Iris A 0 DM. Segmentation eliminates mechanical coupling from neighboring segments, and the distance of neighboring electrodes is such that no noticeable electrical cross talk has been seen. Because there is no inter-segment coupling, the control matrix for the DM is diagonal, greatly simplifying control. Closed-loop control of the DM is further simplified because the PTT controller linearizes the position response. 3. Compact DM and electronics

Although MEMS DMs are typically small devices, the compactness is lost when connected to drive electronics. Iris A 0 is taking the next step towards miniaturization with its second-generation drive electronics and compact flexcircuit interconnect. Figure 4 shows the new electronics and flex-circuit interface lying atop the original Smart DriverTMelectronics.

Figure 4. Second generation drive electronics and flex-circuitmirror interface board atop the first generation electronics and mirror interface board.

100

The 128-channel Smart DriverTMelectronics are housed in a 19” rack-mounted box, whereas the 128-channel Smart Driver IITM electronics are housed in a compact, extruded aluminum box that measures only 5”x6.5”~2”.The secondgeneration, 14-bit electronics will provide better performance and will be easier to use than the original design. It will have multiple computer interface options, including: full-speed USB; high-speed digital I 0 from a PC host, and direct connection to a microcontroller or DSP. In addition to many different interface options, the factory-calibrated Smart Driver I1 electronics will store offset and gain calibration values internally. The flex-circuit DM interface will store DM calibration values in onboard memory. Acknowlegments

This work was supported in part by: 1) the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement AST 98-76783; the National Eye Institute, 1 R43 EY015381-01; 3) The USAF, FA8650-04-M65 18, and 4) NASA, NNG06LAllC and NNG07CA06C.

efere~ces 1. M. A. Helmbrecht, M. He, T. Juneau, M. Hart, N. P. Doble, “Segmented MEMS Deformable-Mirrorfor Wavefront Correction,” Invited Presentation, Proc. of SPIE, Vol. 6376, Boston, MA, Oct. 2006. 2. M. A. Helmbrecht, T. Juneau, “Piston-Tip-Tilt Positioning of a Segmented MEMS Deformable-Mirror,’’ Invited Presentation, Proc. of SPIE, Vol. 6467, San Jose, CA, Jan. 2007. 3. C. Kempf, N. Doble and M. A. Helmbrecht, “Control of a MEMS Based Segmented Deformable Mirror for an Vision Science Instrumentation,” Investigative Ophthalmology & Visual Science, Ft. Lauderdale, FL,,USA, May 2007. 4. N. Doble, C. Kempf, B. Xue, M. A. Helmbrecht and S. S Choi, “The Design and Construction of an Adaptive Optics Confocal Scanning Laser Ophthalmoscope for Focused Delivery of Laser Energy to the Eye,” Investigative Ophthalmology & Visual Science, Ft. Lauderdale, FL,,USA, May 2007.

~ I § ~ AOPTICS L STEFAN0 BONORA AND LUCA POLETTO C ~ R - I ~ F Laboratory M, for Ultraviolet and X-ray Optical Research Department of Information Engineering, University of Padova via Gradenigo 4/b, 35131 Padova, Italy Deformable membrane mirror technology has a lot of advantages compared to other devices for adaptive optics such as liquid crystal modulators, bimorph mirrors, thermal mirrors. Low power consumption, low cost, large dynamic behaviour, achromaticity, no hysteresis, relatively high optical load, good performance in aberrations generation, make this technology interesting and suitable for being used in a lot of optical applications. Visual optics needs of adaptive optics device with a good stroke and spatial resolution. Dalimier and Dainty showed a comparison within adaptive optics mirrors made from different technologies. The results show that membrane mirrors, despite their advantages, do not have enough optical power to completely compensate eye aberrations. We propose an improvement of this technology for: increase the maximum optical power, improve the spatial resolution and use them without biasing the membrane adding push-pull capabilities by the application of additional electrodes over the top side of the membrane.

evice In our prototype ten electrodes were added on the top side, one of these is realized with an indium-tin-oxide (ITO) coated glass to guarantee high transparency and electric conduction. The electrodes pattern of both top and bottom side is shown in Fig. 1.

BOTTOM SIDE

Fig. 1 . Geometry of the actuators: a) non-transparent electrodes placed under the bottom side of the membrane; b) transparent actuators placed over the top side of the membrane.

101

102

The device is composed by a nitrocellulose silver-coated membrane tensioned over a circular frame with a 25-mm diameter. The thickness of the membrane is 5pm and the diameter of the useful area of the mirror is 10 mm. The rms deviation is 29.8 nm (about h120 @633 nm) which is mainly caused by the surface flatness of the glass disc. The possibility of push and pull the membrane allows to use the deformable mirror without biasing the membrane and to obtain better performance in terns of spatial resolution, Zemike polynomials generation and compensation of eye aberrations.

Fig. 2. Example of single electrode deformations. From right to left: deformation due to a bottom electrode of the second ring, deformation due to a bottom electrode of the third ring, deformation due to the central top electrode, deformation due to a top electrode in the second ring.

The device was tested by interferometric measurements of its surface upon the application of determined voltage sets. Fig. 2 shows the interferometric measurements of some electrodes both on the bottom and top side. In order to full exploit the mirror capabilities, even in saturation condition, we have developed an iterative algorithm. The algorithm performs an initially pseudo inversion of the measured influence function matrix. The channels for the ones the voltage level is higher than the maximum are clipped. After that the channels are divided in two subsets, the saturated and the not saturated. Now the pseudo inversion is performed again on the subset of the non saturated channels.

103

Compute p

Some definitions

Compute p” Update p

Following iteratively this strategy we have obtained the Zernike polynomials depicted in Fig. 3.

Fig. 3. lnterferograms of the main aberrations measured with Zygo interferometer.

104

We have compared the results obtained with a deformable mirror equipped with just the actuator on the bottom side and optimized for an active area of lOmm diameter as the Push Pull one. The test has consisted in comparing the capability of both mirrors of generating some Zernike polynomials. The peak to valley results is shown in figure 4. It is evident how the push pull mirror is, in the most of the cases, able to generate a larger peak to valley amplitude with respect to the pull only mirror.

Zernike

Fig. 4.Comparison of the pull only mirror and the Push-Pull mirror in generating a larger peak to valley amplitude &mike polynomial.

2. Simulation of performance in visual optics We followed the approach suggested by Dalimier. We generated a random family of 100 aberrations following the statistics presented by CastejonMochon. The generation was carried out using the method explained in the previous section. The results were compared with the ones obtained from a membrane mirror without top side actuator and biased to exploit it at its maximum optical power. The residual of the corrected wavefronts is 0.3pm for the pull mirror and O.1pm for the push-pull one. We underline that the RMS residual for the pull mirror is in good agreement with the value obtained by Dalimier. The improvement given by the use of a push-pull mirror in the optical system is about a factor 3 as shown in figure 5.

105

Fig. 5. Residual wavefront rms error after fitting with Pull mirror and Push-Pull mirror over a l o r n pupil.

eferences 1. S.Bonora, L.Poletto, Push-pull membrane mirrors for adaptive optics, Optics Express, Vol. 14, Issue 25, pp. 11935-11944 2. S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino and P. Villoresi,

Wavefront active control by a DSP-Driven deformable membrane mirror, Review of scientijk instruments, 2006, September, 77 3. E. Dalimier and C. Dainty, Comparative analysis of deformable mirrors for ocular adaptive optics, Optics Express 13,4275-4285(2005). 4. J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, P. Artal, Ocular wavefront aberration statistics in a normal young population, Vision Res. 42, 1611-1617 (2002).

~

I

M MIRROR O ~ FOR ~ ~ E T A ~ A TLASE T

S BONORA'72,C J HOOKER', S J HAWKES', J L COLLIER', C SPINDLOE' CNR-NFM, Laboratoryfor Ultravioletand X-ray Optical Research Department of Information Engineering, Universityof Padova via Gradenigo 6/b, 35131 Padova, Italy The Central Laser Facility (CLF) at the Rutherford Appleton Laboratory has been involved with the development of adaptive mirrors for more than ten years. During this time we have developed himorph adaptive mirrors of 15Omm diameter, and a control system operating at the few-Hz time scale for the correction of static and thermally induced aberrations in high-power laser chains. Such mirrors have played an important role in optimising the focusability of the petawatt beamline of the Vulcan laser. It would be highly advantageous to apply adaptive control to the full 220mm diameter of the Vulcan petawatt beam. As part of a LaserLab-funded European programme we are developing large-aperture bimorph-type deformable mirrors, and have recently constructed a prototype mirror of 25Gmm diameter. The key feature of this mirror is that the piczoceramic plate is monolithic, rather than segmented. This prototype mirror is, to our knowledge, the largest deformable mirror so far realized with bimorph technology.

1. ~anufacturingprocess For a monolithic device, the size is determined by the maximum size of PZT disc that can be obtained, which is currently 220mm in the material we use. We have used a substrate of Pyrex of 2 5 0 m diameter and 5mm thickness. The completed mirror is able to handle laser beams of 180 mm diameter. The largeaperture mirror assemblies have been constructed, using UV-curing adhesive to attach the piezoceramic (PZT) disc to the substrate. The following stage has been to grind the PZT slab to the required thickness. To deposit the electrodes pattern on the back of the PZT slab we have used a photo resist mask. Spincoating of photoresist is a well-developed technique that is widely used, and produces very uniform and reproducible layers. The pattern is a scaled-up version of one used in previous adaptive mirrors, which has 61 actuators in total. Forty-nine of these control the shape of the mirror inside the beam footprint, and the twelve outer ones mainly contribute gradient control at the edge of the mirror, The resist also covers the outer part of the optic and the copper foil tabs that connect to the common silver electrode on the underside of the PZT. 106

107

."""

Fig. 1. Left panel: back side of the mirror showing the pads and the wiring. Right panel: front side of the mirror.

The sputtering has to be carried out in stages, as the sputtering sources generate a significant amount of heat. Once the resist had been washed away, the resistance between adjacent actuators was more than 20 MQ. The next stage of the fabrication is to complete the polishing of the front face of the optic, and then to deposit a gold coating.

irror characterization The mirror has been characterized in terms of initial flatness, stroke capability, and dynamic behavior. The initial flatness has been measured using a Zygo interferometer. The flatness of the mirror after the final polishing and coating was about 0.178rms (0.891um peak to valley). After that the mirror has been glued in four points to the holder with silicone adhesive. The adhesive points and the weight of the mirror itself have created an astigmatic deformation of about 0.55pm rms (3.35pm peak to valley) as illustrated in Fig 2. Applying the same voltages to all the actuators a parabolic deformation has been added. We have investigated the maximum optical power of the mirror by varying the voltage value from -64 Volts to +64 Volts.The maximum stroke has been estimated counting the number of fringes up to 30 Volts (last interferogram with recognizable fringes) and interpolating linearly up to 64 Volts. The peak to valley ranges from about -12pm to +12km that correspond to a radius of curvature of about 250m. In a second step we have measured the bandwidth of the mirror. The test has been carried out by applying a sinusoidal voltage to all the actuators, then gradually increasing its frequency while monitoring the amplitude of the mirror movement. The mirror movement has been monitored by illuminating the mirror close to its edge with a collimated beam of small diameter. This beam has been cut to create a sharp edge that is projected on a wide area photodiode placed at

108

Fig. 2. Flatness of the mirror before it was glued to the mount. Interferograms of the flat position, applying +30V and applying -3OV.

about 2 metres distance. So if the beam cut is placed in the middle of the active area of the detector in the flat mirror position, each movement of the mirror determines a change in the illuminated area of the photodiode and so a different voltage. Following this technique we have obtained the results illustrated in Fig.3. Since our electronic driver has an operational limit of about 60Hz we have checked as well the rise time of the mirror applying a voltage change from -5OV to +50V. The results show that the rise time is about 1.2msec that correspond to a bandwidth of about 290Hz. Furthermore it is possible to observe that there is a ringing of the mirror position that has duration of about 1Oms.

300

1

0

20

40

60

80

Frequency (Hi)

Fig. 2. Bandwidth of the mirror movements. Rise time with IOmddiv. Rise time with l d d i v .

109

ptical p e ~ o r ~ a n c e The optical performance of the mirror has been tested using an optical set-up composed of a green He:Ne laser beam with a spatial filter and expander to generate a 15cm collimated beam, the deformable mirror and for focalization a lens of 75cm focal length and l5cm aperture. The sensor we used is a Shearing Device Interferometer (SID4, Phasics). This device can measure the wavefront of laser beams up to a numerical aperture of 0.16 so it is suitable for measuring the mirror deformation in our optical set up without adding any collimation optics. We have written a Labview program which, in closed loop, is able to measure the deformation of each single electrode and to combine them in order to generate a desired mirror shape.

Fig. 3. Deformation caused by respectively, the central electrodes and an electrode of the first ring.

An example of electrode mirror deformation is illustrated in Figure 3 where the deformation caused by the central electrode and one electrode of the second ring are displayed. The peak to peak deformation imposed by the central electrode is about 0.6pm and 0.2pm for the electrode in the second ring (these measurements are relative to a circular section of the mirror of 15cm diameter). The software program automatically measures all the deformations generated by each electrode and stores them in a matrix (mirror control matrix). The voltages v, which generate the desired shape, are calculated by the pseudoinversion of the mirror control matrix and its multiplication with the vector of the final shape: v=A' M The pseudoinversion is carried out using the singular value decomposition in order to have the possibility to choose which mirror modes to use for control. The mirror is assumed to have a linear response. The hysteretic behavior of the mirror is illustrated in figure 4. The curve has been obtained applying the same voltage to all the actuators. A good rejection of the hysteresis can be obtained applying a proper relaxation procedure before each measurement.

110

f

w

c

f

20

_.

40

P n

-10

J

Voltage (Volt)

Fig. 4. Hysteresis of the mirror measured applying the same voltage to all the actuators and measuring the maximum displacement of the border from the center of the mirror.

In order to test the effectiveness of the correction the first trial has been the correction of the initial astigmatism of the mirror itself. As shown in figure 5 the initial deformation is 0.880pm pk-pk and after correction is 0.30pm with an rms value of about 1lnm.

Fig. 5. Interferograms of the initial deformation of the mirror, peak-peak 0.88pm, (the measure was taken on an area of 15cm diameter), and after its correction peak to peak 0.3pm and rms deviation from flat of about 1 lnm.

Some other trials to demonstrate the mirror ability in generating arbitrary shapes are depicted in figure 6 where an astigmatism and a coma shape have been chosen as targets.

111

Fig. 6. Astigmatism and coma deformation obtained using the mirror in a circular portion of 15cm diameter. On the left side the aberration generated is astigmatism of 3.2pm pk-pk and in the right side coma of 1.8pm pk-pk.

ysteresis Compensation for a Piezo Deformable Mirror H. Song*, R. Fraanje, G. Schitter and M. Verhaegen

Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, The Netherlands *E-mail: h.songQtudelft.nl

G. Vdovin Flexible Optical B. V. Rontgenweg 1, Delft, 2624 BD, The Netherlands The field of adaptive optics (AO) has received rapidly increasing attention in recent years, the intrinsic hysteresis of the piezo deformable mirror (DM) imposes a limit in the accuracy when the stroke of the piezo-actuator is on the order of micrometers. This contribution discusses the hysteresis compensation of a piezo DM by an inverse Preisach hysteresis model. The inverse Preisach hysteresis model is identified from the measured input-output data with a neural network and with a hinging hyperplane based approach. Experimental results demonstrate that hysteresis of the piezc-actuator can be reduced from 20% t o about 6% and 9% by the neural network and by the hinging hyperplanes, respectively.

Keywords: Hysteresis Compensation; Piezo Deformable Mirror; Feedforward Control; Inverse Hysteresis Model.

1. Introduction

Deformable mirrors (DM) with piezoelectric actuation are widely used in adaptive optics (AO) systems to reduce the wavefront aberration because of the capability of providing large stroke ( w pm) and high stiffness.lt2 However, the intrinsic hysteresis of the piezo-actuators3 impose a limit in the accuracy of the DM when the applied actuation is on the order of micrometers. The error due to hysteresis can be as much as 10%-20% when the actuator is driven at large stroke in open-loop by a voltage source. In closed-loop A 0 systems, if hysteresis is not compensated for, it may affect the convergence speed of the feedback control, which either results in larger residual error or limits the bandwidth of the ~ y s t e m . ~ There have been mainly three approaches for hysteresis compensation: 112

113

charge contr01,~feedforward and feedback 1inearization.lO Although charge control can reduce the hysteresis, the sensitivity of displacement is reduced and hardware modification is required.6 Feedback linearization provides another possibility to compensate for hysteresis;1° however, in this scheme, a dedicated sensor is required to measure the deformation of each piezo-actuator. This is infeasible in terms of cost and volume if there are hundreds of actuators in the DM. In feedforward control, the hysteresis model (or inverse hysteresis model) of the piezo-actuator is involved in the controller such that the actuator is linearized.8 Compared with other two approaches, feedforward control can compensate for the nonlinearity as well as dynamics while keeping the system simple. This paper discusses the hysteresis compensation of a piezo DM by an inverse Preisach hysteresis modeL8 Experimental setup is shown in Section 2. Identification of the inverse Preisach hysteresis model is discussed in Section 3, followed by the results in Section 4. Concluding remarks are given in Section 5 . 2. Experimental Setup

Deformation of one of the actuators in the DM prototype (OKOTech, Delft, The Netherlands) has been measured in the experimental setup shown in Fig. 1, where the movement of light spot in the position sensor is approximately proportional to the deformation of the piezo-actuator. The actuators under investigation are piezoelectric tubes (PT130.00, Physik Instrumente, Karlsruhe, Germany) with a maximum contraction of 8 p m at 500V. Fig. Piezomtualornot activated

Fig. 1. Left: experimental setup for measuring the contraction of piezo-actuator; Right: DM prototype under investigation.

2 shows the input voltage u and the measured contraction y of the piezoactuator, the hysteresis curve which shows hysteresis about 20% and the

114

inverse hysteresis curve. 35

200

..

2 3 100

€

z1

‘0

10

20

30

40

50

60

70

Time (s)

Time (s)

1

3 25 2

8c 1 5 e

1

8

05

‘0

50

100

150

200

Input voltage - u (V)

250

Fig. 2. Left: input and output of the piezo-actuator; middle: hysteresis curve; right: inverse hysteresis curve.

3. Principle

3.1. Feeflomoanl control The block diagram of the feedforward control is depicted in Fig. 3. The piezo-actuator can be considered as the cascade of rate-independent hysteresis and structure dynamics.8 Since the frequency range of the input (less than 1OHz) is much lower than the resonant frequency of the DM (about GkHz), only the inverse hysteresis model is included in the controller. Controller

Piezo-actuator

Fig. 3. Block diagram of feedforward compensation of the piezo hysteresis.

3.2. Identi~cationof inverse Preisach hysteresis model

To identify the inverse Preisach hysteresis model of the piezo-actuator, the inverse Preisach function V ( a , p )(Fig. 4) at each point ( a , @has ) to be identified from the voltage input u and the output y of the actuator, given by the position, where a and /3 correspond to the local maxima and minima of the output(positi0n). To approximate the inverse Preisach function U ( a ,p) at different points ( a ,p), two approaches have been evaluated: neural network and hinging hyperplanes approximation.

115

Fig. 4. Left: points (a, p) where the inverse Preisach function V ( a ,p) has t o be identified ; middle: inverse hysteresis curve for identifying the inverse Preisach function; right: inverse Preisach function.

Neural network Fig. 5 (left) shows the schematic representation of a two-layer neural network consisting of N tangent hyperbolic-neurons in the first layer and one neuron in the second layer," with inputs (a, P), output V ( a ,P). The output U ( Q ,0) of the neural network is determined by the following equation:

U ( Q ,p) = LWtunh (IW

[];

+ bl)

-t- b2

IW E R N x 2and LW E R l x N are vectors containing the input and output weights, respectively; bl E WNxl and b2 E W l x 1 are biases on the input and output neurons, respectively. IW, L W , bl and b2 are obtained via system identification.

Fig. 5. Schematic representation of a two-layer neural network (left) and a hinge function h(a,0) (right)

Hinging h y p e ~ ~ u nupproxi~ation e~ The inverse Preisach function U ( a , P ) can also be approximated by the superposition of hinge functions hi(a,p), where each hinge function con-

116

sists of two hinging hyperplanes (see Fig. 5 (right)).12J3 The input-output relationship is given by: M

i= 1

k(a,P) =

([I a PlPi, [1 a PI%> M E RlX1denotes the number of hinge functions in the approximation of U ( a , P ) , pi E and qi E R3x1 are vectors characterizing the hyperplanes in the hinge function hi(a,p).M , pi and qi are obtained via system identification. 4. Results

Fig. 6(a) and (b) show the identified inverse hysteresis model approximating the inverse Preisach function with a neural network and with hinging hyperplanes, respectively. The neural network is a two-layer feedforward backpropagation network with five neurons in the first layer and one neuron in the second layer, trained by means of Levenberg-Marquardt backpropagation, using the Matlab neural network toolbox. l1 8 hinging hyperplanes are used to approximate the inverse Preisach function where the hinges are estimated by Breiman’s algorithm.12 The control input (uc in Fig. 3) is generated by the inverse hysteresis model when the deformation y measured previously (shown in Fig. 2) is taken as the reference input yr. Then uc is applied to the piezo-actuator and the deformation of the actuator ya is measured. The corresponding relationship between yr and ya is plotted in Fig. 6(c) and (d), denoting that hysteresis reduces to about 6% and 9% by the neural network and by the hinging hyperplanes, respectively. This significantly improves the linearity of the piezo-actuated DM and is an important step towards better operation of these devices when used in adaptive optics systems. 5. Conclusion

Using an inverse Preisach model, hysteresis of a piezo-actuator in the DM has been reduced from 20% to about 6% and 9% by means of neural network and hinging hyperplanes, respectively. Improving the linearization of the DM system further by modifications of the measurement setup are subject of ongoing research. F’uture work will investigate the improvement in bandwidth and accuracy of the A 0 system with hysteresis compensation of all actuators in the piezo deformable mirror.

117 I

250,

250

2" 200 =

...= 150 I

E 100

0

0

1

-

2

Contraction y (

3 p m)

Reference -- y ,(p in)

0 0

1

2

3

Contraction- y ( p m)

-

Referenus y (p rn)

Fig. 6 . Inverse hysteresis model when the inverse Preisach function is approximated by a neural network (a) and by hinging hyperplanes (b); linearized system by neural network (c) and by hinging hyperplanes (d)

References 1. R. K . Tyson, Principle of Adaptive Optics, 2nd edn. (Academic Press, Boston, 1998). 2. M. Loktev, 0. Soloviev, and G. Vdovin, Adaptive Optics Product Guide, November 2006 ed ( O K 0 Technologies, 2006). 3. I. D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications (Elsevier, Amsterdam, 2003). 4. Q. Yang, C. Ftaclas, M. Chun and D. Toomey, J . Opt. SOC.Am. A 22(1), 142 (2005). 5. K. Furutani, M. Urushibata, and N. Mohri, Proc of the IEEE International Conference on Robotics and Automation 2, 1504 (1998). 6. P. Ge and M. Jouaneh, IEEE Trans. Contr. Syst. Technol. 4(3), 209 (1996). 7. A. Dubra, J. Massa and C. Paterson, Optics Express 13(22), 9062(2005) 8. D. Croft, G. Shed and S. Devasia, J. Dyn. Syst., Meas., Control 123,35 (2001). 9. K.J.G. Hinnen, R. F'raanje and M. Verhaegen, Proc. of the Institution of Mech. Eng. Part I - J. Syst. Contr. Engineering 218(16), 503 (Sep. 2004). 10. Y . Okazaki, Precision Engineering 12(3), 151 (1990). 11. H.Demuth, M. Beale and M. Hagan, Neural Network Toolbox 5 User's Guide, (The Mathworks, Inc., 2007). 12. L. Breiman, IEEE Trans. Inform. Theory 39,999 (1993). 13. P. Pucar, J. Sjoberg, IEEE Trans. Inform. Theory 44(3), 1310 (1998)

CA

A. SEAMAN", C.J. COOKSON9b, J.B. MACPHERSONa, E.F. BORRA", A.M. RITCEY",D. ASS EL IN^, H. JEROMINEK~,s. THIBAULY, M.C.W. CAMP BELL^^^ U. of Waterloo & Guelph-Waterloo Physics Institute, Waterloo, Canada'; U. of Waterloo School of Optometry, Waterloo, Canadab; U. Laval, Quebec City, Canada"; INO, Quebec City, Canadad;ImmerVision, Montreal, Canadae Ferrofluidic mirrors can be used to improve images of structures at the rear of the eye and may be an effective, low cost solution for adaptive optics, perhaps allowing it to become wavefront reconstruction widespread in clinical settings. We use a Ha-n-Shack technique to study the static and dynamic responses of a ferrofluidic mirror. The displacement heights versus the current in tbe magnetic field actuators of the mirror have been measured, as well as actuator influence functions (including non-linearites). Finally, we also characterizedthe real-time dynamics of the mirror.

1. Introduction Ferrofluid mirrors used as adaptive optics (AO) could improve ophthalmic images [I]. A 0 can correct the optics of the eye, giving better images of blood vessels, retinal cells and nerve fibres at the rear of the eye. These must be imaged through the imperfect optical elements in front of them. Imaging these structures is important to the diagnosis and treatment of eye disease. The large ferrofluid mirror stroke would be important to the correction of eyes with large amounts of optical aberrations [ 2 ] . However, ferrofluid systems respond more slowly than other, more expensive A 0 devices [3]. Here we study a ferrofluid mirror developed for ophthalmic applications. Our ferrofluid A 0 system consists of magnetic actuators, a ferrofluid, a Hartmann-Shack system [4], and a control system. A metal liquid like film (MELLF) is added to increase reflectivity. Current in the actuators creates a magnetic field which deforms the surface of the ferrofluid. One of the challenges of a ferrofluidic mirror is that it is non-linear, and static and dynamic control is challenging. It also has very broad influence functions that need to be properly characterized in order to understand how to accurately control the system. 118

119

The ferrofluidic mirror consists of 271 magnetic actuators in a hexagonal array which deform a ferrofluid (Figure 1) covered by a metal-like liquid film (~JELLF)placed in a dish over the actuators.

Figure 1 . Illustration of actuators deforming the ferrofluid that in turn shapes an incident wavefront.

2. Methods In-house software controls the deformable actuator system through its driver. The optical component of the system consists of a Hartmann-Shack (HS) arm [4] and a telescope system which is used to increase the diameter of the laser beam from the size of the laser aperture to that of the diameter of the mirror. Once the light reflects from the deformable mirror, the beam diameter is decreased; the beam reflects either from the eye to be corrected or a reference mirror and reaches the lenslet array of the wavefront sensor where it then focuses onto a CCD camera. The ferrofluid mirror, pupil of the system to be corrected and lenslet array are all conjugate to each other. In these experiments, a reference mirror was used. Images of the Hartmann-Shack patterns captured with our CCD camera were analyzed by in-house software. The software is designed to track the resulting movements of spots caused by a deformation of the mirror surface. The local slopes of the wavefront aberration are calculated from the displacement of the spots from their positions for the undistorted mirror. A least-squares method, based on a technique by Cubalchini [5] was used to calculate the

120

wavefront error. The deformation of the surface of the ferrofluidic mirror is proportional to the wavefront error calculated from the spot shifts (Figure 2).

Figure 2. A schematic of a perfect Hartmann-Shack pattern (top) and an aberrated Hartmann-Shack pattern (bottom).

Images of the spot displacement were captured by the control computer at 11 Hz. These recordings were used to view both static images and videos of wavefronts reconstructed during ferrofluid response. The deformable mirror surface was characterized after applying a current to its actuators. Still images were used to view the influence functions and the interactions of actuators and their neighbours. The surface height versus current was analyzed by measuring the maximum height of the peak of the ferrofluid against the current applied to single or multiple actuators. Further characterization of the mirror involved analysis of the mirror’s dynamic behaviour; including its susceptibility to vibration and its response speed to an applied current. Different peak heights of the ferrofluid resulted from different actuator currents and different actuator combinations. The control system recorded the resulting movement of the HS spots as a function of time in response to an initial change in current. Velocities and rise times of the peaks

121

were calculated from the reconstructed wavefronts which were found from the HS spot movements. 3. Results

We analyzed both the statics and dynamics of the ferrofluidic mirror. The static measurements characterized how the mirror responded to the current applied to an actuator, and how neighbouring actuators interacted with one another. The freshly poured ferrofluid did not respond as strongly as the fluid that sat overnight (Figure 3). The surface deflection to a single actuator is nonlinear (quadratic) with the applied current. The influence function of an actuator is the shape the surface takes on when the actuator is increased (pushed) or decreased (pulled). When activating multiple actuators, these individual influence functions combine together. A mirror is said to obey superposition if the resulting surface deformation for multiple actuators is the sum of the individual influence functions. For such mirrors, the actuator values required for a desired surface shape can be calculated very easily 161. Deflection -vs- current for different fluid ages when driving a single cenirnl 5cN~tor

1

I

..

""

I

I

fiesh fluid tiesb Huid with MELLF ovanight fluid with MELLF

actuator cuirent ( ILIA)

Figure 3. Static deflection of the ferrofluid surface versus current applied to a single actuator.

The ferro-hydrodynamic response of a ferrofluid to an applied magnetic field is known to be non-linear and not obey superposition [7]. The surface shape resulting from currents in multiple actuators can neither be calculated from the sum of individual actuator influence functions, nor vice-versa. Our static measurements confirm this. When predicting the surface height due to two

122

nearby actuators, summing the influence functions predicts a peak height 68% larger than what is actually observed. Our dynamic results agree with aspects of our static results: The fresh ferrofluid does not respond as strongly as the fluid that sat overnight (Figure 4), and it is also more susceptible to vibrations. The fluid that sat overnight had a stronger response and less vibration susceptibility. The fresh ferrofluid reaches its maximum equilibrium height faster than the fluid that sat overnight, but because the older fluid responds more strongly, it has a higher average velocity. The freshly poured ferrofluid's 90% final height is 7.5 times smaller than the day old ferrofluid. The dynamics of a ferrofluid (of a given age) during a change in height were well modeled by an over-damped harmonic oscillator. Using this, it was shown that the rise time to 90% of the final height was independent of the change in height of the ferrofluid. This observation indicates that to make the mirror respond faster, the current must be overdriven and then decreased when the mirror begins to approach its final height. Dynamic responses for fresh and aged ferrotluid peak height of B single ilctllitor

_.I.-

Figure 4. The change in maximum height versus time of the ferrofluid in response to a current applied to a single actuator for different fluid ages.

4. Conclusions By analyzing the static behaviour of the ferrofluidic mirror with our HartmannShack wavefront system in response to the applied actuator currents, we have

123

shown that the ferrofluid and actuators comprise a non-linear system which does not satisfy superposition. The dynamic analyses have shown that the vibration susceptibility, rise time, and response strength depend on the age of the ferrofluid, with a considerable change in responses observed overnight. Given that the rise-time to 90% of the peak height for a given fluid age is independent of the change in height, to decrease this rise-time, a simple proportional-derivative control system may be used to overdrive the actuators.

5. ~ c ~ n o w l e ~ g ~ e n ~ This work was funded by the National Centre of Excellence: the Canadian Institute for Photonics Innovation (CIPI) and supported by INO. The authors thank M. Kisilak for advice. They are grateful to M. Chong and R. Chong for assistance with the ferrofluid.

efer~nces

[I] J. B. Macpherson et al. “A ferrofluidic deformable mirror for ophthalmology” Proc. SPIE, 5969 (2005) [2] D. Brousseau, E. F. Borra, H. Jean-Ruel, J. Parent, and A. Ritcey, “A magnetic liquid deformable mirror for high stroke and low order axially symmetrical aberrations,” Opt. Express 14, 11486-11493 (2006) [3] Borra et al. “Nanoengineered astronomical optics” A & A 419, 777-782 (2004) [4] J. Liang, B. Grimm, S . Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wavefront sensor,” J. Opt. SUC.A. 11(7), 1949-1957 (1994). IS] R. Cubalchini. “Modal wavefront estimation from phase derivative measurements” J. Opt. SOC.Am. 69 972-977 (1979) [6] C. Boyer, V. Michau, and G. Rousset, “Adaptive Optics: interaction matrix measurement and real time control algorithms for the COME-ON project,” Pruc. SPIE. 1237,406-421 (1990) [7] R. E. Rosensweig, “Ferrohydrodynamics”, Cambridge University Press, Cambridge (1985)

aseStefan Osten, Sven W g e r , Andreas Hermerschmidt, HOLOEYE Photonics AG, Albert-Einstein-Str. 14, 12489 Berlin, Germany Abstract Here we present a new developed phase-only LCOS (Liquid Crystal on Silicon) spatial light modulator (SLM) based on an electrically controlled birefringence (ECB) liquid crystal mode for wave front control as well as for dynamic diffractive optics applications, optical tweezing, digital holography and beadpulse shaping. Three versions have been developed and investigated: One is designed for a 2n phase modulation in the visible wavelength range (420nm-800nm) the second one, with a thicker LC cell, for near IR wavelength range applications (2n phase modulation for up to 1064nm) and the third one provides a phase shift of 2n up to 1550nm. eywords: Spatial light modulator, phase-only modulation, HDTV, liquid crystal devices, wave from control

1. Introduction Liquid-crystal (LC) based micro-displays can be used to modulate incoming light waves with respect to amplitude, phase and polarization. Twisted-nematic LC displays produces a combined phase-polarization modulation so that it is difficult to achieve pure phase modulation without amplitude modulation. Here we present a new developed phase-only LCoS (spatial light modulator (SLM) based on an electrically controlled birefringence @CB) liquid crystal mode. This device is the first phase-only SLM showing HD (1920x1080) resolution and a small pixel pitch of only 8pm (87% fill factor) on a digital silicon back plane. Here the LC molecules are aligned parallel to the electrodes and an applied electric field forces them to tilt in the direction of this field. In this way, the refractive index, seen by the light, is changed for one polarization direction. This leads to a pure phase modulation without any polarization change ( 4 % ) if the incident light is polarized linearly parallel to the director axis of the LC molecules. 124

125

na~on of Phase ~odulationDepth The phase modulation depth of the presented phase only SLM has been measured by different techniques. A common way to measure the phase modulation is the usage of interferometric methods. We shortly present a simple two beam interferometer but further investigations have shown that such measurements doesn’t describe the exact behaviour of an SLM for all applications. Therefore we introduce another very simple technique which is based on diffraction.

renee ~ e a s u r e m e n ~ Here a two beam interference setup and the software “Phasecam” [5]have been used. Figure 1 shows the optical set-up and on the left hand side a measurement result that will be explained in the text.

FIG.1: Two beam interference set up and a PhaseCam result (explanation in text) An expanded and collimated laser beam is guided through a double hole mask. Each of the two created coherent beams is incident to a dedicated area of the micro-display under a small angle. A zero angle of incidence would be optimal but that would require a beam splitter element that might affect the measurement. One half-screen of the display will be addressed with a constant gray level, whereas the other half-screen will be addressed with a gray level varying from 0 to 255. The reflected and modulated beams will interfere in the focal plane of the second lens. This interference pattern will be enlarged and imaged onto a CCD camera. The software “Phasecam” will detect one line of the interference pattern for each addressed gray level. The shift of the interference pattern is directly proportional to the phase shift. The image on the right hand side of figure 1 shows a result of such a measurement at 633nm. It consists of 256 rows showing the 1D intensity profile of the interference pattern for one addressed gray level. If the gray level changes from 0 to 255 (y-axis) the interference pattern has moved depending on the phase shift between the two beams. The shift of the position of a chosen intensity minimum in the interference pattern represents the phase shift. The total phase in the image is approximately 3 n.

126

iffraction ~ e a § u r e ~ e n t § An interference technique as shown in section 2.1 can not cover the influences of crosstalk effects between neighbouring pixels on the phase modulation what is of importance for applications with high spatial frequencies. That's why measurements of the diffraction efficiency for a changeable binary grating have been done where the influences of changing spatial frequencies can be observed easily. From the scalar diffraction theory of an ideal rectangular phase grating with equal ridge and groove widths it is straightforward to derive that there should be no power transfer to any diffracted orders for phase modulations of 2n a with n = (0,1,2,. ..), and there should be maximum power transfer to the diffracted orders with no power left in the 0-th order for phase delays of (2n+l) a with n = (0,1,2. * .). The experimental setup is shown in figure 2. The LCoS display is illuminated with a collimated laser light and addressed successively with gratings where the groove phase level is changed from 0 t 0255. The intensity of the diffraction orders are measured with a photodiode.

(rectangular)

(honzontal)

photo diode

FIG.2: Optical setup for diffraction measurements Figure 3 shows, as a result of a diffraction measurement, the intensity distribution of the undiffracted light and the plus first diffraction order as a function of the groove gray level while the ridge gray level was kept constant. The extrema show phase differences between ridge and groove of n a. With Jones matrix analysis it is even possible to determine the slope of the phase modulation. But this is out of consideration for this presentation and is presented in reference 141.

127

543nm(horizontal) 45 40 35

I I

I

\I

30

I

I

I

---an

-1st 1-1

1-1

15

10 5 0

f

51

0

R

2R

3n

Phase modulation

FIG.3: Intensity distribution of the O"hand 1'' diffraction order as a function of the groove phase level at 532nm for an horizontally binary diffraction grating

The influences of the spatial frequency on the phase modulation or in other word optical performance could be determined by doing the same measurements with varying lattice parameter. Figure 4 shows that the phase shift for very high spatial frequencies is lower compared to coarse addressed structures. This is not a problem if this is taken into considerations for the calibration of such SLM because the dynamic range or the voltage to gray level look up table can be modified in order to adapt the optical response to a certain application. This will shortly be explained in chapter 4. Groove gray level that give a phase difference of n and 2% 175

1

150

125

5 100 0

75

50

0

5

10

15 20 Lattlce Parameter

25

30

FIG.4: Phase shift as a function of the lattice parameter

ave Front Generation Micro displays do not have a physically flat surface. This is an inherent property of such displays caused by the manufacturing process and has to be evaluated especially for wave front control. We have done measurements on the panel surface deformation using a TwymanGreen interferometer (p-shape from "FISBA optic") with integrated phase

128

shifter and CCD camera. This gave very good information about the exact deformation in terms of direction, peak-to-valley value and expression of the wave front in Zernike polynomials. With this information one is able to calculate a function containing modulo 2n phase map that compensates the distortion of reflected wave front caused by the display deformation.

On the image in figure 5 one can see the reflected wave fronts for an unaddressed LCoS display (a) and for the same display with addressed compensation function (b). It has been shown here that the inherent slightly spherical surface deformation can be compensated down to hf4 by addressing a compensation wave front. W RMS 3008

m

a

b

FIG.5: Reflected wave fronts for a non compensated (a) and a compensated (b) surface deformation

To evaluate the quality of the compensated display deformation, a superposition of the compensation function and several test optical functions have been addressed and investigated. Figure 6 illustrates two examples of such a superposition. The right one shows a created lens array that can be used for a dynamic wave front sensor and the image on the left hand side shows a prism function applicable for e.g. phase shifting and beam deflection.

FIG. 6: Reflected wave fronts for a non compensated (a) and a compensated (b) surface deformation

129

These 2 images show that the inherent display deformation can be compensated and that artificial wave fronts can be generated using this phase modulator by addressing mod 2n phase functions.

lieation§ Because of its high resolution the € E O 1080P is especially suitable for adaptive optis applications in microscopy, interferometry, optical data storage and beadpulse shaping. In microscopy we have implementations as holographicoptical tweezer and beam shaping for high-resolution microscopy. The adaptive wave front control is used in e.g. dynamic interferometry systems and ophthalmological systems. Furthermore, the device is used for pulse shaping in fs-laser applications, holographic mastering and lithography. In very general terms it has been implemented in many photonics applications, where a high-resolution addressable optical component is desired.

.~onclusion§ A new phase only SLM with HD resolution a small pixel pitch a special LC mode and has been presented. We have shown some methods for the determination of the optical phase response that give the possibility for the adoption of the device calibration for certain applications and wave lengths. It was also shown that with this kind of SLM a creation of almost any kind of artificial wave fronts in mod 2n is possible. The surface deformation caused by the manufacturing process of the micro display can also be compensated by addressing an optical function that can be determined by the use of common interferometer technologies.

References [ l ] C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography”, Appl. Opt. 45 ( 5 ) , pp. 960-967 (2006) [2] S. Wu, D. Yang, “Reflective Liquid Crystal Displays, Wiley SID (2001) [3] R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint Holographic Optical Velocimetry in Microfluidic Systems”, Phys. Rev. Lett. 96, 134502 (2006) [4] A. Hermerschmidt, S. Quiram, F. Kallmeyer and H.J. Eichler, “Determination of the Jones matrix of an LC cell and derivation of the physical parameter of the LC molecules”, EEC-SPIE-6587-46 (2007) [5] www.holoeve.co~downloaddatenPhaseCam ManuaLpdf

MONOMO~H LARGE A P E R T ~ ~ DEFORMABLE MIRROR§ FOR LASER APPLICATIO~§ J.-C. SINQUIN, J.-M. LURGON, C. GUILLEMARD CILAS, 8 Avenue Buffon - Z.I. La Source, 45100 Orlkans - France

We present a novel architecture of deformable mirror dedicated to lasers. The new monomorph mirror presents the advantage of avoiding high spatial frequency on the residual wavefront enabling propagation of the laser beam without any energy modulation. The obtained residual wavefront is lower than 4 nm rms wavefront.

1. In~roduction High intensity laser systems rely on the use of many optical elements so it is very difficult to obtain an aberration free laser beam. The solution that is used to correct the distortions in such laser system is to position a Deformable Mirror (DM) in the path of the beam. After the correction the distortions are reduced and the Strehl ratio can be higher than 90% [ 11. The Strehl ratio is the ratio between the experimental peak intensity and the calculated peak intensity of the experimental distribution associated to a flat wavefront. From this result one can conclude that the correction is very efficient in the far field. Nevertheless some drawbacks of that technique appear in the mid-field. The remaining phase distortions exhibit the frame of the actuators of the mirror even if the mirror is not segmented. These very low distortions have a relatively high spatial frequency that leads to a deterioration of the energy distribution during the beam propagation. Modulations appear in the beam profile, which is a very negative effect for all the components that are in laser chain after the deformable mirror and it can lead to damning optical damage. The solution we propose to overcome this propagation effect is to change the technology of the deformable mirror. The new design is based on a simple monomorph structure that is made of a PZT plate and a glass plate assembled together. 130

131

2.

o~o~orp approac~ h

2. I . Bimorph and monomorph deformable mirrors The well-known bimorph architecture is given figure 1. Optical surfnce

Ground

Electrode (+I-)

Contactingpin

Figure 1. Cross section of a bimorph deformable mirror

Thanks to its symmetrical structure this family of deformable mirrors shows very small temperature dependence. Besides, the use of two PZT plates allows obtaining a relatively large sensitivity. This means that such DMs are well suited to applications in astronomy for medium and large size telescopes where thermal stability and large strokes are decisive. Nevertheless, for most of laser applications these advantages are less important: the temperature of the environment is often stable and the required strokes are smaller than for atmospheric correction required in astronomy. One of the key issues for laser applications becomes the residual wavefront quality. A drawback of bimorph architecture is that the electrodes are in the centre of the DM: this means that the thickness between material discontinuities and the optical plate is relatively small. A consequence is that some “print through” effects may appear on the optical plate surface. Then a simple monomorph architecture appears very interesting to study: since the electrodes are on the backside of the DM, as shown on figure 2, any “print through” effect should be very weak. Optical surface

Ground

Electrode (+I-)

Contacting pin

Figure 2. Cross section of a monomorph deformable mirror

Of course, since there is only one active FZT plate, the obtained stroke is relatively lower than for bimorph. Furthermore, since the structure is not

132

symmetric, the thermal behaviour of the monomorph is not stable. These issues can easily be taken into account in the design of a DM for laser applications: the stroke is sufficient to comply with correction needs and to compensate for thermal curvature.

2.2. Technological aspect Since the monomorph structure is quite simple, the associated technology is also simple. The use of a micro-lithography technique allows to obtain easily any shape and arrangement of electrodes (see figure 3) with a very small spacing between these ones (< 0.5 mm).

Figure 3. Possible shapes and arrangements of electrodes From left to right: former 36 electrode DM, Voronoi shaped 61 and 84 electrode DMs

This technology allows to manufacture large aperture DMs (up to more than 100 mm diameter) with number of electrodes well within laser applications needs.

2.3. Analytical approach of a monomorph behaviour 2.3.1. Stroke Following formulas give an estimation of the global curvature radius that can be achieved by a monomorph mirror under a given voltage. These equations are obtained from theoretical result [2] and adapted from our experience concerning this type of mirror.

133

where:

RO=- h2 is the overall scaling factor, Vd31 -1 w=is a function of the Poisson’s ratio of each material (vc for glass and v-1 v for PZT), VG

k = -EG

is the ratio of Young’s moduli (EGfor glass and Ell for PZT),

El 1

r = -hG h

is the ratio of thicknesses of each plate ( h for ~ glass and h for PZT),

C is a correction factor, V is the applied voltage (V), dj, is the transverse PZT coefficient (m/V).

2.3.2. Needed voltage for thermal compensation The temperature curvature of a monomorph mirror can be derived using the following thermal analogue equation [2]:

Vd,, = (a, - a)hAT

(2)

where: arc; and a a r e the thermal expansion coefficients, AT is the temperature difference. Using this equation, we can easily infer the percentage of the stroke needed for thermal compensation.

3. ~btainedresults 3.I . “Print through effect ”

In order to compare a former 36 electrode bimorph DM with a new 36 electrode rnonomorph prototype we made some interferometric measurements of the optical surface. By filtering out spatial defects that can be corrected by the DM (spatial frequencies lower than 20 mm-’) we obtained the results given figure 4.

134

Figure 4. Filtered shape at rest Left: former 36 electrode DM (see figure 3 left) Right: new 36 electrode monomorph prototype

Due to an electrode location relatively close to the optical surface and also to a relatively large spacing between electrodes (= 1 mm), the “print through” effect is visible for a bimorph DM - the residual defect is 7 nm rms wavefront. Thanks to the monomorph architecture, the “print through” effect is weak for the prototype - the residual defect is 3.4 nm rms wavefront. Note that the visible dots correspond to contacting locations, this effect will be reduced for next DMs.

3.2. Stroke We measured the stroke of the monomorph prototype, the result is given figure 5.

Figure 5. Obtained shape for 200 V on all the pupil electrodes of the monomorph prototype

The measured curvature radius is 50 m for 400 V.

135

This value has to be compared with the one given by equation (1) using the following parameters: VG = 0.206, v = 0.290, EG = 8.10 E l 0 Nlm2, E I I = 8.20 E l 0 N/m2, hG = 2 mm, h = 1 mm, C = 1.2, V = 400 V and dJ1=1.30 E-10 m N , which is also 50 m.

3.3. Needed voltage for thermal compensation From equation (2) and using the following parameters: = 7.1 E-6 K-’ a=5.8 E-6 K” we can calculate that 6 % of the stroke is needed to compensate for 5°C of temperature variation.

4. Conclusion The use of adaptive optics improves largely the focusing quality yielding to an increase of the intensity but also generates energy distribution modulation in the mid-field. To reduce this effect we have manufactured a new type of deformable mirror, which is based on a monomorph structure instead of the classic bimorph one. The obtained results show the “pertinence” of this new type of DM for its use in intense lasers where the mid-field energy distribution is of great importance. Indeed the amplitude of the residual wavefront is not only lower but also does not present periodic high spatial frequency structures. This will avoid energy distribution modulations as the beam is propagating.

References 1. Planchon T. A., Rousseau J. P., Burgy F., Chbriaux G. and Chambaret J. P. in Optics Communications, Volume 252, Issues 4-6, (2005), 222-228. 2. Ellis E. M., in “Low-cost Bimorph Mirrors in Adaptive Optics”, (Imperial College of Science, Technology and Medicine, University of London, 1999).

acknowledge men^

A part of this development has been supported by the Laboratoire d’Optique Appliqube (LOA), we thank them here.

IGH SPEED CONTROL FOR A ~ A ~ ~ ~ V E CHRISTOPHER D. SAUNTER & GORDON D. LOVE Department of Physics, Durham University, South Road Durham, DHI 3LE, UK The outcomes of research at the Durham University Centre for Advanced Instrumentation into the use of low cost devices such as field programmable gate arrays in the construction and operation of adaptive optics systems is presented. An embedded low cost sensing and control system for high speed A 0 is presented where the 0 we demonstrate the components for sensing and control cost under ~ ~ $ 4 0and possibitity to build and operate an A 0 system where the sensor and controller have a 0 .closed loop A 0 system using these low cost devices combined cost of under ~ ~ $ 2 0 A is presented.

1. IntrQductiQn Most recent work to date on implementing low cost control for adaptive optics has focused primarily on using a commodity PC, either augmented by signals processing hardware (11 or directly [2,3]. In either case the total cost will include that of the PC and a framegrabber for interfacing to the WFS camera and the use of a PC prevents the control system form being either physically compact or low power. Our work at the Durham University Centre for Advanced Instrumentation has concentrated on investigating the use of Field programmable gate array (FPGA) devices and CMOS imagers as technologies to significantly lower the cost of high speed A 0 sensing and control. The design and operation of a low-cost A 0 sensing and control system is presented. FPGA devices are under examination for constructing A 0 control systems for future astronomical systems due to their ability to deliver very high performance, for example see the high end ESO SPARTA system [4] and lower order work by the IAC [5]. The highly parallel nature of FPGAs and the scaling of their technology from small, low cost devices through to high end devices all with the same architecture makes them suitable for low cost developments as well as complex high order astronomical systems. 136

137

ur~am’sF ~ G ~ A framework O Below we present the design of a laboratory FPGAIAO demonstrator consisting of an A 0 Pipeline - FPGA code that performs all closed loop A 0 calculation, a supporting System-on-a-chip fhmework that controls the A 0 pipeline and an associated laboratory demonstration A 0 system. An enhanced prototype is then presented based on experience gained with the system.

2.1. A 0 P ~ e ~ i n e A control pipeline for A 0 was constructed by writing a series of FPGA based logic cores in the VHDL design language. These modules include a ShackHartmann wavefront sensing core and two figure reconstructors optimised for different memory architectures - effectively domain-specific matrix vector multiplication units. The cores were specifically optimised for modern FPGA devices from Xilinx. The WFS module processes images of up to 64k pixels of 8-16bits resolution, with a run-time configurable SH geometry of up to 16x16 spots in a hexagonal or square pattern. When targeting a Spartan-3 device the maximum pixel rate is 8OMHz and significantly faster for a Virtex-4 or -5. At the 80MHz speed this would, for example, support a 16x16 SH array on a 160’ pixel detector with 10 pixel spot spacing at a 3.125KHz framing rate. Two reconstructors were created, the first one being parameterised to use any number of available on-chip memories internal to the FPGA for matrix storage. This is the reconstructor used in the experimental work. For the work presented a 6144 element matrix was used, requiring six internal memory units. When operating in a Spartan 3 at its maximum clock of -100MHz this enables 6e8 reconstructor elements/second to be processed. This equates to a maximum frame rate for reconstruction of loOKHz - whilst significantly faster than required this is accompanied by a low reconstruction latency of less than 1 p . The second reconstructor created uses memory (SRAM type) external to the FPGA. This is slower than accessing the parallel memories within the FPGA but is necessary to support larger matrix sizes.

2.2. System-on-a-ch~architecture This A 0 pipeline alone is not sufficient for a full system, for example in the ESO SPARTA system the A 0 pipeline is connected to a host Power PC CPU that configures and monitors the pipeline, interfacing it to the outside world and such.

138

For our compact system this functionality was placed inside the FPGA in the form of a custom System-on-a-chip architecture (SOC), essentially an entire computer system existing within the FPGA of which the A 0 pipeline is a peripheral. This custom SOC combined with a USB2.0 interface allows laptops and computers to access arbitrary data from any point in the pipeline for display and logging, and to configure the pipeline. Off the shelf SOC components are available such as the Xilinx EDK but are typically not suited to the smallest devices targeted by this work, and are not optimised for high framerate streaming data. All of the SOC and A 0 components operate using only memory internal to the FPGA. Ultimately more effort was consumed in the design of the SOC than the A 0 components. The SOC communicates with PC host software written in the Python language, allowing the A 0 pipeline to be manipulated directly from the scripts or from a GUI shown in figure 2.

Figure 1 - Simplified architecture of the FPGNAO system. A CMOS imager passes wavefront sensor (WFS) frames to an A 0 pipeline within the FPGA where all the A 0 calculations are performed leading to DM command data being output to the drive electronics. All this occurs in the ‘hard real time’ area above by the dashed line where latency and bandwidth are guaranteed by the use of dedicated FPGA components. Below this line is a custom SOC which uses a more flexible CPU to interface to the pipeline to a host PC over USB2.

139

Figure 2 - GUI created for control and visualization of the FPGAfAO system and A 0 pipeline. Live WFS images and centroids are retrieved from the FPGAfAO pipeline and displayed along with derived data such as a phase plot, and options are present for configuring the system.

2.3. ~ b o r ad te m ~ o~n s ~ ~ t o r To test these components a complete laboratory A 0 system was built including a controllable dynamic turbulence source. The A 0 pipeline and SOC were implemented within a Xilinx Spartan-3 200 FPGA, connected to a 128x100 pixel 580fps CMOS imager viewing a 9x9 Shack-Hartman array, and to the drive electronics for the DM - a 37 channel O K 0 MMDM. The initial implementation used a Digilent ‘Spartan 3 starter board’ (US$99), a Digilent ‘USB2 module’ (US$47.95) and an evaluation board for the CMOS imager (cost c US$200) and two custom PCBs for the DAC drive electronics. Excluding the drive electronics the sensing and control system was constructed for a cost of under US$400. The various circuit boards used for this are sown in figure 3.

140

To High Voltage A ~ ~ ~ i f i e r s

Figure 3 - Circuit boards used to host the FPGNAO system in the laboratory demonstrator. Clockwise from top right. LM9630 heaboard (US$200) - this board hosts the CMOS imager used. Digilent Spartan-3 board (US$99) -FPGA board that performs all A 0 computation, communicating with a host PC via the Digilent USB2 module (US$50) and emitting DM drive commands over a 2wire high-speed serial link to two more boards that form our DM drive electronics. (The Digilent Spartan-2 generates 40 digital pulse trains that are filtered into analogue signals by the low pass filter board.)

Long exposure point spread functions (PSFs) for dynamic turbulence propagated through the system with the A 0 running (closed loop) and disabled with a flat DM (open loop) are shown in figure 4,demonstrating A 0 correction. The degree of correction seen was poor due to strong static aberrations on the O K 0 MMDM using much of the devices dynamic range.

141

Figure 4 - Time averaged PSFs showing closed loop correction of dynamic turbulence vs uncorrected (open loop) achieved with the FPGNAO framework and lab demonstrator. Different turbulence strengths are shown.

2.4. ~ ~ ~ u nprototype ced To overcome sever bandwidth limitations arising from a design issues with the Digilent USB2 module and supply issues with the imager board custom PCBs were produced, one combining the WGA and USB functions and the second housing the imager. The total component cost for these boards was under US$200, and based on experience from producing these it is estimated that all the components required for the imager and the control system, excluding DM drive electronics, could be integrated on one PCB of perhaps 4 0 m x 25mm, with a component cost of under US$l50 - various devices included in the enhanced prototype were not required making it significantly larger than necessary. The two boards are shown mounted in a camera enclosure in figure 5. A variant of the system was tested for tiphilt control only intended for use in a free space optics communications system, with this control system fitting within a Spartan-3 50 FPGA - the smallest in the range.

3. Future d~rections A new system is being constructed with an improved CMOS imaging chip that will offer significantly higher framerates combined with higher resolution. Further work is underway examining novel uses of the FPGNAO system as an open loop ‘smart camera’.

142

Figure 5 - PCBs mounted to form a camera. The optical rail at the front can include a c-mount plate and/or a microlens holder.

eferences 1. C. Paterson, I. Munro, and J. C. Dainty. A low cost adaptive optics system using a membrane mirror. Optics Express volume 6, Issue 9, Page 175,, April 2000. 2. C. U. Keller, C. Plymate, and S. M. Ammons. Low-cost solar adaptive optics in the infrared. Innovative Telescopes and Instrumentation for Solar Astrophysics. Proc. SPIE, Volume 4853, pp. 351-359 (2003)., pages 351359, February2003. 3. A. Ghedina, W. Gaessler, M. Cecconi, R. Ragazzoni, A. T. Puglisi, and F. De Bonis. Latest developments on the loop control system of AdOpt@TNG. Proc. SPIE, Volume 5490, pp. 1347-1355 (2004)., pages 1347-1355, October 2004. 4. S. J. Goodsell, E. Fedrigo, N. A. Dipper, R. Donaldson, D. Geng, R. M. Myers, C. D. Saunter, and C. Soenke. FPGA developments for the SPARTA project. In Proc. SPIE, Volume 5903, pp. 148-159 (2005)., pages 148-159, August 2005. 5. L. F. Rodriguez-Ramos, T. Viera, J. V. Gigante, F. Gago, G. Herrera, A. Alonso, and N. Descharmes. FPGA adaptive optics system test bench. Proc. SPIE, Volume 5903, pp. 120-128 (2005)., pages 120-128, August

P WQQ~ER-TWEETERCONTROL ON - ~ O N J ~ ~ AADAPTIVE TE OPTICS TES EDWARD LAAG Department of Earth Sciences, UC Riverside, 900 University Ave Riverside, CA 92521, USA DONALD GAVEL Laboratory for Adaptive Optics, 1156 High St. Santa Cruz, CA 95060, USA MARK AMMONS Laboratory for Adaptive Optics, I156 High St. Santa Cruz, CA 95060, USA

Advances in micro deformable mirror (DM) technologies such as MEMs have stimulated interest in the characteristics of systems that include a high stroke mirror in series with a high actuator count mirror. This arrangement is referred to as a woofer-tweeter system. In certain situations it may be desirable or necessary to operate the woofer DM in open loop. We present a simple method for controlling a woofer DM in open loop provided the device behaves in an approximately linear fashion. We have tested a mirror that we believe meets our criterion, the ALPAO DM52 mirror. Using our open loop method we fit several test Kolmogorov wavefronts with the mirror and have achieved an accuracy of approximately 25 nm rms surface deviation over the whole clear aperture, and 20 nm rms over 90% of the aperture. We have also flattened the mirror in open loop to approximately 11 nm rms residual.

1. ~otivation 1.1. The ~ C A Testbed O The Lab for Adaptive Optics (LAO) currently has a testbed dedicated to the development of two key A 0 technologies for large telescopes (called multi-

'

The LAO is funded by a grant from the Gordon and Betty Moore Foundation. This work was supported in part by the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement AST 98-76783.

143

144

conjugate A 0 (MCAO)[l] and multi-object A 0 (MOAO)). Both of these technologies take advantage of tomographic reconstructions using multiple guidestars (a.k.a. reference sources) [2]. In particular, MCAO attempts to achieve a high strehl over a large field of view (FOV) by accounting for anisoplanatism, using multiple deformable mirrors at optical conjugates. MOAO attempts to achieve very high strehls over small FOVs embedded in larger uncorrected fields. First results from the testbed were shown in h o n s 2OO6[3]. Recent results have demonstrated the effectiveness of tomography at finding the layers of turbulence, and high strehls have been achieved with both MCAO and MOAO. The testbed uses three optically addressed spatial light modulators (SLMs) from Hamamatsu Photonics. The SLMs allow us to have nearly 600,000 control elements, far more than any current W M s . SLMs have been used with some success in the biological sciences (for example, a demonstration is described in Awwal 2003)[4]. Because their stroke is limited to approximately 1 wavelength deviation (about 650 nm on the testbed) and we would like to avoid phasewrapping, we are incorporating a high stroke mirror into the testbed both to eliminate the need for the SLMs to phase wrap, and to test possible A 0 configurations for future systems called “woofer-tweeter” setups. Phase Slice Plot

Figure 1 A slice through the ground layer wavefront (shown as a solid line), with the woofer wavefrout (dotted line) and the tweeter wavefront (dashed line) overlaid.

145

Taking an analogy from audio technology, the woofer-tweeter configuration in A 0 refers to the pairing of a higher resolution DM that has small stroke together with a high stroke (and consequently low resolution) DM called a woofer. Though our testbed uses SLMs, woofer-tweeter combinations will also be useful for ~ M DMs. s In addition to our lab, similar architectures are being studied at U. Victoria 151 and at NU1 Galway.

ign Cons~erations We created a model of the ideal woofer DM by considering the influence functions to be an array of Gaussians that add linearly. The ideal DM was configured with as few as 5 actuators across and as many as 9 across. Using wavefronts measured on the testbed, we then tried to fit these shapes with our simulated DMs in software. It was determined that a mirror of at least 6-7 actuators across was necessary to avoid phase wrapping which occurs any time peak to valley (P-V) aberrations exceed 650 nm on our testbed. Figure 1 shows an example of one of the simulations. We looked into several mirror options on the market, starting with a small electrostatic device. Due in part to the complex nature of the aberrations we are trying to correct, and the high predictability we need for open loop performance, we eventually settled on an ALPAO DM52 mirror. The importance of this high predictability (linearity) will be discussed below.

o o f e ~ Linear ~ t ~ ~Super-Position~ e t h o d We have put together some simple software for controlling a woofer-tweeter system in open loop (schematic shown in Figure 2). We call the routine that produces the open loop command signals for the mirror “Wooferfit”. Wooferfit runs after the tomography reconstructor has determined the turbulent layers in the volume. We put the low order components of the ground layer wavefront on the woofer. Wooferfit uses a simple linear super-position method to determine the commands which we will detail below. This method makes the important assumption that the DM is approximately linear with input voltage commands and that the response functions superimpose linearly. Obviously, due to hysteresis effects and force cross-coupling through the mirror face sheet, most DMs will not meet this requirement. The ALPAO DM52 was designed with reduction of these effects in mind.

146

.-----+

Ui

-.-----

woofer

* controller

I

]

@&)

tweeter Figure 2 Schcmatic diagram showing data flow for woofer-tweeter control. The measured wavefront comes in at left.

The first step in our open loop control process is to obtain good representations of the actuator influence functions using an interferometer. Then, given a mirror with number of actuators n, the cross-talk matrix I?,, is an n x n sized array generated from:

where ri(x) are the influence functions over the mirror surface x, previously measured when a unit of voltage is applied to actuator i. The voltage commands aito the DM controller device are simply:

and the wavefront will be given by:

3. Results The particular AL,PAO DM52 mirror we have in the lab has about a 133 nm m s focus shape when initially powered on but with no commands sent. In order to generate a flat shape we measured and inverted this wavefront and ran it through Wooferfit to generate flattening commands. Our first attempt at flattening the DM.52 in open loop resulted in a residual of approximately 11 nm rms of surface flatness deviation over the full clear aperture of the mirror.

147

0

50

Pixels

100

150

Figure 3 A lineout of a random row from the comparison of the predicted wooferfit WF (dashed line) and the measured Zygo wavefront (dotted line).

We then tried to fit a typical Kolmogorov wavefront. The testbed uses etched glass Kolmogorov phase plates as turbulence generators. The phase plates are meant to simulate a normal atmosphere's worth of wavefront aberration. We measured the wavefront using a set of Shack-Hartmann wavefront sensors. After doing a tomographic reconstruction of the estimated volume, there is a residual on the ground layer with approximately 250 nm rms tipkilt removed wavefront error. We then fit this Kolmogorov wavefront with the ALPAO DM52 using Wooferfit. We compared the surface of the mirror as measured by a Zygo interferometer to the wavefront generated by the tomography software. Our comparison shows a 25 nm rms disagreement between the ALPAO DM52 and the Wooferfit predicted shape over the clear aperture (see figure 3 above). The fit was noticeably better within the central portion of the mirror and when apertured down to 90% of the clear aperture the agreement was roughly 20 nm rms.

148

It is important to note that these results are significant because they represent open loop “go-to’’ control of the surface without the benefit of feedback from residual wavefront measurements. Hence these results are applicable to systems which need to run open loop like MOAO configurations mentioned earlier.

~oncl~ion We have tested the suitability of the ALPAO DM52 as a woofer DM and have shown it has promising open-loop characteristics. Initial results look good for woofer-tweeter implementation in our MCAO testbed.

Ac~owledgmen~ Special thanks to David Anderson from the Herzberg Institute of Astrophysics who graciously supplied me with influence functions for the ALPAO mirror.

References 1. J. M. Beckers, ESO Conference on Very Large Telescopes and Their Instrumentation. 693 (1988). 2. M. Tallon and R. Foy, A&A. 235,549 (1990). 3. S. M. Ammons, Proc. SPZE.. 6272, (2006). 4. A. A. S. Awwal, B. J. Bauman and D. T. Gavel et al, Proc. SPZE. 5169, 104 (2003). 5. 0. Keskin, P. Hampton, R. Conan, C. Bradley, C. Hilton, and C. Blain, Proc. Of the First NASNESA Conference on Adaptive Hardware and Systems. (2006)

This page intentionally left blank

WAVE FRONT SENSOR-LESS ADAPTIVE OPTICS FOR IMAGING AND MICROSCOPY M. J. BOOTH*, D. DEBARRE and T. WILSON Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, United Kingdom *E-mail: martin. boothQeng.ox,ac.uk acara. eng. ox.ac.uk/som/ We present an overview of a wave front sensor-less adaptive optics scheme based upon the optimisation of the low spatial frequency content of images. Aberrations are expanded as a series of Lukosz functions as this permits the independent optimisation of each aberration mode. The scheme is demonstrated in an incoherent transmission microscope.

Keywords: Adaptive optics, microscopy, wave front sensing.

1. Introduction

Adaptive optics systems normally use a wave front sensor to measure aberrations, which are in turn corrected using an adaptive element, such as a deformable mirror. In imaging systems, however, direct wave front sensing is not straightforward and wave front sensor-less schemes are often employed. Such wave front sensor-less schemes have already been implemented in adaptive scanning optical microscopes using either model-free stochastic optimisation1a2 or deterministic model-based In all of these systems, the adaptive element is reconfigured in order to maximise a metric related to image quality. The optimisation procedure generally involves measurement of the metric for a number of trial aberrations, followed by the estimation of an improved correction aberration. This process is repeated until the image quality is considered acceptable. The number of measurements required depends upon the optimisation algorithm employed. In microscopy, it is desirable to have the minimum possible number of image measurements to ensure the fastest acquisition and minimum specimen exposure. It is therefore essential to use efficient algorithms. In this paper, we present a summary of an efficient image-based adaptive optics 151

152

scheme that uses an aberration expansion as a series of Lukosz functions and the low spatial frequencies of the image as the optimisation m e t r i ~ . ~ The scheme is demonstrated using an incoherent transmission microscope. 2. Aberration correction by image optimisation

In an incoherent imaging system, the image I ( z ,y) is formed as the convolution of the object function t(x,y) and the intensity point spread function

h(x,y): I ( & Y) = t ( z ,y) * h k ?Y)

'

(1)

Although the effects of aberrations are contained entirely within the function h, it is not straightforward to retrieve aberration information directly from the resulting image, which depends on both the aberrations and the object structure. An effective adaptive optics scheme should be object independent, so should permit the separation of aberration and object influences on the measurements. A general optimisation process for measuring and correcting aberrations is summarised in Figure l(a). A chosen aberration is introduced by the adaptive element, an image is acquired and an image quality metric is calculated. This is repeated for a sequence of chosen aberrations, after which the correction aberration is estimated from the sequence of measurements. The specification of such a scheme requires three choices: the aberration representation (the mathematical functions used to describe the aberrations), the optimisation metric (a quantity representing the image quality) and the estimator (the algorithm for estimating the correction aberration). The number of measurements required during this process depends critically upon these choices but an appropriate mathematical model can enable efficient aberration correction with a minimal number of measurements. We present here a scheme based around optimisation of the low spatial frequency content of the image. Although only the low spatial frequencies are used in the optimisation metric, the scheme results in the correction of all spatial frequencies. The scheme is predominantly independent of the object structure. The aberrations are represented by a series of Lukosz function^.^^^ These modes are similar in form to Zernike modes, consisting of the product of a radial polynomial and a sinusoidal azimuthal variation (see Table 1). Whereas a Zernike function is defined so that a function of a given order minimises the wave front phase variance, a Lukosz function of a given order minimises the mean square focal spot radius (or equivalently its second

153

(a)

I

Chooseaberration

P)

/+--

I Condensor Object

Calculate quality metric

Tube lens 4f relay lenses

Deformable mirror

Fig. 1. (a) Flow chart detailing the steps involved in the wave front sensor-less correction scheme. (b) Schematic of the adaptive incoherent microscope for demonstration of aberration correction.

moment). These functions are ideally suited for the modelling of the effects of aberrations on the imaging of low spatial frequencies (i.e. frequencies much less than the cut-off of the imaging system). The total aberration @ is expressed as a series of N Lukosz modes, Li, with coefficients at: N

where (r,0) are the normalised polar coordinates in the pupil plane of the imaging system. The optimisation metric g is obtained by first taking the Fourier transform (FT) of the image and then integrating the squared FT over a range of spatial frequencies:

where 5 is the FT operator and (u,TJ)are the coordinates in the FT plane. (u2 v2)1/2 5 m2, The range R corresponds to the annular region ml I where ml and m2 are small compared to the cutoff frequency of the imaging system. It has been shown that the metric g can be written in terms of the

+

154 Table 1. Zernike and Lukosz mode definitions Index

i 1 2 3

Zernike mode zd(r.8 ) 1 2r cos(6 ) 2r sin(@)

Lukosz mode L;(r,8 ) 1

r cos(8) r sin (8)

- 1)

d3(2r2 - 1) fir2 C O S ( ~ ~ ) f i r 2 sin(28)

4 5

6

7

2&(3r3 - 2r) cos(8)

8

2&(3r3

- 2r) sin(@)

-&'cos(28)

5~~ sin(28)

Name Piston Tip Tilt Defocus

Astigmatism Astigmatism

&(3r3 - 3r) cos(8)

Coma

&(3r3 - 3r) sin(8)

9

2dr3COS(~~)

+3

cos(3e)

Coma Trefoil

10

2 . ~ sin@@) 3 ~ ~

5 T 3 sin(38)

Trefoil

11

&(6r4

- 6r2 + 1)

4

(3r4 - 4r2

+ 1)

Spherical

aberration coefficients as5 N

i=l

where qo and q1 are positive quantities that depend solely upon the object structure and not the aberrations. Expression 4 is valid for all objects, except those where there is a significant low frequency component predominantly in one direction, for example a one-dimensional grid at tern.^ As g is a quadratic function in each of the aberration coefficients, it is possible to estimate each coefficient, ai, independently using a parabolic maximisation algorithm. The maximum of any parabolic function can be found from three function evaluations. In the adaptive imaging system, these three evaluations correspond to three image measurements with different amounts of a chosen aberration mode applied. These are referred to as bias aberrations. One can be taken as the initial image (with no bias aberration), giving an optimisation metric value go. The other two images can be obtained by adding first a positive amount of the chosen mode (+bLi) and then a corresponding negative aberration (-bLi), where b is a suitable step size. The respective values of g calculated from these two images are denoted g+ and g - . The correction aberration amplitude a, is then estimated as8

and a correction aberration a,Li is added using the deformable mirror

155

(DM). This process is illustrated in Figure 2. Each of the N modes can be corrected sequentially in this manner, requiring a total of 3N image measurements. Alternatively, all of the metric values could be obtained before correction is applied. In this case, go would be identical for each mode; hence, a total of 2N 1 measurements would be required.

+

~~

(a) Optimisationmetric

ied aberration Fig. 2. Illustration of the parabolic maximisation algorithm: (a) in one aberration mode; (b) using independent calculations in two modes t o find the combined maximum.

3. Results The correction scheme has been demonstrated for imaging in an incoherent transmission micro~cope.~ The experimental set-up is shown in Figure 1(b). An LED (wavelength 650nm) provided illumination to a transmissive specimen, which was imaged through the objective lens. This pupil plane of the objective was imaged onto the DM (Boston Micromachines Corp., MultiDM) using a 4f relay system. The DM was then re-imaged through the same 4f system onto the pupil plane of the tube lens, which formed an image of the specimen on the CCD camera. For the purposes of this demonstration, aberrations were both introduced and corrected using the DM. An initial aberration containing N = 8 Lukosz modes, corresponding to i = 4 to 11, was applied using the mirror and a sequence of bias aberrations was added in turn to this initial aberration. The correction of theses modes required 2N 1 = 17 measurements. The aberration was then corrected by removing these modes from the deformable mirror using the scheme described above. An example correction is shown in Figure 3. The image on the left shows a USAF test chart when the random combination of eight Lukosz modes was present. The image on the right shows the same object after a

+

156

cycle of aberration correction. This correction corresponds to a reduction in root-mean-square phase error from 2.01 t o 0.38 radians.

Fig. 3. Demonstration of the image-based adaptive optics correction scheme: with initial aberration (left); with aberration correction (right).

4. Conclusion

We have described a new approach t o image-based adaptive optics based upon the optimisation of the low spatial frequency content of an image. By expanding the aberrations in Lukosz functions, one obtains a mathematical representation that permits the separation of the aberration effects and the object structure. This permits the use of simple quadratic maximisation algorithms. Moreover, each aberration mode can be optimised independently of the others. The correction of N aberration modes has been demonstrated with only 2N 1 image measurements.

+

References 1. L. Sherman, J. Y. Ye, 0. Albert and T. B. Norris, J. Microsc. 206,65 (2002). 2. A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine and J. M. Girkin, Microscopy Research and Technique 67,36 (2005). 3. M. A. A. Neil, R. JuSkaitis, M. J. Booth, T. Wilson, T. Tanaka and S. Kawata, J. Microsc. 200, 105 (2000). 4. M. J. Booth, M. A. A. Neil, R. JuSkaitis and T. Wilson, Proc. Nut. Acad. Sci. 99, 5788 (2002). 5. D. Debarre, M. J. Booth and T. Wilson, Optics Express 15,8176 (2007). 6. W. Lukosz, Optica Acta 10, 1 (1963). 7. J. Braat, J. Opt. SOC.Am. A 4, 643 (1987). 8. W. Press, S. Teukolsky, W. Vetterling and B. Flannery, Numerical Recipes in C, 2nd edn. (Cambridge University Press, 1992).

A fundamental limit for wavefront sensing C. Paterson The Blackett Laboratory, Imperial College London, London SW7 2BW E-mail: [email protected]

A fundamental upper limit to the information obtainable from any optical wavefront sensor is found, The error variance in the wavefront estimate must satisfy r2 2 N ~ l ( 4 n )where N A is the number of independent parameters describing the wavefront and n is the number of photons detected. The limit is independent of the type of the wavefront sensor and applies to both closedand open-loop operation. Keywords: wavefront sensing, adaptive optics, information theory

The performance of adaptive optics at low light levels is limited by the wavefront sensor’s ability to measure the wavefront aberration. Although this is particularly true for astronomy applications, it is also the case for applications such as imaging the eye and microscopy, where the returning optical signal for wavefront sensing is often very weak. In such situations, accuracy is ultimately limited by detector noise and photon noise. Detector noise is a technological Limitation rather than fundamental and recent advances in photodetector technology have produced photon-counting detectors, albeit with limited quantum efficiency. Photon noise is more fundamental, a consequence of the quantum nature of light. There have been several comparative studies of different wavefront sensors, e.g. ,l-* However none of this work precludes the existence of better (possibly yet-to-be invented) wavefront sensors. So, how much information is it possible to obtain from a limited number of photons? To address this question, we will try to find the most efficient wavefront sensor. We begin with a description of a wavefront sensor in its most general form. A wavefront sensor may consist of a system of any number of optical elements (lenses, beamsplitters, mirrors, gratings, and suchlike) and any number of photodetectors. The field at the input of the wavefront sensor is u(x),where x represents the generalized coordinates 157

158

of the input of the sensor, which may be a single aperture, or multiple apertures. We write the perturbed field as u(z)= uo(z)exp[i#(z)] and express $(z) in terms of an arbitrary set of real functions $j (z),orthonormal with weight Ju0(z)J2, i.e., +(z) = Cju j $ j ( z ) , where uj are the coefficients that we wish to measure. Then for small aberrations (l$(z)1 < 1) such as for a functioning closed-loop system,

+

u(z)= uo(z) x a j A u j ( z ) ,

(1)

j

where the functions Auj(x) iuo(z)$j(z)form a complete orthonormal basis for the complex amplitude perturbations. The role of the optical elements is to transform the optical field at the wavefront sensor’s input so that aberrations at the input give rise to measurable intensity modulation at the photodetectors. Representing the action of the wavefront sensor optics by the linear operator S , we write the field at the photodetectors as 4 Y ) =S(4z))

+

= S(uo(z))

z:

ajs(Auj(5))

(2)

j

We assume that the optical elements are efficient in the sense that all light entering the sensor reaches the photodetectors. In fact this in no way limits our description since it is always possible in principle to substitute lossy elements by a combination of lossless optical elements plus photodetection (where any potential information from the photodetection is ignored) that yields the same or more information. The operator S is then a unitary transformation: the operation of the optics is reversible and no information is lost. However, the quantum nature of light limits what we can measure at the detectors: the photodetection process is irreversible. The irradiance at the photodetectors, I ( p ) = /u(y)I2,is just the probability density function for photon detection events. The positions of photons recorded at the detectors are used to estimate the aberration coefficients a j . The Cram&Rao lower bound places a fundamental limit on the accuracy achievable in terms of the Fisher inf~rmation.~ We now calculate the Fisher information matrix for the general wavefront sensor. It is given as the covariance of the score vector, whose elements are defined Vj = dl0gp/d6~,where p is the probability for the data. Taking I(y) as the probability and aj as the parameters, the elements of the score

159

vector are

which expanding gives

where %[.I denotes the real part and where cpj(y) = arg[u(y)Au;(y)] is the complex angle between the j t h perturbation component and the total field on the detector plane. Taking the covariance gives the Fisher matrix elements for the general wavefront sensor output (per photon and assuming Poisson statistics)

From the Cram&-Rao lower bound, the accuracy for the estimate of is limited by $ 2 ( J - l ) j j . The Fisher matrix J is a real, symmetric, positive semi-definite matrix. It is clear that the diagonal elements of J-l are minimized when the diagonal elements of J are maximized. From Eq. (5) they must satisfy aj

5 4,

(7) the maximum value being achieved when cpj(y) = 0 or n over all y. (This can be considered as a generalised phase contrast condition-the perturbation components are required to have phase parallel to the total field.) Therefore, uncertainty in the estimate of aj must satisfy

We are rarely interested in estimating the whole aberration, but a projection onto a subspace of the aberration parameter space-for example the subspace defined by the influence functions of a deformable mirror in a closed-loop adaptive optics system. Choosing the arbitrary basis functions #j(z) such that 4 j ( z ) for j = ~ . . N Adefines the deformable mirror influence function space, we only need to estimate parameters aj for j = ~ . . N AThen . the total phase variance for the estimation of the projected aberrations is NA

160

Thus we have found an upper limit to the information (and accuracy) we can obtain from an arbitrary wavefront sensor. Applying the limit to an adaptive optics system for diffraction limited imaging, using the Markchal criterion (equivalent to X/14 rms wavefront aberration), requires c2 5 0.2 which gives a limit on the number of photodetections

n 2 (5/4)NA, (11) n being the number of photodetections during the coherence time r of the aberrations. As an example, consider the performance of an ideal pyramid wavefront sensor.6 The pyramid wavefront sensor is usually thought of as a wavefront gradient sensor in the context of a geometrical (ray-based) optical model where the distribution of intensity between four images of the pupil at the detector is determined by the local wavefront gradient. The position of the pyramid apex is usually modulated to obtain a linear gradient signal. However, it is instructive to treat the sensor under a diffractive model, in which the pyramid subdivides the Fourier domain (i.e., the image plane) into four quadrants and each output pupil intensity pattern is due to the field on a single quadrant of the Fourier domain. If we consider a single spatial fre-

Fig. 1. Pyramid wavefront sensing in the diffraction regime for for a single spatial frequency aberration (p = ac0sk.x. Amplitude in the Fourier domain (left) and the corresponding intensities at the four conventional output pupil planes I(y).

quency component of the phase perturbation, #(x) = a cos k.x, we see that the intensity modulation at the output is due to the interferences of terms ( a / 2 )expik.x and its conjugate with the unperturbed components (Fig. 1).

161

For high spatial frequency, the corresponding diagonal Fisher matrix element (Eq. 6 ) is given by J j M 2. Figure 2 plots the diagonal Fisher matrix

Zernike Fig. 2. Diagonal Fisher matrix elements Zernike aberration basis.

Jj

for the pyramid wavefront sensor in the

elements J j for the first 35 Zernike aberrations calculated numerically. The diagonal elements are approximately J3 M 2 even for the low order terms. We can see that an ideal pyramid wavefront sensor can achieve an efficiency of about half of the fundamental limit. The generalized phase contrast condition for maximum information indicates the form for an efficient wavefront sensor: at the detectors, the perturbation components due to the aberrations should be in phase or anti-phase with respect to the total field. Note that for reasonable dynamic range and to avoid reconstruction ambiguities the perturbed components should not be separated spatially from the unperturbed field. This suggests the use of point-diffraction wavefront sensing with a Zernike phase contrast mask to shift the unperturbed component by 7r/2 with respect to the perturbed components. The principle is illustrated in Fig. 3. The physical separation of the perturbed and unperturbed components in the image (mask) plane increases with spatial frequency and such a system can approach the information limit for higher spatial frequencies. In conclusion, we have derived a fundamental limit to the information obtainable by any wavefront sensor. The limit indicates the form of an optimum sensor configuration via a generalized maximum phase-contrast condition. Although we have treated the sensor as operating in a closed-

162

loop system, since we placed no limitation on the operation of the optical elements, allowing for the subtraction of arbitrary phase functions, the information limit applies whether or not the sensor is operating inside a closed-loop adaptive system. Since we have placed no restriction on the form of the wavefront sensor, we can consider the limit as being intrinsic t o the nature of optical wave propagation and photodetection rather t o any specific wavefront sensor. The author wishes t o acknowledge the support of the Royal Society.

Fig. 3. Point-diffraction wavefront sensing with a Zernike phase contrast mask for a single spatial frequency aberration Cp = ucos k.x. Amplitude at the mask/image plane (left) and the corresponding intensity at the output (detector) plane I(g).

References 1. B. M. Welsh, B. L. Ellerbroek, M. C. Roggemann and T. L. Pennington, Appl. Opt. 34,4186 (1995). 2. F. Roddier, Opt. Commun. 113,357 (1995). 3. T. J. Schulz, W. Sun and M. C. Roggemann, Cramer-Rao bounds for estimation of turbulence-induced wavefront aberrations, Proc. SPIE 3763 1999. 4. T.Y. Chew, R. M. Clare and R. G. Lane, Opt. Commun. 268,189 (2006). 5. S. M. Kay, Fundamentals of statistical signal processing: estimation theory (Prentice Hall, New Jersey, 1993). 6. R. Ragazzoni, J. Mod. Opt. 43,289 (1996).

C

ENT FI

LE WA~EFRONT$ENS

B. VOHNSEN,+I. IGLESIAS AND P. ARTAL Laboratorio de bptica (ediJicio ClOyN), Universidad de Murcia, Campus de Espinardo, ES-30071 Murcia, Spain A novel wavefront sensor based on a coherent bundle of single-mode fibres is proposed. Such a sensor holds potential for fast registration and does not require a collinear design. The pros and cons of it, as compared to more conventional sensor designs, is examined in order to evaluate its potential and to identify possible areas of application.The concept is illustrated with wavefront measurements that have been performed for simplicity with an individual fibre scanned across the wavefront of interest. We find that the tiny core of current single-mode fibres is ill suited for general purpose wavefront sensing, but future developments may make a fibre-based design a liable alternative to current techniques.

1. Introduction Coherent optical fibre bundles, commonly used in endoscopes to transfer an image, consist of an ordered array of multimode fibres that operate as intensity carries of a sampled light distribution. A similar example can be found in the composite structure of the retina in the human eye where waveguiding is central for the transfer of a sampled retinal image to the visual pigments located in the outer photoreceptor segments [I, 21. This process, considered to be the underlying cause of the classical Stiles-Crawford effect, i.e., a reduced visual sensitivity to light rays that impinge obliquely onto the retina [3,4], plays also a role for high-resolution retinal imaging [ S ] . The amount of incident light that couples to any given photoreceptor is determined by the amplitude and phase gradient of the illumination field at the retina and is therefore directly influenced by wavefront aberrations [2]. Clearly, this scenario may be transferred to a sensor design in which a coherent fibre bundle samples an incoming wavefront. In the following, we examine design considerations relevant for the realization of a fibre-based wavefront sensor and show preliminary results obtained with commercially-available single-mode fibres. Precursors to this idea that have previously been explored include a waveguide-based quadrant detector 161 and a I-D Mach-Zehnder interferometer array; the latter successfully used to characterise the wavefront from a pulsed dye laser [7].

esign considerations for a fibre-based wavefront sensor The main idea consists of making use of the sensitivity in coupled light power to the wavefront gradient present at the entrance facet of each fibre in a bundle. A waveguide-based wavefront sensor can be realized with low-order multimode 'E-mail: [email protected]

163

164

fibres (for highly multimode fibres the power coupled would be insensitive to the exact wavefront slope within the numerical aperture, NA) but for simplicity of analysis single-mode fibres are to be preferred. A fibre design gives direct access to different parts of the wavefront for modulation or sensing applications similar to the interferometric approach [7]. When realized with a coherent bundle the entire wavefront can be sampled simultaneously and the operational principle resembles that of a conventional Hartmann-Shack sensor. Nonetheless, it is potentially faster as no centroids need to be determined and it does not require a collinear geometry. The probed wavefront can be reconstructed from the coupling-dependent power attenuation measured in each fibre. Thus for a Gaussian-like mode yf,(x,y) = (2/n~~)~.~exp[-(x~+y~)/w~] of width w,and for an incident field with a linearly expanded phase around the centre of each fibre core yfi,(x,y) = &exp[i(cpo+cp&+qyy)], the power P,, coupled to any given fibre (mn) can be estimated as

1

[2

(1) (cp: + cp;) w2 where cp, and cpy denote first-order derivatives of the wavefront at the centre of the core. Fresnel losses may be assumed constant when the wavefront slope is small and can in that case be ignored (a constant scaling). Amplitude variations of the field matter less than phase variations and it therefore suffices to consider the amplitude (&), and wavefront slope (cp,..cp,), at the centre of each fibre core. A sensor design based on this idea is shown schematically in Figure 1.

p, (cp,, cp, 1= p, (0,O)exp -

0.4

0.2

,

0.04 ~~

0

2

4

0

6

8

10

Figure 1: Wavefront probed with single-mode fibre(s) and coupled power fraction versus wavefront slope (in degrees) for fibres of 1 and 2 pm mode width respectively at h = 632.8 nm. The angle of incidence is related to the phase derivates as cp: = cp: + 9,”= k’sin’0 where k = 2dh.

It is apparent that the simple fibre-based sensor shown would be incapable of distinguishing between phase gradients of the wavefront in two orthogonal directions, a problem not encountered with the Hartmann-Shack sensor. This is of no concern when measuring only rotational symmetric aberration terms (defocus, spherical aberration), but more generally this limitation may be

165 remedied with two separate detectors that measure orthogonal components of the phase gradient, i.e., cpx and qy.It should also be noted that the sensor makes no distinction between positive and negative derivatives which makes it imperative, for the general case, to bias the detector with a tilt of the fibre ensemble. This has the added benefit that the sensor may be adjusted to an approximate linear region of the angular-dependent coupling regime where its sensitivity is largest. The linear signal dependence AP on angular excursion A0 of the wavefront at a given fibre (mn), biased to an angle 00,may be written as

where the angle of bias, 00,is obtained from the relation: sin-200- c 0 s ~ = ~ k02w ~2 . To remain in the linear regime of the sensor care should be taken that A0 < 00 remains well satisfied across the sampled wavefront. The LPol mode of a stepindex dis~ibutionwould indicate a slightly smaller angle of bias than the chosen Gaussian mode but its sensitivity when biased AP/A0 would remain practically unchanged. Finally, if intensity variations are present across the probed wavefront a separate reference measurement (for example with a CCD) needs to be made as these cannot, in general, be unambiguously separated from phase variations unless perhaps if probed by multimode fibres incorporated into the coherent bundle. Alternatively, the proper bundle may be used to characterise spatial intensity variations a priori by measuring without bias (i.e., 0 0 -0) which corresponds to having made the sensor insensitive to small phase variations. The resolution of a ~artmann-Shacksensor in its common configuration with an array of microlenses and a CCD for centroid imaging is essentially pixel limited. With a typical 6.3 mm focal length and a CCD pitch of 7.4 pm this amounts to an angular resolution of 60 -4' (higher resolution may be obtained at a sub-pixel level). As the fibre-based wavefront sensor is not based on an angular reading but rather on power the sensitivity can, in principle, be made arbitrarily large but would in practise be power limited. The larger the fibre core, while remaining single mode, the steeper a power coupling curve and the higher the sensitivity (see Figure 1). At the bias setting of steepest slope, a fibre with a typical mode width of 2 pm exposed to a wavefront deviation of -4' would produce a relative change in power of -2%. However, with a 125 pm cladding typical of commercial fibres only about - l o 3 of the incident power would couple which is highly energy inefficient. The situation may be improved with large core single-mode fibres (obtainable with a reduced core-cladding index difference and NA) that hold promise for larger signals (= w3)as well as higher sensitivity (= w). On the contrary, a large range of operation, attainable

166

with tiny core fibres is even more problematic due to the aforementioned power limitation.

3. First experi~entaltrials Commercial fibre bundles used as image conduits or for illumination purposes have high NA, are highly multimode and in consequence are poorly suited for a power-based wavefront sensor. Multicore single-mode fibres could be an alternative, but for simplicity we examined only the suitability of scanning an individual single-mode fibre manually across the wavefront of interest. Two types of standard single-mode fibres were tested: (I) 3M 3224-SN and (11) Nufern 630-HP. The two have nominal NAs of -0.12 and -0.13 respectively, both with a mode field diameter (Petermann I1 spot size) of -4.0 k 0.5 pm, and are single mode for red light (>620 nm and >600 nm respectively). The entrance facet of fibre (I) has been cut in-house (a potential source of unwanted scattering) whereas fibre (11) has been flat cleaved with a diamond wedge scribe at the manufacturer. The coupled and transmitted power is measured with an amplified Si-photodiode PDA36A with a maximum sensitivity of - 2 ~ 1 0V~W that is, in the case of fibre (11), directly connected with a FCPC adaptor. Fibre (11) has a slightly broader tuning curve than fibre (I) due to the different NA and in consequence it is less sensitive at the indicated bias angle. Sensitivities &/A0 of -O.l9/deg and -O.l6/deg respectively can be read from Figure 2.

-10

-5

0 00-4.6' 5

10

Figure 2: Normalized angular tuning curves P(0) of coupled power measured for two single-mode fibres of 5 m length using a linear-polarized 10 m W HeNe laser (h = 632.8 nm).

We have performed initial trial measurements on the wavefront from a 1OmW HeNe laser with beam diameter (e-2) 0.65 mm. Ideally, wavefront aberrations should be introduced with a deformable mirror as this would allow changes without otherwise modifying the optical path, but in this first attempt we have chosen to use only ophthalmic trial lenses. As already commented on, power is a limiting factor with current single-mode fibres. Measured powers for the HeNe laser beam are typically on the order of -100 nW or less and with a

167

NEP of about 0.2 nW for the chosen detector noise does become an issue offaxis for the sampled Gaussian beam. In order to compensate for the power variation across the sampled beam it was first scanned along one axis by the fibre in the unbiased orientation (0, 0) and the scan was then repeated with the fibre inclined to the incident wavefront at an angle €lo 4". The scan across the laser beam corresponds to multiplying Eq. (1) and Eq. (2) for the signal with a Gaussian function exp[-2x2/wbem2] representative of the beam. Some results obtained are shown in Figure 3 (only results with the 3M fibre are shown). The different spot size in the case of a negative and positive lens reflects the fact that the lens is located at a distance from the end face of the fibre (therefore also the change in absolute power coupled). As expected the wavefront slope changes with off-axis distance. Nevertheless, it is clear that the measurement is far from the ideal of reproducing a linear change. Position inaccuracies (clearly the case for the -2D lens), a limited scan range and a small sensitivity (noise) are all factors that can corrupt the measurement and wavefront reconstruction.

-

-

Measured power P(x>[V] 1.4

0.55

1.2

0.50

1 .o

0.8

0.45

0.6

0.40

- OOO OOO

0.30

0.0

0

50

100

150

200

250

300

0

50

100

150

200

250

300

3.0 2.5 2.0 1.5

I

0.35 -/

1 .o

0.5

1

0.0 0

50

100

150

200

250

Displacement x [pm]

300

0.30-/ 0

I

1

50

1W

150

200

250

300

Displacement x [pm]

Figure 3: Measured power dependencies [markers] with 2 diopters of negative and positive defocus (left) and estimated wavefront change (right) for the 3M fibre as obtained with a HeNe laser and trial lenses. Also shown (right) is the ideal theoretical outcome for this fibre [dashed line].

168

4. ~ Q n c l u s i Q ~ A coherent fibre-bundle wavefront sensor has been proposed. Special constructs (including multicore fibres) can be imagined that make advantageous use of micro-fabrication techniques to avoid the posterior assembling of numerous fibres. If cut at the bias angle a bundle could presumably be used directly in its linear range and an embossed end face could allow simultaneous rapid measurements of orthogonal wavefront slopes with a single sensor unit. We have shown preliminary results obtained with the scanning of an individual fibre across the wavefront. This serial probing impedes a high speed of operation and is prone to error if power or pointing instabilities are present. The removal of intensity variations to access only the phase has proven problematic for narrow beams probed with standard fibres. The power limitation may be circumvented with large core single-mode fibres, but powerful and wider beams may allow for an easier reconstruction. We are conducting further research on this issue. Finally, scattering, back-reflections and bending losses are all additional factors that have to be tackled in order to improve precision and applicability of the proposed sensor.

Acknowledgments This research has been made possible with support from the Ministerio de Educacidn y Ciencia (projects RYC2002-006337 and FIS2004-02153) and Fundacidn Seneca (project 03115PU05) Spain.

eferences 1. B. Vohnsen, “Visual implications of retinal photoreceptor waveguiding,” Proc. ICO Topical Meeting on Optoinformatics/Information Photonics (St Petersburg, Russia, 2006) pp. 248-250. 2. B. Vohnsen, “Photoreceptor waveguides and effective retinal image quality,” J. Opt. SOC.Am. A 24,597-607 (2007). 3. A. W. Snyder and C. Pask, “The Stiles-Crawford effect explanation and consequences,” Vision Res. 13, 1 1 15-1137 (1973). 4. B. Vohnsen, I. Iglesias, and P. Artal, “Guided light and diffraction model of human-eye photoreceptors,” J. Opt. SOC.Am. A 22,2318-2328 (2005). 5. B. Vohnsen, I. Iglesias, and P. Artal, “Directional imaging of the retinal cone mosaic,” Opt. Lett. 29,968-970 (2004). 6 . W. Klaus, K. Kudielka, Y. Arimoto, and K. Araki, “Novel wavefront sensor for optical space communications,” IEEE Conference on Lasers and Electro-Optics Europe, 2000, abstract p. 149. 7. R. H. Rediker, B. G. Zollars, T. A. Lind, R. E. Hatch, and B. E. Burke, “Measurement of the wave front of a pulsed dye laser using optics sensor with 200-nsec temporal resolution,” Opt. Lett. 1

~aximum-likelihoodmethods in wavefront sensing: nuisance parameters D. LARA*, J . C. DAINTY, and Applied Optics, National University of Ireland, Galway Galway, Republic of Ireland *E-mail: d . l a ~ ~ n u i g a l w a y . i e http://optics. nuigalway. ie

H. H. BARRETT College of Optical Sciences, University of Arizona Tucson, Arizona, United States E-mail: b a ~ e t t ~ r a d ~ o l o g y . a r i z o n a . e d u

In wavefront sensing, an accurate likelihood model offers a reliable way to relate directly a chosen set of global parameters of interest (e.g. the actuator signals of a deformable mirror) to the fundamental data (e.g. the CCD pixel photoelectrons in the wavefront sensor), without lossy pre-processing stages like centroid calculation or wavefront reconstruction. We have shown, through numerical simulations, that at low light levels maximum likelihood estimation can offer advantages in residual wavefront error against traditional least-square estimation from centroid data. We discuss the importance of nuisance parameters in the likelihood model. Keywords: Wavefront sensing; Stochastic modeling.

1. Introduction

This work builds upon a recent publication led by H. H. Barrett.l The goal is to explore the fundamental limits of wavefront sensing in order to optimise existing Adaptive Optics technologies and to design better solutions; in particular for low light level applications. Optimal wavefront reconstruction methods started gaining attention in 1983 with a paper by Wallner,2 but it is surprising that many authors still use estimates of individual spot centroids as the"fundamenta1" data in Shack-Hartmann sensors like Wallner did. The issue was first seriously studied by Cannon3 in 1995, who considered viewing Shack-Hartmann (SH) wavefront sensing as a global estimation problem. Canon did not study low light level scenarios, and he 169

170

focusesd his work on wavefront reconstruction. In the particular case of a typical SH sensor the fundamental data are the pixel values of the CCD image that contains the spots, and not the local tilt estimates. Likelihood theory requires an accurate probability model that includes all sources of randomness in the measured fundamental data, but through this challenge offers a reliable way to relate directly the chosen set of global parameters of interest (e.g. the actuator signals of a deformable mirror) to the fundamental data, without lossy pre-processing stages like centroid calculation or wavefront reconstruction. We have shown' using numerical simulations ML vs TraditionalWFS: 50 noise realizations for each light level

Average number of photons per subaperture (200 subapertures)

Fig. 1. Comparison of traditional least-square estimation of wavefront coefficients from centroid data vs. direct ML estimation from photodetector outputs. Parameters used in the simulation were X = 680 nm; pupil diameter 24 pm * 128 = 3072 pm; lenslet size = 192 pm; CCD pixel size = 24 jm, and focal length = 9.9 mm. The markers represent the mean and the error bars the standard deviation of the residual wavefront after the estimation of 50 Poisson noise realisations for each light level.

that at low light levels maximum likelihood (ML) estimation can offer up to a four-fold advantage in residual wavefront error against traditional leastsquare estimation from centroid data. See Figure 1. It can also be noted in the figure that a significant reduction in wavefront error could be achieved even with an average of 0.32 photon per subaperture. 2. Maximum Likelihood estimation

Maximum likelihood is a general method to find an estimate of a set of parameters from an stochastic model, and is defined as

171

Where the argmax operator returns the 0 argument at which pr(gl8) is maximised. In other words, we choose as the estimate ~ M the L value of the parameters of interest 8 that maximises the probability of occurrence of the data g that we actually observed. There are many desirable properties in ML estimation;* e.g. ML estimates are efficient if an efficient estimate exists. However, these advantages require that we undertake some important challenges: (1) Obtaining an accurate probability model, accounting for all sources of r andomness, (2) Accounting for nuisance parameters, (3) Accounting for null functions. These sources of randomness, nuisance parameters, and null functions, are present in any estimator, not only in ML; but they are often ignored. ML estimation requires that we deal directly with the sources of error and bias in the estimators we design, and that we make choices on how to deal with them. Furthermore, likelihood theory also provides a way to optimise the design of an estimator such that the influence of nuisance parameters, for instance, is reduced.l Nuisance parameters are named as such because they are those that can influence the data we measure g, but are of no interest or use in our estimation. In an adaptive optics system with a given deformable mirror (DM) and wavefront sensor, for instance, the nuisance parameters are those that can be picked by the wavefront sensor, but there is nothing that the DM can do to correct them; i.e. they are in the null space of the DM. In the wavefront sensing literature they are often thought of as the non-correctable modes of the residual phase, but they can also include the brightness of the guide star and sky background. An exhaustive list of strategies to deal with nuisance parameters can be found in references 1 and 4. Null functions, on the contrary, are parameters that do not alter the sensor data; i.e. they are in the null space of the sensor, but they could well be in the range of the DM.

3. ML estimation for Poisson statistics Recent advances in photodetector technology can help to eliminate the randomness introduced by the detection process. Photon noise, on the other hand, is a fundamental consequence of the quantum nature of light. Poisson events are inherently independent and the Poisson probability is determined fully by its mean. Since the logarithm is a monotonic function of its argu-

172

ment, maximizing a likelihood is equivalent to maximizing the log of the likelihood. One can show4 that the log-likelihood for estimation of 6' under pure Poisson statistics is given by M

lnPr(gI0) =

m=l

{ - Bm(8) + grn1n[$m(e>l- ln(grn!>>.

(2)

Where Bm is the data that would result from the set of parameters 6' in the absence of noise, which can be obtained through calculation or, preferably, calibration; and gm is the data that is actually measured. The log-likelihood for a measured SH image is a scalar number that is easy to calculate, and the estimation process consists simply on finding the values in the parameter vector 9 that maximise the number in Eq. 2. Figure 2 shows two surfaces with log-likelihood values from a SH wavefront sensor simulation as an example. The wavefront contained a combination of Polynomial pair Zernikes (X,Y): 2(2,2)and 2(4,2)

Fig. 2.

Polynomial pair Zernikes (X,Y): 2(2,0)and 2(3,3)

Log-Likelihood.

the 12 Zernike polynomials between the 2nd and 4th radial order, and the 12 parameters to estimate were the magnitude of these polynomials. The graphs show the value of the log-likelihood on two different 2-D slices of this 12-D parameter space. The surfaces show a smooth profile with a maximum near the correct value (0.1 A) of the two parameters shown, which means that the maximum is possible to find, and that the parameters that give the maximum likelihood are a good estimate of the true parameters. The parameters to estimate need not be Zernike polynomials, they can be the influence functions or modes of a deformable mirror instead. ML estimation

173

can relate the measured data directly to the parameters of interest - without reconstruction step. 4. Preliminary results including nuisance parameters

Nuisance parameters can have a negative impact on the accuracy of the probability model. As a preliminary part of a more comprehensive study, we generated Kolmogorov phase screens using N. Roddier's method5 including Zernike terms up to the 30th radial order. We simulated an open-loop adaptive optics system that was formed by a SH wavefront sensor with 200 subapertures and a 19 actuator membrane DM. Figure 3 shows a comparison between ML vs traditional SH with centroid estimation. The centroid estimation was first made using what we call a typical number of mirror modes to reconstruct the sensed phase, and also with the number of modes that gave the best a-posteriori correction at each light level. There are two ML vs Typical centroid WF estimation 50 noise realizations for each light level

71

25

-.

ML vs best a-postariori centroid WF estimation 50 noise realizationsfor each light level 0

A

ML Estimation Best a-posteriori Centroid Estimation

-6.

.-2 .'

m ..

; .a 20 c

;5.,,

5 el5

'ii

-

&.I'

m

Dlro = 8

v)

1

:lo f

fn 5 0.3

1 3.2 10 32 100 Average number of photonsper subaperture

o'O:3

3:2

Ib

32

Average number of photons per subaperture

IW'

Fig. 3. Preliminary results for a non-optimised SH wavefront sensor. The A 0 simulation consisted of a 19 actuator membrane DM and a SH sensor with 16 subapertures across the pupil diameter (200 in total). In the typical centroid estimation the number of modes used in the wavefront reconstruction were 7,9,12,16, 19, and 19 for the respectively increasing light levels. In the best a-posteriori reconstruction the respective number of modes were 2, 4,6, 6, 11, and 11.

important facts reflected on these graphs. The first is that unless we can know a-priori the optimum number of mirror modes to use in the phase correction, ML can present significant advantages on the residual rms error over traditional centroid estimation. Secondly, that the correction of both methods is worse when compared to Fig. 1, where there were no nuisance parameters.

174

marks and future work We have started numerical work using experimentally measured influence functions of a deformable mirror fitted with two superposed gaussians, and we are in the process of obtaining more results using Kolmogorov statistics. We have obtained results for diverent values of D/ro and we have observed that the larger the relative contribution to the wavefront variance by the nuisance parameters the poorer is the performance of the system; for lower values of D/ro (e.g. 4 and 6 ) the statistical model is less accurate. In addition, we expect that ML estimation will show a larger improvement with respect to centroid estimation for values of TO and subaperture size that result in local wavefronts with significantly more structure than pure tip and tilt; i.e. TO much smaller than the subaperture size. ML estimation has other desirable properties. From the statistical description of the data (i.e. the likelihood) it is possible to compute the Fisher information matrix and then the Cramr-Rao bound, which is a fundamental lower bound on the variance of the parameters to estimate. This can be used as an optimisation criterion in the design of new wavefront sensors that “match” existing corrective devices; in the sense that a wavefront component that the device cannot correct has a minimum effect on the new sensor data. We are continuing this study first to estimate the correct number of subapertures in a SH given a DM, using Fisher information matrices. ML wavefront sensing is computationally demanding and we are studying strategies and hardware implementations to address the computational exigency of estimating a large number of parameters (e.g. large number of actuator signals). References 1. H. H. Barrett, C. Dainty and D. Lara, Journal of the Optical Society of America A 24, 391(February 2007). 2. E. P. Wallner, Journal of the Optical Society of America 73,1771 (1983). 3. R. C. Cannon, Journal of the Optical Society of America A l2,2031(Septem-

ber 1995). 4. H. H. Barrett and K. Myers, ~o~ndations of Image Science, 1st edn. (Wiley Interscience, October 2003). 5. N. Roddier, Optical Engineering 29, 1174(0ctober 1990).

TIME WAVE FRO^ SENSING FOR FAST ~ I ~ H - P O W ELASER R ~EAMS J. M. BUENO,+B. VOHNSEN, P. M. PRIETO, L. ROSO* AND P. ARTAL Laboratorio de dptica (edifcio ClOyN), Universidad de Murcia, Campus de Espinardo, 30071 Murcia, Spain *Servicio Lriser, Universidad de Salamanca, Salamanca, Spain A real-time Hartmann-Shack sensor adapted to measure ultrafast and high-power laser beams has been built. Wavefront aberrations were measured at two different temporal rates. Results show that for a 7-mm pupil, most of the root-mean square wavefront error is due to low order aberrations. This still happens after re-alignment of the optics inside the cavity. Wavefront was found to be stabIe over time, indicating an initial potential benefit with only static correction. For higher intensity regimes, we expect larger temporal variability and the need for real time corrections.

1. Introduction In an ultrafast (femtosecond) high-power (Gigawatt to Terawatt) laser, the emerging beam is affected by the amplification processes and the beam transport. Pump shots, vibrations and thermal changes might affect the laser stability and modify the wavefront aberrations (WAS) of the beam. High-power lasers are dynamic optical systems and the WAS of the emergent beam might suffer fluctuations at different temporal rates. All this results in undesired optical path differences, reduced output power, increased spot diameter at the focal plane and decreased intensity at the focus. During the last years there has been an increased interest in measuring and improving the quality of high-power laser systems by means of wavefront sensing techniques [1,2]. The knowledge of the wavefront of the laser beam is the first step to produce well focused and driven high-energy short pulses by subsequent wavefront correction using adaptive optics. In this sense, a fast and reliable instrument is required for an accurate pulse wavefront measurement. Wavefront sensing devices in high-power lasers are often placed within the cavity [2,3], however many of these lasers are laboratory protypes (PHELIX, Vulcan,. ..) that are not commercially available. Moreover, a large number of the optical elements are customized and/or home-made to be suitable. A few commercial elements based on shearing interferometry have become available. Here we analyze the WA stability of a commercially available high-power laser at two different temporal rates. For this aim we have developed a Hartmann-Shack (HS) wavefront sensor able to measure the WA of the laser

'E-mail: [email protected]

175

176

beam in real time at 25 Hz (video rate). The sensor has been placed at the output of the laser system.

2. ~ x p e ~ m e n t asystem 1 and procedure Figure 1 shows a schematic diagram of the system used in this work. We used a Ti-Sapphire laser [Legend, Coherent, St. Clara CAI with 1 Mlz repetition rate, 130 fs pulse width and peak powers of up to 10 GW. The 797-nm horizontally polarized high-power emergent beam is incident onto an optical window at approximately its Brewster angle (cps). This results in a reduction in power of about 1/1000. The reflected beam passes an aperture (AP),a set of metallic neutral density filters (NDF) to avoid the damage of the microlens (ML) array and the CCD camera. This CCD finally records the HS images which are continously monitored and acquired at a rate of 25 Hz. Both ML and CCD are commercial off-the-shelf with no special requirements. The inset in Figure 1 is an example of a typical HS image registered with this experimental configuration. From the HS images the WA of the laser beam is reconstructed as a Zernike polynomial expansion up to 6” order within a 7-mm pupil [4].

NDF

Figure 1 . HS wavefront sensor to measure the WA stability of a high-power leaser beam.

The experimental procedure is described in the following. Laser beam WAS were measured at two different temporal rates: 25 Hz (short term) and 10” Hz (‘slower’ short term) Hz. All measurements were carried out during a unique experimental session which lasted several hours. Three months later, the optics inside the laser cavity was re-aligned, cleaned and the pumping optimized. The experiments were then repeated at the same temporal rates.

177

3. Results Figure 2 shows two-hour apart WAS and the corresponding calculated far-field point spread funtions (PSFs) of the laser beam for a 7-mm pupil. The root-mean square (RMS) error was 4.42 microns for both WAS.

Figure 2. Phasewrapped (2n) WAS including Zemike terms from 2"dto 6" order (left) computed from HS images registered 2 hours apart, and corresponding PSFs (right).

Figure 3 presents the values of total RMS for the WAS computed at two temporal rates, together with the mean. The plot on the left corresponds to the 25 images registered during 1 second (one every 40 ms -short term-). Data of the Hz plot on the right are those computed from HS images registered at during 3 hours (i. e. one image every 15 minutes -'slower' short term-). For the former the difference between the maximum and the minimum values was 0.032 microns, which corresponds to 0.7%. This difference was 0.020 microns for the 'slower' short term set of measurements (0.5%). These results show that the measured WA was stable over time, albeit noise may also play a role due to the limited number of HS sampling points and Zernike terms included.

-1

4,50

4.45

J.I

.r;

F: 4.40 cl

4,35

4.30 0

250

500

750

Time (ins)

1000

0.0 0.5

1.0

1.5

2.0 2,5

3,O

Time (hours}

Figure 3. RMS values for the WAS computed from HS images registered at two different temporal rates: (left) 25 Hz during 1 second and (right) 0.001 Hz during 3 hours. The white symbols correspond to the mean and the error bars are the standard deviation.

178

In order to analyze the influence of individual Zernike terms in the total WA as well as the changes with time, Figure 4 shows the average values of these coefficients up to 4” order during both 1 second and 3 hours. The analysis of these Zernike terms shows that for the pupil size used about 95% of the RMS wave-front error is contained within the 2”dorder Zernike modes: primarly astigmatism (z-,”and z:)and defocus (2;;). Comparing both temporal scales, the values for the Zernike coefficients hardly change, which corroborates the stability also shown in Figure 3. To explore the laser WA stability we also computed the WA taking the first HS image as a reference (instead of using a plane reference). Figure 5 shows the results. The “residual” RMS values range between 0.042 and 0.062 microns.

-2

‘

I

Zm1*

ta1m

Figure 4.Individual Zernike coefficient values of the WA (up to 4” order) for the high-power laser beam. Data correspond to the mean during 1 second (white bars) and 3 hours (black bars).

Figure 5. Wrapped WAS for the high-power laser beam using the first HS image (time=O) as a reference. Left to right panels correspond to the time sets of 1 s, 1 hour, 2 hours and 3 hours.

After three months of this first experiment, the elements inside the amplifier were re-aligned to optimize the output energy. Then the measurements were repeated again for the same conditions and temporal rates. Figure 6 presents two WAS computed from HS images registered 1 hour apart together with the corresponding PSFs. For this case the RMS values were 2.16 microns for both

179

WAS. The Strehl ratio was also the same for the two PSFs (0.002). Although some small changes do occur, the WA is still found to be very stable.

(right) computed from HS images the optical elements inside the cavity were re-aligned.

Figure 7 depicts the RMS values of the WA of the high-power laser beam as a function of time, before and after the cavity re-alignment. Moreover, the RMS values for 3rd order and higher are also shown (plot on the right). The variability was similar in both sets of measurements. The maximum difference in RMS was 0.016 microns, which corresponds to 0.7%. An overall decrease in the total RMS of approximately 50% was found. Despite the careful alignment of the internal laser optics, the 2ndorder Zernike modes are still dominant (-90%). Conversely, when excluding defocus and astigmatism, the RMS increased around 50% after the internal optics re-alignment.

0

0.5 (I)

1.0

1s 30 4S

Time

(Inin)

05

0

(s)

1.0

15 30 4S

Time

(min)

Figure 7. Values of RMS for the laser beam WAS as a function of time: total RMS (left) and RMS for 3* order terms and higher (right). White and black symbols correspond to the data before and after the cavity re-alignment respectively.

With regard to individual Zernike coefficients (not shown), astigmatism was noticeably reduced, although a large amount of defocus was still present (about 2 microns). Values for spherical aberration remained similar.

180

Once the stability and magnitude of the high-power laser beam WA has been explored, the question would be: How would laser focality improve if wavefront corrections with adaptive optics would be implemented? To partially answer this question we have simulated the effect of an element of correction (i.e. a deformable mirror or alternatively a liquid crystal spatial light modulator) for the different orders of the WA (Figure 8).

Figure 8. Predicted improvement in the quality of the high-power laser beam by removing different terms of the Zernike expansion: WAS (upper row) and PSFs (lower row). No defocus, far left column; no second order terms, second column from the left; no third order terms, third column from the left and no fourth order terms, far right column.

The WA in the far left of Figure 6 includes all orders (excluding piston, tip and tilt) and is taken as a reference for correction. We first removed the defocus term. Panels on the left of Figure 8 present this result for both the WA and the PSF: both noticeably improved, although some astigmatism still remained in the PSF. RMS was 0.33 microns and the Strehl ratio of the PSF increased up to 0.148. When eliminating the 2"d order astigmatism terms from the WA (second column from the left), RMS and Strehl ratio values were 0.28 microns and 0.175 respectively. The removal of 2"d order terms is the classical static correction. There is a slight improvement in the WA and PSF when eliminating the contribution of 3rd order terms (third column of panels, RMS=0.25 microns, Strehl=0.199). This operation requires an active corrector element, as does the removal of the 4" order terms. When these 4" order terms are not taken into account the PSF noticeably improves and the energy concentrates in a much smaller spot as the panel at the far right bottom corner shows (RMS=O.14, Strehl=0.349).

181

4. Conclu§ion§

We built a real-time HS sensor to measure WAS in ultrafast and high-power laser beams using conventional optics. The laser WA was assessed at two different time rates and was found to be stable over time. After intracavity alignments 2ndorder Zernike terms were also dominant. Static aberrations depend on the internal components of the laser, but dynamic ones are directly related to the laser operation. The WA laser stability indicates an initial potential benefit with a static correction only. This correction would lead to a high-quality stable focus and therefore to the energy density required for many experiments. Since a larger temporal variability is expected for higher intensity regimes, corrections using adaptive optics might be required.

Acknowledgments This research has been supported by the Spanish Ministerio de Educacicin y Ciencia (grant FIS2004-02153). eferences 1. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,”

Rev. Sci. Instrum. 71, 1929-1960 (2000). 2. M.-H. Heuck, U. Wittrock, C. Hafner, S. Borneis, E. Gaul, T. Kuhl, and P. Wiewior, “Wavefront measurement and adaptive optics at the PHELIX laser,” Proc. 4” International Workshop on Adaptive Optics for Industry and Medicine (Munster, Germany, 2003) pp. 283-290. 3. W. Lubeigt, P. van Grol, G. Valentine, and D. Burns, “Use of intracavity adaptive optics in solid-state laser operation at 1 pm,” Proc. 4” International Workshop on Adaptive Optics for Industry and Medicine (Munster, Germany, 2003) pp. 217-227. 4. P. M. Prieto, F. Vargas-Martin, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann-Shack sensor in the human eye”, J. Opt. SOC. Am. A 17, 1388-1398 (2000).

WA~EFRONTSENSING WITH A RANDOM SCREEN M. LOKTEV1*2*,G. VDOVIN1p2 and 0. SOLOVIEV1 Flexible Optical B. V. ( O K 0 Technologies), Rontgenweg 1, 26.24 BD Delft, the Netherlands 2Electronic Instrumentation laboratory, EEMCS faculty, TU Delft, Mekelweg 4, 2628 CD Delft, the Netherlands *E-mail: mishaQokotech.com A wavefront sensing method is described which is based on comparison of two intensity patterns generated by a random intensity or phase screen in the near diffraction zone. This approach allows t o determine the wavefront slope in any arbitrary aperture point with the resolution limited only by the statistical properties of the setup. Applications include wavefront sensing and optical shop testing. Keywords: Wavefront sensors; correlation analysis; random screen.

1. Limitations of the Hartmann and Shack-Hartmann tests

We propose a novel geometrical wavefront test, which is applicable for highresolution wavefront sensing in optical metrology and adaptive optics. There are many approaches for wavefront measurement in optics, based on estimating the local slopes of a wavefront. The most simple and straightforward technique is suggested by Hartmann in 1900 and modified by Shack in 1971.l The wavefront to be reconstructed is sampled by a mask with many sub-apertures (in Hartmann test) or by a dense array of lenslets (Hartmann-Shack test). The results of the test are very robust and easy to interpret. Various methods of calculation of the spot centroids or Fourier demodulation techniques are used for analysis of the intensity patterns in Hartmann-Shack gensors based on CCD or CMOS imagers. Correlationbased algorithms2 are applied for detecting shifts of spots generated by extended objects and scenes (such as laser beacons, planets and granulation of the sun) - the situations where other methods are not applicable. However, Hartmann and Hartmann-Shack tests have some limitations. 182

183

These are listed below. The aperture is spatially sampled. This sampling limits both the spatial resolution of the HS sensor and the maximum range of the measured slopes. The spots are indistinguishable for periodic arrays, and it is sometimes difficult to determine in which direction a, certain spot has moved; thus, the reconstruction is ambiguous. The wavefront tilts are available only in the points coincident with the centres of subapertures. A large number of subapertures is required for a high spatial resolution. This requirement is in a conflict with the requirement of a large dynamic range. The dynamic range of Hartmann and Hartmann-Shack sensors is limited by the maximum wavefront tilt (i.e., direction of the rays with respect to the optical axis), as for successful reconstruction the spots should not overlap with each other. It means that higher dynamic range can be achieved by using a microlens array with shorter focal length (or, in case of a Hartmann sensor, the distance between the mask and image sensor). At the same time, the precision of the wavefront sensor improves proportionally to the focal distance of the microlens array (or distance between the mask and image sensor). Thus, choice of a proper microlens array or Hartmann mask for a particular application should be a trade-off between the spatial resolution, the range of aberrations to be measured and the precision. If a certain requirement to the spatial resolution, the precision and the range are formulated, the microlens array/mask should be chosen accordingly. In many cases the choice is impossible. Methods to increase the dynamic range without sacrificing the precision have been proposed. Adaptive Hartmann-Shack sensor3 uses a liquid crystal spatial light modulator (LC-SLM) to display diffractive microlenses instead of a static microlens array; this sensor is highly flexible. Another method uses a translatable plate with subapertures placed in conjugate with the lenslet array.4 To increase the dynamic range by a factor of two, three translations of the plate and acquisition of four images are required. However, these methods require relatively expensive hardware and long acquisition procedure. 2. Proposed method

The method we propose can be considered as a modification of a widely used Hartmann-Shack test. In our method, a random amplitude or phase screen

184

Fig. 1. Principle of the wavefront sensor based on a random screen.

is used to test the incoming electromagnetic wave, as shown in Figure 1. The inhomogeneities of the screen develop into a random intensity pattern, which can be registered with an image sensor behind the screen. If scattering is weak, the registered intensity can be considered as a geometrical shadow of the screen. For random phase screens with Gaussian statistics, the spatial scale of inhomogeneities is described by the parameter rg, and the autocorrelation function of phase has the form P(E, ). = (@(x,Y)@(Z

+ E, Y + .I)

= (a2)exp { -(E2

+ ."/.,"}

1

(1)

where @(x, y) is the phase function of the screen. The depth of the intensity modulation behind the screen can be characterized by the scintillation index

I;" =

< I2 > - < I < I >2

>2 1

where I is the intensity. An analytical expression for the scintillation index at a distance z behind the screen was derived in Ref. 5 for the case of weak scattering ((a << 1):

I;" = 2 ( @ 2 )

{A} 1+2;

(3)

where 2, = z/zf and zf = 27rr;/4X. It gives a good insight into the propagation of intensity. It follows from Equation (3) that the phase inhomogeneities develop in the intensity at a distance z M zf,which is determined by the spatial scale of inhomogeneities, and increase to a saturation value at z N 425. The scintillation index increases proportionally to the square of the amount of phase modulation induced by the screen. It should be

185

also noted that fine details of the phase function are converted into intensity modulation first, while large spatial features appear only for larger distances . Speckle patterns are observed in the case of strong scattering, where every speckle is formed by scattering from the whole screen. In this case, features of the intensity pattern (speckles) are no longer localized according to the fine structure of the phase screen, and the geometrical approach to the wavefront testing cannot be applied anymore. Fkom practical point of view, we propose choosing TO according to the minimum resolution that should be achieved by the wavefront sensor. The depth of phase modulation should provide sufficient intensity modulation at a given distance behind the screen but should be sufficiently small to prevent forming of the speckles. The distortion of the wave incident on the screen will result in the distortion of the shadow intensity pattern. Provided the wavefront contains only much lower spatial frequencies than those forming the fine structure of the random pattern, local wavefront slopes can be evaluated from local displacements of the test pattern with respect to a reference pattern (i.e., those generated by a reference wave with a priori-known structure). Local pattern displacement at a certain position within the aperture can be found by locating the maximum of cross-correlation function of the test and reference patterns within a window centered on this point. To make it possible to find the correlation between the sub-patterns, the window should contain as many intensity features as possible; however, it should be sufficiently small to minimize the pattern distortion within the window area. For the reference pattern, the window should be extended by including substantial margins to secure a high range of measured local displacements. When the whole area of the reference pattern is used, the method provides a dynamic range of shifts that potentially covers the whole sensor area, making it suitable for testing large wavefront deformations. The local tilts over the whole aperture can be reconstructed by scanning the position of the measurement window. Pixel-by-pixel scanning allows for a resolution that is limited only by the statistical properties of the screen; however, it may take a significant processing time. To speed up the processing, the aperture can be scanned with a lower resolution or divided into zones according to the sampling required. In the latter case, the most s t r ~ g h t f o ~ asolution rd is to use rectangular sectioning; however, it can be done in a more flexible way. For instance, in adaptive optics applications, the structure of zones should provide a certain geometrical match to the structure of actuators of the wavefront corrector.

186

As the structure of the phase screen is random, it can be considered as an analogue of a random Hartmann mask with non-regular Fourier spectrum. On average, this kind of mask allows to double the number of decomposition modes compared to a regular mask with the same number of sub-apertures.6 The irregular pattern structure allows for location of pattern shifts as large as the aperture size. Based on this result, we expect that the wavefront sensor with a random screen will provide statistically better wavefront representation and higher measurement range compared to a regular Hartmann-Shack sensor. 3. Experimental results

Fig. 2. Experimental intensity pattern generated at 3 mm distance behind a random phase screen illuminated by collimated incoherent light from a red LED (left); reconstruction of a shape of tilted spherical lens using orthogonal sectioning with subsequent modal reconstruction (center) and scanning with a sliding window (right).

Figure 2 shows the results of experimental reconstruction of the phase profile of a tilted spherical lens, illuminated by collimated incoherent light from a red LED and tested by a random phase screen. The reconstruction was performed by two different methods: (1) 8x8 sectioning with subsequent modal reconstruction using 25 Zernike polynomials and (2) scanning with a window of 64x64 pixels with subsequent integration of the wavefront slopes. Both methods produced similar results. In the second series of tests we have measured three different shapes generated by a 37-channel piezoelectric deformable mirror with 30 mm aperture (from O K 0 Technologies); the results are shown in Figure 3. 4. Conclusion

We described the concept of wavefront sensing based on random amplitude or phase screen and presented first experimental results. The method offers

187

Fig. 3. Reconstruction of the shape of 37-channel piezoelectric deformable mirror; response of the central actuator (left); response of three actuators at the edge (center); response t o random combination of the actuator signals (right).

a number of advantages. As we have shown, the dynamic range of this sensor is not limited by the mask sampling. A random structure of the mask provides statistically better representation of the wavefront compared to the methods using regular sampling. The method is highly flexible for the user - the number of samples and structure of sub-apertures can be chosen without changing the mask. The resolution of measurement is only limited t o the width of the autocorrelation function of the mask. It also means that a high-resolution mask does not need t o be manufactured with a high precision, which is required for microlens arrays providing similar resolution of measurement. At the present stage, the method is slow for high resolution analysis; however, faster devices can be implemented using optical crosscorrelators and FFT processors. In our opinion, the sensor proposed has a great potential for metrology and adaptive optics applications.

References 1. I. Ghozeil, Hartmann and other screen tests, in Optical shop testing, ed. D. Malacara (John Wiley and Sons Inc., 1992). 2. R. R. Radick, T. R. Rimmele and C. K. Richards, Correlating Shack-Hartmann wavefront sensor (2000), U.S. Patent No. 6,563,572. 3. L. Seifert, J. Liesener and H. J. Tiziani, Optics Communications 216, 313

(2003). 4. G. Yoon, Large dynamic range Shack-Hartmann wavefront sensor (2004),U.S. Patent Application No. 20040227932. 5. B. 3. Uscinski, The elements of wave propagation in random media (McGrawHill Inc., 1977). 6. 0. Soloviev and G. Vdovin, Opt. Expr. 13,9570 (2005).

AVE LATERAL SHEARING I ~ E R F E ATURE TECHNIQUE FOR WAVE FRO IN ADAPTIVE OPTICS

B. WATTELLIER, I. DOUDET, S . VELGHE PHASICS XTEC BAT 404 - Campus de 1 'Ecole Polytechnique F-91128 Palaiseau, France [email protected] J. PRIMOT ONERA Chemin de la HuniPre F-91128 Palaiseau, France We present in details the principle of Quadri-Wave Lateral Shearing Interferometry and its inheritance from the Hartmanu family. We show how this new technique has been optimized for laser metrology and how its features make it a good candidate for adaptive optics not only for laser applications but also for astronomy, ophthalmology or microscopy. We finally insist on its application to the control of segmented beam or optics.

1. ~ntro~uction Since the first experiments in astronomy, adaptive optics has been used in more and more applications, from laser to eye correction, including telecommunication, microscopy and biology. Until recently the deformable mirrors actuator density was very low and the constraint on wave front sensor resolution was low. However demands for high resolution wave front shaping has dramatically increased from the need for image deconvolution to the use of liquid-crystal spatial light modulators, including membranes based on MEMS or MOEMS which now have more than 1024x1024actuators.

uadri-Wave Lateral Shearing I n t e ~ e r o m e t ~ In the 90s, the concept of lateral shearing interferometry has been extended to more than 2 waves by Primot and coworkers [ 11. This has lead to the invention 188

189

of multiwave lateral shearing interferometry and, in particular, to the compact quadri-wave lateral shearing interferometer (QWLSI). The principle of this technique is very simple : the wave front is divided in replicas by a diffractive optics (see Figure 1). Each replica propagates and therefore separates from the other ones. In the region where they still overlap, the interference pattern gives access to the phase difference between each couple of diffraction orders. Because they have separated and if the propagation is short enough, this phase difference is proportional to the local phase gradient. Consequently each couple of replica gives an information on the gradient along one direction (which is determined by the two replicas k-vector difference). The phase gradients are recovered thanks to Fourier analysis around each carrier-frequency associated to each replica couple. CCD chip

2-3rnrn

Figure 1. Principle of the Multi-Wave Lateral Shearing Interferometry, illustrated in the case of four wave interference. The beam is incident from the left. It is first diffracted and the interferences are recorded by the CCD chip.

This principle has been applied in laser metrology to 3-wave interferometers [2], which are the simplest version, The optimization process led to 4-wave interferometers, thanks to the so-called Modified Hartmann Mask (MHM) [ 3 ] . This 2D diffractive optics has been designed to concentrate more than 90% of the power in the 4 first +I-1 diffraction orders only. It is therefore a good candidate to make a Quadri-Wave Lateral Shearing Interferometer (QWLSI). In the case of QWLSI, the observed interference pattern is a Cartesian grid of sinusoidal fringes. If the wave front is flat, the grid pitch is the same everywhere in the pupil. If the light contains aberrations, the grid is deformed and the deformations are proportional to the local phase gradients. Since the fringes are sinusoidal, they are very easy to sample and deconvolve with

190

Fourier-based algorithms (see Figure 2). Signal processing theory indicates that 2 points per fringe could be enough for such a sampling. However, for a sack of measurement dynamics, a lower resolution of 4 sampling pixels per fringe is preferred. With a conventional VGA CCD camera, 160x120 phase maps are recovered, which represents the top of the resolution for other techniques based on grid deformation, like the QWLSI, that are for instance Hartmann, ShackHartmann, etc...

Figure 2. Schematic of the QWLSI algorithm based on Fourier analysis. It is here illustrated for a spherical aberration. Please notice the coma shape the harmonics, which contain the phase gradient information.

3. Adaptive optics with QWLSI Multiwave lateral shearing interferometry has been quickly applied to laser metrology for high power laser correction [4]. The introduction of the MHM made it possible to have a compact version of the interferometer, which eased its diffusion among laboratories. Several high power laser projects around the world chose to use this technique for their adaptive optics loops, mainly because of its low sensitivity to intensity modulations. Because of its resolution, the wave front sensor acts as the error signal generator for the loop but also as a near-field diagnostic both for intensity and wave front. QUrLSI is a good candidate for adaptive optics and especially for high resolution adaptive optics. It has been coupled to optically-addressed spatial light modulators in the aim of correcting binary phase plates [5] or to shape laser beams in the focal plane [ 6 ] .It can be used to control holograms used in optical tweezers for instance. For instance, we managed to generate aberrations higher than 10 waves with a 2n only phase modulator (see Figure 3).

191

Figure 3. Example of high resolution wave front control with a QWLSI used with a liquid-crystal spatial light modulator. The top figure is the desired Fresnel lens hologram. The bottom left image is the measured wave front. The Peak-to-Valley is 13.3 waves at 635 nm. The bottom right image is the difference between the wave front and a perfect parabolic wave front. The error RMS is 0.2 wave. Some rings are clearly seen on the error map. They are due both to the fact that the 2p level was not perfectly set and to the finite size transition of the spatial light modulator.

For astronomy applications, because not many pixels are necessary to sample a phase measurement point, the computation time is potentially very short. For low light detection, the interest of sinusoidal patterns with respect to sinc-like Shack-Hartmann patterns, is that the signal is less contrasted, making it less sensitive to noise at equivalent detection signal-to-noise ratio.

earn or Mirror Phasing with a QWLSI In addition to the application of QWLSI to classical adaptive optics for lasers, new prospects have been discovered for the metrology of stepped and multipupil wave fronts. If we consider the theory of multi-wave lateral shearing interferometry, we see that we have access to the phase difference between two points separated by the shearing distance. If the wave front is not continuous, the recovered information is the height of the discontinuous step. It has been also shown that the combination of two measurements at two different wavelengths increased the step height dynamic range from half a wave to potentiaIIy 10 to 50 waves[7].

192

It was also experimentally demonstrated 181 that it is possible to use QWLSI to measure multi-pupil laser beam wave fronts, even with no energy between the pupils (see Figure 4). This technique will ease adaptive optics in the case of segmented optics for astronomy, because a unique device will phase the segments and be able to control the residual aberration correction. The technique is already applied in a Petawatt project, where the final optics need to be segmented.

-C 8

$

600 500 400 300 200

$100

1

0

50 100 150 200 250 300 350 400 450 500 Mirror displacement (nm)

Figure 4.Measurement of the relative piston between two sub-pupils of a segmented laser beam, as measured with a QWLsI. The accuracy of this measurement is within 40 nm, whereas this has been improved recently with averaging techniques and more robust interferogram analysis algorithm. (Extracted from ref [8])

5. Conclusion In summary, Quadri-Wave Lateral Shearing Interferometry is a good solution for adaptive optics, though it has currently been mostly applied to laser correction. Its potential is very big, because of its high resolution (no need for large cameras), its insensitivity to intensity modulations. New prospects for segmented or multi-pupil beam adaptive optics are expected, which opens wide the road to coherent addition of hundreds of laser beams.

eferences 1. 2. 3. 4. 5. 6. 7. 8.

J. Primot et al, JOSA A, 12, p. 2679-2685 (1995). J. -C. Chanteloup et al., Opt. Lett. 23,621-623 (1998). J. Primot et al, Appl. Opt., 39, p. 5715-5720 (2000). B. Wattellier et al, Opt. Lett., 29, p. 2494-2496 (2004). J. -C. Chanteloup et al, Opt. Lett. 23,475-477 (1998). B. Wattellier et al, Opt. Lett. 27,213-215 (2002). S . Velghe et al, Opt. Express, 14, p. 9699-9708 (2006). S . Mousset et al, Opt. Lett., 31, p. 2634-2636 (2006).

N VI

U ~ ~ E OF N T 0 R T EG ~ ~ ~ I N G

IT

P. HARRISON, D.M. CUEVAS, G.R.G. ERRY, P. FOURNIER Kestrel Corporation, Albuquerque, NM, 87109, USA

L. DIM-SANTANA, C. TORT1 Henry Wellcome Laboratories for Visual Science, Department of Optometry and Visual Science, City University, Landon Kestrel Corporation with the collaboration of City University is in the process of demonstrating a novel methodology to measure in vivo ocular aberrations that employs a Distorted Grating Wavefront Sensor (DGWFS) as a more efficient alternative to the well known Shack Hartmann (SH) wavefront sensing technique. The SH sensor is the most common sensor available to measure ocular aberrations. However, the SH sensor’s dynamic range is limited, very sensitive to opacities, and to retinal and intraocular scattering. An alternative sensor is the DGWFS. The performance of the DGWFS is relatively unaffected by opacities, scattering and speckle. Also it bas an added advantage of an extended dynamic range whilst maintaining high sensitivity allowing high precision measurements to be made without the need for complex defocus and astigmatism correction. The DGWFS was used to take in vivo measurements in a laboratory environment. Seven eyes, from four subjects were successfully measured with the system. Dynamic measurements of accommodation were recorded with targets at distances ranging from 0.25 to 3.2 meters from the subject’s eye.

1. ~ntrQdu~tiQn There has been a growing need for a device that will measure accommodation in a human subject; not only for measurement per se of accommodation, but also in the detection of the benefits or toxicity of drugs. Further applications may include the detection of abnormal brain function that may manifest itself as an inability to correctly accommodate to objects at different ranges. Such accommodation measurements require a high performance instrument. The human eye can accommodate from infinity to close range in under half a second [ 11. As it is required that measurements occur during this time there is a requirement for the system to essentially ‘freeze’ the aberrations during measurement, and that there is enough temporal resolution to see progression from frame to frame. A further requirement is that the device can measure the 193

194

large change in focus aberration when a person changes from viewing an object far away to a close by object. This ideally needs to be achieved with no moving parts in the instrument. Finally as the subjects for this instrument will tend to be older, there is a requirement that the device will operate under conditions where there are opacities in the eye. With such extreme specifications on the instrument, a Shack-Hartmann sensor is not ideally suited to this application, so another technique using a distorted diffraction grating as a curvature sensor was investigated.

vefront sensing technique The theory [2] and general implementation [3,4] of the DGWFS have previously been published and will not be discussed in detail here, however a schematic of the implementation is shown in Figure 1. An imaging system with a distorted diffraction grating images planes either side of the pupil plane onto a detector. The two sets of data that are collected on the detector can then be used, via application of the intensity transport equation [2] to give the wavefront at the pupil plane.

Figure 1: Implementation of wavefront curvature sensing using a distorted diffraction grating

3. Experimen~lImplementation The DGWFS has been used to measure aberrations in the eye in the past however these experiments used a complex instrument including both DGWFS and SH wavefront sensors and defocus and astigmatism compensation mechanisms. These features greatly complicated the optical system and made obtaining good measurements from the human eye difficult and unreliable. The aim of this experiment was to implement a much simpler optical system to

195

obtain the best data possible and to show some of the expected benefits of using a D G W S for ophthalmic aberrometry. The DGWFS was integrated into a complete system as shown in Figure 2.

L

-

\

Relay

Wavefront Sensor

Figure 2: Schematic representation of the optical set-up

A small diameter laser beam is projected onto the retina, the returned signal is captured and relayed to the wavefront sensor. Included in the illumination leg of the system are two targets that the subject can visualize. The near target was 400mm from the eye, and the far target was 3100mm from the eye. The light source was a 780nm laser diode, with a 2mm input beam at the eye. The grating in the wavefront sensor had a plane separation of 0.7382m, and a maximum input diameter of 14mm, although only lOmm was used in this experiment. The W S camera was a Phoenix 7.1 camera from Vision Research, capable of 102,000 frames per second if required. For these experiments the camera was run at either 100 frames per second or 1000 frames per second. A total of four subjects were imaged during the experiment.

. Calibration Initial testing of the experiment was performed with an artificial eye, the properties of which can be closely controlled. The eye consists of a 22mm focal length lens and a hemispherical backing made of Spectralon with a 4% reflectivity. In front of the artificial eye, aberrations in the form of ophthalmic lenses can be introduced from -4SD to 4.5D. Data using the artificial eye was collected to calibrate the wavefront sensor. The data is shown in Figure 3. The data has a RMS error of 0.37 waves over the measured range (220 waves of defocus), the majority of which is not due to the wavefront sensor, but manufacturing tolerances of the ophthalmic lenses used to introduce the defocus aberration.

196 30 20 10

0

- 10 -20 -30

Figure 3: Theoretical and actual defocus values measured by the DGWFS

5. Results The first results from the experiment were taken statically, that is the subject focused on one of the two targets, and then data was collected. This was done to ensure that the W S had sufficient dynamic range to collect data from the two extremes of the range. Figure 4 shows the raw data, the calculated wavefront, and the Zernike coefficients for the two wavefronts.

Figure 4(a): Raw data and calculated wavefront (near). (b): Far measurement. (c): Zernike coefficients.

197

Once the static testing had been completed, a set of dynamic measurement were taken. The camera was set to record 100 frames per second, and the subject was told to focus on one target and then refocus on the other target. A summary of these results is shown in Figure 5.

Figure S(a): Subject focused at close target. (b): Focused at far target. (c): Focused close to far. (d): Focused close to far, camera set at 1000 fps.

This data shows that the WFS successfully collected the data with sufficient temporal resolution to resolve the changes that occur as the subject changes accommodation from one target range to the other. It is also interesting to note that when this subject is focused on the near target there is a marked increase in higher-order aberrations. Figure 5(d) also shows that the WFS was capable of collecting data at 1000 frames per second. The data in this case has more noise due to the decrease in signal-to-noise ratio of the collected data. The final experiment performed on the WFS was to examine the problems of observing through opacities that can appear in the eye. The artificial eye was used for these experiments, to try and control the opacities that were being introduced into the system. Applying high vacuum grease to the front surface of the lens allowed an opaque region to be defined; varying the amount of grease changed the density of the opacity.

198

To provide a visualization of the density of the opacity that had been applied to the lens an image was taken through the lens and grease prior to collecting the wavefront from the artificial eye. The resultant images and wavefronts are displayed in Figure 6. The data in Figure 6 shows that the WFS still measures a wavefront as the opacity increases, but the wavefront tends to be smoothed out by the scatter. Further work will concentrate on mitigating this effect.

Figure 6(a), (b), (c): Images and resulting wavefronts as the amount of applied grease is increased.

6. ~ o n c l ~ i o and n s Future Work

A distorted grating wavefront sensor (DGWFS) has been shown to work when collecting high speed aberration data from human eyes. The dynamic range of the WFS is compatible with the range of accommodation of an eye without the need of resorting to external defocus or astigmatism correction schemes, in this case 24.5 Dioptres of defocus. This allows the WFS to be compact and very robust as there is no need for moving parts. The WFS has also been shown to be sensitive enough to cope with the low signal-to-noise when taking such measurement from an eye, even up to 1000 frames per second. Some work on characterizing the performance in the presence of opacities has been started, although this will need expanding to properly give quantitative results. Further work on this experiment will fully examine the sensitivity of the wavefront sensor to opacities within the eye by using appropriate, well-defined scatter sources placed in the artificial eye structure.

199

eferences 1. Maruenda, F. B., Ref's eye for the fast guy. Student BMJ, Jan 2005, p8-9. 2. Woods, S. C., and Greenaway, A. H., Wave-front sensing by use of a Green's function solution to the intensity transport equation. J. Opt. Soc. Am.A, 2003.20: p. 508-512. 3. Otten, L. J., Lane, J., Erry, G. R. G., Harrison, P., Weaver, L. D., and Martin, G., Comparison between a Shack Hartmann and a distorted grating wavefront sensor. in Optics in Atmospheric Propagation and Adaptive Systems V, SPIE 4884,2002. Crete. p. 176-185. 4. Harrison, P., Erry, G. R. G., Otten, L. J., Cuevas, D. M., and Weaver, L. D., Closed Loop Adaptive Optics Comparison between a Shack Hartmann and a Distorted Grating Wavefront Sensor. in Optics in Atmospheric Propagation and Adaptive Systems VI, SPIE 5237.2003. Barcelona, Spain. p. 186-197.

OSITION-SENSITIVE DETECTOR DESIG FOS U ~ S U CMOS A ~ LAYOUT S T ~ T E ~ I E ARTMA~-SHAC WAVE ~ FRO^ SENS DAVIES W. DE LIMA MONTEIRO, LUCIANA P. SALLES, PEDRO RETES 0ptMAlab,Department of Electrical Engineering, Universidade Federal de Minas Gerais Av. Antdnio Carlos, 6627 - Pampulha ([email protected]) Belo Horizonte - MG, 31270-010, Brazil ANDRE s. 0. FURTADO Centerfor Semiconductor Components, UNICAMP, Campinas, Brazil GLEB VDOVIN Electronic Ins~rumentationLab., Delft University of Technology DelJi. The Netherlands

A bi-dimensional array of position-sensitive detectors (PSDs) can be used as the focalplane of a Hartmann-Shack wavefront sensor. CMOS is a mature standard silicon technology with a potential for low cost mainly because of its vast availability and high yield, however it is not optimized for photodetection and its layout rules are intended to guarantee reliable electronic functionality. This paper presents a position-sensitive detector based on active pixels and fabricrated in a n-well single-poly 1.6pm CMOS technology, where several unusual strategies in both electronic and imaging layout have been employed to improve the photogenerated signal and to decrease noise. A 2D array of these detectors can be later integrated together on a single chip to serve as a wavefront sensor suitable for low-light applications. This work is part of an effort to later combine sensitivity, signal-processing functionality and high refresh rate into a single chip, while also maintaining a potential for serial production and low cost for this wavefront front sensor.

1. Introdu~tion In applications where only faint light is available for measurement, such as ophthalmology, a Hartmann-Shack wavefront sensor must rely on sensitive photodetectors with an acceptable signal-to-noise ratio (e.g.: SNR> 20dB). An array of position-sensitive detectors (PSDs) and CCDs or CMOS cameras are 200

201

eligible options. The advantages of a custom sensor, based on PSDs, compared to currently available cameras have been reported in reference [l], where the major advantages are the flexibility of layout and electronics tuned to the application. This paper presents the results of alternative active pixel structures clustered as a PSD and fabricated in a standard 1.6p.m CMOS technology. The use of a supra-micro technology is beneficial both in terms of photodetection and dynamic range of the signal in the analog domain. The chosen PSD is the quadcell (QC) because of its simplicity, high optical fill-factor and the absence of either thermal resistive noise or the requirement for complex embedded electronics for centroid computation [2,3,4]. Each of the four detectors in the QC, together with its respective electronic circuit, constitutes an active pixel; the term active meaning the employment of an in-pixel buffer stage. According to the American National Standards Institute (ANSI, Z- 136.1 standard)[5], the maximum permissible exposure (WE) for 25ps, at h=0.63p.m, is 1.7XmW. Considering that no more than 1% of the incident light is reflected by the retina, a very faint reflected beam reaches the wavefront sensor, where in case of 36 sampled spots, each takes up at maximum less than about 0.5p.W. These statements lead to two main issues: the photodetector noise equivalent power (iWP) should be considerably lower than 0.5p.W; and each pixel should be able to detect and store a signal from a chopped light source, until it is transferred to the readout electronics. We pursue high quantum efficiency and low noise by solely selecting convenient circuitry and violating some recommended design rules, without either employing any additional process steps or modifying the traditional process flow and specifications [6].

2. Pixel S t ~ ~ t u r e The alternative character of the structures lies on in-pixel circuit strategies and on the intentional violation of standard process design rules. The perimeter of each photosensitive area is that of a quarter-circle (200pm radius), leading to minimization of leakage current, which is directly related to dark-current noise [4,5]; it features about 20% less noise than its equivalent square structure, which is more significant immediately after pixel reset, when reverse bias is at its maximum. On top of the photosensitive area the base of a dielectric-layer stack has been chosen to be a very thin oxide (25+2.5nm), traditionally meant as gate oxide, instead of a thick LOCOS oxide (710rt70nm), intended for device isolation. This choice enhances transmittance for 633nm light and minimizes non-uniformity across pixels in a larger array due to process variations.

202

In the chosen standard 1.6-pm CMOS technology, the main junction is that between n-well and the p-epitaxial layer, and its depth is 2.9pm. This enhances effective photoconversion in silicon for wavelengths above 600nm, as compared to other shallower junctions available in the process (e.g.: p+/n-well, n+/p-epi). In ophthalmology h>600nm are preferred over shorter wavelengths[6]. The deep n-welUp-epi junction is spatially modulated to increase the junction area and the space-charge volunie in order to enhance the drift component of the photogenerated signal. The modulation is obtained by designing concentric n-well band rings whose border distances are shorter than the minimum recommended spacing, which leads to partial diffused n-well superposition. Figure l a shows a top view of the quad-cell (QC) layout: %-circle photodetectors plus adjacent rectangular regions comprising the electronic circuitry. The response of a QC is known to be non-linear, exhibiting a sigmoidal behavior. To counterbalance this non-linearity the region closest to the rightangle corner, with a radius of 65pm, features an additional shallower junction, conventionally intended as source/drain to PMOS-FETs, to improve sensitivity (proportional to the quantum efficiency) at the central part, resulting in the linearization of the QC response (Figure lb). Optimal linearization depends on the ratio of the central junction lateral size to the effective spot radius, which can be assessed for each particular spot profile. A linear response reduces considerably the computational effort to obtain the spot-cebntroid coordinates from the pixel signals, consequently reducing the power and footprint of an intended on-chip processor.

Figure 1: (a) Layout of the quad-cell with %-circlepixels; (b) photodiode cross-section:modulated junction and additional junction at one comer.

203

In contrast to traditional imagers, the intended QC pitch for the regarded wavefront sensor will lie between 8OOpm to lOOOpm, which grants sufficient interstitial room for the proposed circuitry plus any additional pre-amplifier, analog-to-digital converter, and signal-processing circuitry. The integrated electronics includes: buffer amplification to isolate the pixel capacitance from the signal line, increasing operational frequency; transfer switch (T,) to store a given signal level at the signal node before readout (important for pulsed sources); a FTT to reset the reference voltage level at the signal node just prior to signal detection; a pixel select switch (Ts); and an address-signal delay line and dummy analog switches to mitigate undesirable charge-injection in the circuitry (71. Figure 2 shows a simplified schematic of the current pixel.

Figure 2: Simplified pixel schematic.

3. Results Response linearization due to the increased efficiency (double-junction) in the central region can be seen in the simulated fit-error graph shown in Figure 3. For a sinc spot with 80-pm effective radius, the truly sigmoidal response of a square homogeneous QC is contrasted to the less intense sigmoidal response of a circular homogeneous QC and to the more linear response obtained with the circular double-effiency QC, whose central p+/nwelYp-epiregion renders a 50% increase in quantum efficiency. In the interval [-8Opm, 8Opm], the standard deviation of the latter QC is below 0.4%. There is a compromise between optimal linearity, position resolution and response range; the latter two parameters are associated with the curve slope, which incidentally depends on the spot effective radius and profile.

204 0,081 -0-sauare

QC

C -0.06-50 0 50 x, spot-centroid position Cm]

-100

100

Figure 3: Response of a homogeneous quad-cell and that of an enhanced circular cell.

To estimate performance, several parameters demand mutual optimization: spot profile (sampling masMlens dependent), radius of the central region (design dependent) and relative efficiency between central and peripheral regions (technology and wavelength dependent). When the active quad-cell is swept with a 0.2pW spot slightly out of a lens focal plane (effective radius 30pm), its measured response is indeed linearized and yields a standard deviation of 0.7% from a linear fit in the range [-5Opm, 5Opm], which translates as a position resolution of 2pm (Figure 4).

-

2

-1,o

x8 -150 -100 -50 0 50 100 150 x, spot-centroid position [pm]

Figure 4: Response of the active QC for a close to sine-spot.

The alternative pixel structure fabricated has outperformed the previous design, which was based on square conventional passive-pixel quad-cells [S]. In a randomization of Zernike polynomials, based on no specific turbulance statistics, the resolution of the double-efficiency QC in terms of the detected spot-centroid position suggests a wavefront precision of h/50 (h=633nm) for a 0.2pW spot (SNR=SOdB), and h/30 for a 0.04pW spot (SNR=38dB). For 2 5 p

205

signal integration, dark current is negligible and does not corrupt the integrating signal. If left exposed in the dark the pixel only saturates after 150s.

. ~onclu§ions This presented CMOS position-sensitive detector is a key structure for the design of a new dynamic wavefront sensors version. The presented PSD is a traditional quad-cell device based on active pixels and featuring several unusual yet compliant layout strategies. This is a promising solution to combine low-light sensitivity, processing functionality and high speed (f52kHz) on a single wavefront sensor silicon chip, also offering potential to serial production and affordable costs.

Ac~nowledg~en~ The authors acknowledge the support of the State of Minas Gerais research agency FAPEMIG, the national agencies CAPES and CNPq; STW (Dutch Technical Foundation) and DIMES in The Netherlands. They also acknowledge the support given by Edilla M. Fernandes, Prof. Fltivio Plentz, Prof. Ado Jcirio from the Physics Department (UFMG); and Prof. J. A. Diniz from UNICAMP.

eferences D. W. L. Monteiro, T. Nirmaier, A. Theuwissen and G. Vdovin, IEEE Sens. J 5 , 1530 (2005). 2. M. Tartagni and P. Perona, Electronic Lett. 29, 181I (1993). 3. T. Nirmaier, G. Pudasaini, and J. Bille, Opt. Express 11,2704 (2003). 4. B. H. Pui, B. Hayes-Gill, M. Clark, M. G. Somekh, C . W. See; S. Morgan and A. Ng, IEEE Sens. J. 4,787 (2004). 5. J. Liang., A new method to precisely measure the wave aberrations of the human eye with a Hartmann-Shac~-Wavefront-Sensor, PhD Thesis, University of Heidelberg (1991). 6. S. A. Campbell, The Science and Engineering of Microelectronic Fabrication, 2nd ed., Oxford University Press (2001). 7. S. Sze and K. Ng, Physics of Semiconductor Devices, 31d ed., Wiley (2007). 8. M. Johnson, Photodetection and Measurement, McGraw-Hill(2003). 9. J. Potter, H. Queener, J. Lin, K. Thorn and A. Awwal, Adaptive Optics for Vision Science, Wiley (2006). 10. P. Allen and D. Holberg, CMOS Analog Circuit Design, 2"d ed., Oxford University Press (2002). 1 1. D. W. L. Monteiro, G. Vdovin and P. Sarro, Sens. Actuators A109,220 (2004). 1.

APT~VEOPTICS SYSTEM TO COM COMPL~X- SHAPE^ ~ A V E F ~ O N T S MIGUEL ARES Center for Sensor, lnst~mentationand System Development, UPC (www.cd6.upc.edu), Terrassa, Spain SANTIAGO ROY0 Center for Sensor, Instrumentation and System Development, UPC (www.cd6.upc.edu), Terrassa, Spain Free-form lenses are being continuously introduced in the m k e t due to their superior performance when compared to classical designs. The fabrication of accurate free-form lenses depends strongly on the possibility and accuracy of measurement. We present an adaptive optics (AO) system within an open-loop configuration to accurately measure in a single shot lenses that have a complex shape. Once the compensation capabilities in open-loop have been demonstrated, we tested a commercial progressive addition lens by compensating the whole transmitted wavefront.

1. Introduction The continuous improvements in optical design and manufacturing capabilities are allowing new lenses with complex shapes to become real-world options to many recent commercial products. The introduction of wild aspheric lenses to enhance the optical performance and weight in complex optical systems, the new generation of more comfortable ophthalmic progressive lenses following the market trend of a lens design personalized to the user [ 11, and the novel imaging systems based on folded lenses which extremely reduce the volume and weight of traditional imagers 121, are just some examples that involve new complexshaped lenses. In the lens fabrication process, iterative steps of testing and repolishing are typically needed to ensure a high quality product. Therefore, the fabrication of accurate free-form lenses depends strongly on the possibility and accuracy of measurement. Measurements are commonly done with contact profilometers due to the large dynamic range required, despite the extremely high measurement time taken to get a good spatial resolution. Non destructive high speed sensing solutions are also nowadays available, like the classical 206

207

Shack-Hartmann optical wavefront sensor, although its more limited dynamic range can not typically deal with very complex wavefront shapes. Following this reasoning, we present an adaptive optics (AO) system within an open-loop configuration to accurately measure in a single shot lenses that have a complex shape, by means of compensating the whole transmitted wavefront.

2. Adaptive Optics System The A 0 principle is based on the local modification of the phase of a distorted wavefront to compensate for its aberrations. Although A 0 systems can be rather complex, the basic principle is quite simple. In conventional AO, the distorted wavefront is measured with a wavefront sensor and compensated by introducing its conjugate in the phase correcting device by means of a control system. As mentioned, two optical elements are involved in every A 0 system to perform the wavefront compensation: a wavefront sensor and a phase correcting device. Figure 1 shows the A 0 system that we have constructed. A 635 nm point light source obtained from a laser diode coupled with a monomode optical fiber is collimated using a diffraction limited achromat. The resulting plane wavefront passes through a linear polarizer, crosses the optical system of interest (an ophthalmic lens), and is directed towards a liquid crystal programmable phase modulator (PPM) by means of a pellicle beam-splitter (BS1) which does not alter the optical path length. The aberrated wavefront is compensated and reflected by the PPM [3], which is conjugated with a proprietary cylindrical Shack-Hartmann sensor ( C S H W S ) through a 4: 1 telescope system 141. The sensor, formed by two identical arrays of microcylinders (NA=0.02) oriented along the vertical and horizontal directions, samples the wavefront (previously divided by a second pellicle beam-splitter BS2) in the form of a vertical and horizontal focal line patterns simultaneously recorded by two identical CCDs. By processing the patterns, the average wavefront slope across the microlenses is computed following the usual Shack-Hartmann principle, and, from these data, the wavefront is finally reconstructed in terms of the circular Zernike polynomial decomposition [5]. Because of the non temporal dynamics of the samples to be tested and the excellent linear response of the PPM (as demonstrated later in Sec.3.1) we have chosen to work in an open-loop adaptive configuration (i.e. active compensation), with the important advantage of a very fast measurement process.

208

Figure 1 , A 0 system constructed to test commercial lenses with complex shapes.

2.1. ~ a ~ e f ~ sensor ont A novel Shack-H~mannwavefront sensor based on a cylindrical microlens array (CSHWS) has been developed in order to extend the dynamic range of the classical Shack-Hartmann sensor (SHWS) with a good vertical resolution of r s the wavefront measurement (U25 at k635 nm used). The ~ ~ r o c y l i n d efocus to be measured onto the CCD in the form of focal lines instead of focal spots of a classical Shack-Hartmann sensor. By easily tracking connected data along the continuous lines, a correct localization of all the data is achieved, even where the wavefront has steep curvatures or abrupt shape changes. The expansion of dynamic range using the CSHWS is illustrated in Figure 2. As it may be seen, the part of the wavefront which is less aberrated and passes through the central column of the array of spherical microlenses (numbered as 1) or through the

209

central microcylinder (l), is properly localized in both cases. However, in the wavefront area where steep phase changes appear, it may be noticed how in the conventional SHWS the spots tagged with capital letters leave their corresponding subapertures in area 3 and merge with those belonging to area 5. This implies an uncertainty in the assignment of spots a5 and A5, b5 and B?, and g5 and G5. The use of the CSHWS solves this problem as all the wavefront samples refracted by each microcylinder are connected in the same focal line and may be easily tracked with a simple algorithm. Thus, samples within lines number 5 and number 3 are unequivocally assigned to microcylinders 5 and 3, respectively. 1

Figure 2. Example to illustrate the detected patterns of a complex wavefront with (a) a conventional SHWS with spherical microlenses which has an uncertainty on the localization of spots a5 and A5, b5 and B?, and g5 and G5; and (b) our sensor based on an array of microcylinders from which all the data are correctly localized.

3. Results 3.1. ~ a v e f r o ngeneration t performance of the PPM To validate the compensation capabilities of the system in open-loop, the wavefront generation performance of the PPM was analyzed in terms of the amount of aberration considered. Spherical wavefronts of different curvatures (0.25 D, 0.5 D, 1 D and 1.5 D) were introduced in the 768 x 768 pixelated LCD of the PPM in wrapped phase map representation over the whole 20 x 20 mm liquid crystal active area. The incident plane wave in the PPM was modified and reflected as an output beam which should take the spherical shape introduced, and was measured by the CSHWS. Table 1 shows the comparison between the theoretical wavefront written on the PPM and the measured wavefront for the 20 mm pupil. In all the cases, a very good correlation between the desired and real wavefronts has been found (relative rms error below 0.15%), demonstrating the

210

good linear response of the PPM and its suitability for active compensation in open-loop. Table 1 . Comparison between the ideal and real spherical wavefronts created by the PPM. Ideal Spherical Wavefront [diopters] 0.25 0.5 1 1.5

Idea'

[waves] 19.68 39.36 18.12 118.08

Measured Spherical Wavefront [diopters]

RMS difference [waves]

0.252 0.499 0.986 1.513

0.022 0.013 0.062 0.080

3.2. omp pens at ion of the wavefront ~ a n s m ~ by e da c o m m e r c ~ l To show the capabilities of the A 0 system, we tested a commercial progressive addition lens (PAL,) which had a nominal null distance power and +2.5 D power addition. A 20 mm diameter area was scanned in a single shot, covering the whole power progression corridor of the lens. The intersection of the vertical and horizontal line patterns detected by the CSHWS and the reconstructed wavefront are shown in Figures 3a and 3b, respectively. As expected, in the near vision region where there is a higher power, the width of the focal lines increases from the diffraction-limited size and are also displaced outside the corresponding microcylinder area of the CCD array. In order to improve the measurement accuracy, the conjugate of the measured wavefront was placed in the active device for compensation. As a result shown in Figure 3c, several additional points (within the white circles) appear now to compute for wavefront reconstruction and the width of the focal lines reduces close to the diffractionlimited size. The original wavefront of more than 60 pm peak to valley becomes flat after the compensation, with a RMS deviation of 71 nm (Figure 3d). Unfortunately, the line pattern also clearly shows the diffractive behavior of the PPM device. When a large aberration is written on it, the period of the wrapped optical path function is shortened, and the diffraction efficiency noticeably decreases; i.e. the intensity of the first diffraction order (which is the phasemodulated) becomes highly reduced relative to the zeroth order (which is the non-modulated original wavefront). This undesired zeroth order light is superimposed to the compensated pattern, making the image processing task more difficult and time-consuming. At present, two alternatives are under study to overcome the problem: either the introduction in the system of a filter element to block the zero order light, or to tilt the PPM while adding to the wrapped phase map the opposite tilt.

211

Figure 3. PAL tested with the A 0 system: line pattern detected and reconstructed wavefront before (a) (b), and after (c) (d) the A 0 compensation.

Ackno~ledg~en~ The authors would like to thank the Spanish Ministry of Education and Science for the AP2003-3 140 grant received, and for the project DPI2005-00828,~which has partially funded this research. eferences

1. 2. 3. 4.

http://www.essilor.com E. J. Tremblay et al., Appl. Opt., 46 (4), 463 (2007). N. Mukohzaka et al., Appl. Opt., 33 (14), 2804 (1994). M. Ares, S. Roy0 and J. Caum, Opt. Lett., 32 (7), 769 (2007). 5 . J. Porter, H. M. Queener, J. E. Lin, K. Thorn and A. Awwal, Adaptive Opticsfor Vision Science (book),Wiley-Interscience,Apendix A (2006).

OF NOVEL LINEAR PHASE RETRIEVAL ~ A V E F ANI) ITS APPLICATION IN CLOSE-LOOP A~APTIVE OPTICS SYSTEM XINYANG LI, MIN LI, BO CHEN, WENHAN JIANG Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209 China The basic principle and the characteristicsof a novel linear phase retrieval (LPR) method were analyzed. it is proved that the unknown phase can be retrieved uniquely from only one far-field image and a former calibration. The experiment results showed that the LPR method can realize highly precision measure by using less amount of detect elements with comparing to Hsensor. The LPR sensor was tested in a close-loop adaptive optics (AO) system with deformable mirror of 32 actuators. The real-time reconstruction algorithm for the A 0 system with LPR sensor was proposed. The experiment results showed that the LPR sensor work well in close-loop A 0 system. Key words: Linear phase-retrieval, wave-front sensing, adaptive optics system

1. Introduction The problem relating the phase and magnitude of the imaging system has received much attention over the years, and many solutions to the problem also have been got [ 1-51. It needs at least two far field images to capture at the same time for normal phase retrieval method, for example one image on focus and another image out of focus. Such methods have been used to measure aberration or apply in a close-loop adaptive optics (AO). But sometimes there is not enough energy for more than two images. Can we get wavefront with only one far-filed image in real-time? Now we will provide a novel solution to phase retrieval problem by using only one far field image with phase aberration, but a calibration image without aberration must be gotten formerly on same imaging system to solve the problem uniquely. It will be proved that there is linear relationship between the difference of the two images and the phase aberrations. Therefore we can use the linear relationship to retrieve the phase aberration expediently. This method is called Linear Phase Retrieval (LPR) in this paper. 212

213

2. Principle of LPR Method For an imaging system as showed in Fig.1, the far field image of the incident wavefront is measured with a CCD camera. Let A(?)exp[i@(Z)] is the field in input aperture, which A($ is magnitude and is always supposed as constant A,

@(?) is phase aberration to be measured. According the principle of Fourier optics, the field in focus plane is:

w(Z)= F[Aexp[i@(?)]] In which F[f(?)]

=I

(1)

is the Fourier transform. Then the intensity on focus plane

1"

is I($) w(Z) If there is a small phase change A@(?) added to @(?),then the field on imaging plane and the intensity on focus plane changed too

$(Z) = F{Aexp[i@(?)+iA@(?)]} = F{Aexp[i@(Z)].[l+iA#(Z)]} Aw(u') = G(Z)-w(Z) = F{iA@(Z).Aexp[i@(?)]}

f(Z)= Z(Z)+AZ(Z)=[W(Z)+AW(Z)]*.[W($)+AW(Z)]

(2) (3) (4)

AZ($) = w(Z)*-AW(Z)+ w(Z)*AW(Z)*+A?~W(Z)**AW(Z)] ( 5 )

IAw(G) 12=

0 . Then we can get: AZ(Z) = 2Re{ F{Aexp[i#(?)]} *.F{iA@(?)- Aexp[i@(?)]} } = 2Re[w(u')*.Aw(Z)]

If the change of aberration is small,

(6)

The equation above means that there is a linear relationship between the change of phase A@ and the change of intensities AI on focus plan, The linear relationship can be described as matrix format: ffZ=H.A@ (7) Which €€ is the response matrix.

Fig. 1 Principle diagram of the linear phase retrieval wavefront sensor.

The phase can be described as the sum of several Zernike modes[5]:

214

Which P is mode number, aiis ith coefficients and M i(x,y ) is description of ith Zernike modes. There is a linear relationship between the change of phase and the change of mode coefficients: (9) Or in matrix format:

(10) By using Eqt. 7 and 10, the result is

AI = H D . A a = Z * A a (1 1) It is proved that there is a linear relationship between the change of Zernike coefficients and the changes of intensities. The matrix 2 represents the relationship between them. Matrix 2 can be got formerly according the parameters of the imaging system. Then we can reconstruct the Zernike coefficients by Aa = 2' * A1 (12) Which Zf is the pseudo inverse of matrix 2.If we using a wavefront sensor system as showed in figure 1, the imaging system be calibrated with an ideal parallel source to get the change of intensities with aberration, then the linear calculation results of Eqt. 12 Aa are Zernike coefficients of aberration, which is exactly what we want. 3. Numeri~aiand Experiment Results of LPR Sensor The characteristics of the LPR sensor was tested by numerical simulation on measuring the atmosphere disturbed wavefront. The normalized error, or named as the error ratio q, is used as a criteria to check the performance of LPR method. The LPR method will be better if q is smaller than 1.

r = RMSI~tX,Y)-63^tX,Y)llR2MS[~(X,Y)l

(13)

Table 1. Reconstruction error of LPR on different wavefront aberrations.

Data Wavefront F2MS Residual wavefront RMS Error ratio ( rad 1 rl Group (rad) 0.0367 0.179 1# 0.205 2# 0.366 0.1146 0.313 0.3429 0.526 3# 0.652 0.9133 0.786 4# 1.162

A series of Kolmogorov atmosphere disturbed wavefronts were calculated using the method given by N. Roddier with 65 Zernike polynomials [6]. Different series of wavefronts with different strength were tested. The results are showed in Table.1. The 3D shape of atmosphere disturbed wavefront and those from LPR

215

method are showed in Fig.2. The results showed that the LPR method has good ability for small aberrations. The precision of LPR method descend faster with the increase of atmosphere strength. Approximately say, the LPR can work better in the condition of RMS less than 1 rad. The LPR sensor and Shack-Hartmann sensor have been compared through experiment to measuring various stochastic wave-front aberrations at the same time. There are 26x26 sub-apertures in the Hartmann sensor, and the results of Hartmann were thought as correct enough. The wavelength is 0.532pm, and beam size 3.7mm to match the size of microlens. Different pixel resolutions of far field images from 4x4 to 128x128 are changed to compare the results of LPR sensor. The experiment results verified that the LPR sensor can realize highly precision as Hartmann sensor but using less amount of detecter elements. It is very useful while the LPR sensor is applied in astronomy A 0 systems.

i

i

Y

-1 -1

x

Y

.l

-1

x

Y

-1 -1

x

Fig.2 Compare of the atmosphere disturbed wavefront and those reconstmeted from LPR method.

Zernlke order

Fig.3 Results of experiment between LPR sensor and Shack-Harhnann sensor.

rinciple of LPR Sensor in Adaptive Optics System The LPR method can be using in a close-loop adaptive optics (AO) system as showed in figure 4. Which M(x,y) is the compensated wavefront of deformable mirror, and the residual wavefront after compensation is

216

E ( x ,Y ) =

(14) Y )-M(& Y ) The wavefront reflected from the deformable mirror can be described as the sum of influence functions of all actuators, $

0

7

M ( 4 Y )= ~ ~ , v t V I ( x ’ Y )

(15)

Y(x,

Which V , is control voltages of ith actuator, and y ) is the influence function of ith actuator, N is number of actuators. By using the similar principle as Zernike modes, it can be proved easily that there is a linear relationship between the change of control voltages Av and the changes of intensities A1 on focus plane. dI = D * d v (16) The response matrix D can be got formerly on the A 0 system by adding unit voltages to actuators of deformable mirror one by one and record the changes of intensities on focus plane at the same time. Then the control voltages can be reconstructed from the changes of intensities by using linear method:

dv = D+ .dI (17) Which D+is the pseudo inverse of matrix D.In the close-loop A 0 system, it is the residual wavefront or the residual intensity Ale be measured by LPR sensor, therefore it is the residual control voltages be calculated = close-loop A 0 system can run in real time by using the integral control algorithm. V ( t )= V ( t - l ) + k . V e (18) Which k is the gain of the integral controller.

ve

Fig. 4 The sketch diagram of a close-loop adaptive optics system with LPR sensor.

217

Fig. 5 The experiment setup of LPR sensor in close-loop A 0 system and the arrangement of the deformable mirror with 32 actuators.

,

Fig. 6 The experiment results of LPR sensor in close-loop A 0 system. From left to right: the calibrated far-field spot without aberration, SR=I.O the spot with aberration, SRS.38; and the spot after correction, SR=0.85.

5. Experiment Results of LPR Sensor in A 0 System The performance of the LPR sensor was tested in a close-loop A 0 system with deformable mirror of 32 PZT actuators. The setup of the experiment and the arrangement of the deformable mirror are showed in Fig.5. The wavelength of Laser source is 0.532 urn, the CCD camera is 25 Hz are used. A Pentium IV computer with image grabber and DAC are used as data processor. The integral controller are executed in Microsoft VC++6.0 program. The performance of the A 0 system is checked with the Strehl ratio (SR), which is related to the variances of residual wavefront. The results of one experiment are showed in Fig.6. The SR of far-field spot before correction is 0.38, and the SR of far-field spot after correction is 0.85. This is the first experiment result of the LPR in A 0 system. More experiments will be done in detail later to check the performance of LPR sensor in close-loop A 0 system.

6. Conclusion The basic principle and the characteristics of a new kind of linear phase retrieval (LPR) wavefront measuring method were analyzed. It is proved that the unknown phase can be retrieved uniquely from only one far-field image with calibration. The performances of the LPR sensor were tested by numerical simulation and the

218

experiment comparing to Hartmann sensor. The LPR sensor was tested in a close-loop adaptive optics (AO) system with deformable mirror of 32 actuators. The experiment results showed that the LPR sensor works well in close-loop A 0 system.

~c~owledgement The project is funded by the Chinese Natural Sciences Fund with item number 60408005. Authors want to thank prof. Rao Changhui, prof. Xian Hao, and prof. Shen Feng for the helpful discusses and useful advices. References 1. 2.

3. 4.

5. 6.

Walther. The question of phase retrieval in optics, Opt. Acta, vol. 10, 4 1-49,1963 J. R. Fienup. Phase retrieval algorithms: a comparison, Applied Engineering, 21(15), 2758-2769,1982 R.A. Gonsalves, R. Chidlaw. Wavefront sensing by phase retrieval. Proc. SPE, V01.207,32-39, 1979 R. A. Gonsalves. Small-phase solution to the phase-retrieval problem, Optics letters, 26( lo), 684-685,2001 W. J. Wilde. Linear phase retrieval for wavefront sensing. Optics Letters, VO1.23, N0.8,573-575, 1998 N. Roddier. Atmospheric wavefront simulation using Zernike polynomials. Optical Engineering, 29( lo), 1174-1180, 1990

A C K - ~ A R WAV~FRO ~ ~ A ~ APPLICATIONS DANIEL R. NEAL AMO- WaveFront Sciences, lnc. 14820 Central SE Albuquerque, NM 87123 USA [email protected] One of the most common applications of the Shack-Hartmann wavefront sensor is to measure the human eye. There are a number of instruments that have been designed for this purpose and are used extensively in laser refractive surgery. 'while conceptually the sensor is similar to those used for astronomy applications, there are key differences adaptive optic and measurement sensors. These sensors have led to a range of applications and diagnostics that are providing key new information about how the eye functions.

While Shack-Hartmann wavefront sensors have been used for a wide variety of applications for more than 35 years, by far the most common (in terms of number of sensors in routine use) is the measurement of the human eye. These sensors have become the norm for supporting laser refractive surgery, and increasing applications are being seen throughout ophthalmology and optometry. The system architecture for a Shack-Hartmann aberrometer is similar to a laser guide-star arrangement. Light is projected into the eye and scattered from the retina. This light is collected by the S W S and used to analyze the aberrations of the eye (see Figure 1). The aberrations of the eye are readily separable into low and higher order effects, with defocus and astigmatism as the primary low orders, and coma, trefoil, spherical aberrations, and other aberrations as the higher orders. The eye can be extremely aberrated, with defocus ranging from -16 to +8 diopters, and cylinder can be as high as 6 diopters. It is common to use a Keplerian telescope with adjustable focus to optically correct the defocus term (spherical equivalent). This method is used in a one-degree-of- freedom closed-loop adaptive optics system to minimize the SHWFS error. In a few seconds the instrument can find the appropriate defocus condition and neutralize it optically, so that the sensor only measures the cylinder and higher order aberrations. Some commercially available systems use a fixed optometer, and others also include correction for the astigmatism terms.' 219

220

Figure 1 - Arrangement for guide star measurement of the eye.

The instruments produced are accurate to a fraction of a wave, have 50 to 70 pm of dynamic range, and measure an eye in a few seconds. Approximately ten different companies, serving various markets, manufacture such an instrument. The customized LASIK ablation market is the largest at this time. These aberrometers are examples of using a Shack-Hartmann wavefront sensor for direct measurement rather than for closed loop applications. While conceptually the SHWFS is used for both types of systems, in practice there are significant differences. Table 1 lists some of the key parameters for these two types of systems. In principle the wavefront sensor designed for measurement is similar to that used for adaptive optics, but in practice there are some important differences. For example a typical adaptive optics system may have about the same number of sub-apertures as there are actuators in a deformable mirror. This number can vary from as low as 37 to as high as 1000. The number of subapertures is minimized so that the processing can proceed extremely rapidly, with minimal delay in the control loop. However, a typical measurement sensor might have more than 1500 sub-apertures, and a high resolution one up to 10,000 lenslets. While some adaptive optics systems have been built to compensate for aberrations in the eye2 (to allow better viewing of the structure of the retina), there are relatively few such systems installed around the world today.

22 1 Table 1 Comparison between adaptive optic and measurement wavefront sensors.

Adaptive Optics

Measurement

Accuracy

Only very important near zero (accuracy achieved by nulling with deformable mirror). Accuracy driven by noise, photon count, and electronics.

Must be accurate throughout the measurement range. Accuracy driven by pixelization of focal spot measurement

Linearity

Only very important near null. Even highly non-linear sensors can provide good feedback for A 0 as long as an accurate zero is retained

Must be linear throughout the measurement range

Dynamic Range

Dynamic range determined by the deformable mirror

Dynamic range determined by the lenslet parameters

Bandwidth

As high as possible (especially for atmospheric correction systems)

Nearly static. Often a single measurement or small sequence is all that is needed.

Lenslet focal length

Typically long to get good sensitivity (since dynamic range is achieved by the DM)

Typically fairly short to give good dynamic range

Lenslet resolution

Typically low to minimize amount of processing needed

Typically high to give good sampling and accuracy

Pixels per focal spot

Minimized to increase the intensity on a single pixel to enable extremely low light level applications (typically 4-16 pixeWfocal spot)

May be optimized to about 50 pixels/focal spot to maximize the instrument accuracy

Parameter

Figure 2 shows a photograph of the COAS (complete Ophthalmic Analysis System) built by AMONVaveFront Sciences. This measurement mode aberrometer is based on a Shack-Hartmann sensor with a resolution of 44 X 33, which in a typical 7 mm pupil results in more than 800 measurements. The instrument has been shown to have excellent accuracy and repeatability when compared to other instruments as well as to manifest refra~tion.~ Four basic clinical applications are currently in common use for ocular measurement systems: Wavefront guided ablation in laser refractive surgery, auto- ?Ite Ophthalmic Analysis system provides complete refraction for spectacle and contact lens characte~zation of the fitting, diagnostics of kerataconus, eCt&Sia,or refraction and higher order aberrations.

222

other aberrated conditions, and research in accommodation, scattering, tear-film, customized contacts, or other application. Wavefront guided ablation has become the preferred mode for nearly all forms of laser refractive surgery. Prior to the introduction of the wavefront instruments, Lasik and PRK procedures induced a significant amount of higher order aberration (mostly spherical aberration). These aberrations were undetectable except through variations in manifest refraction as a function of pupil size. With the wavefront guided treatment, the aberrations are now measured directly, which gives the physician the information needed to adjust the nomograms to optimize the surgery. This method has been so successful over the last 7 years that the majority of all procedures are now customized. In Figure 3, the same wavefront measurement was analyzed at two different pupil sizes resulting in significantly different refractions (note sphere change from +0.28 D for a 4 mm pupil vs. -1.31 D for a 5 mm pupil).The disparity is a consequence of a large spherical aberration component in this subject. This patient may be best served by two pairs of spectacles-one for normal daytime wear and another for night time use, particularly driving. Alternatively, some form of customized correction may be used. The ocular wavefront measurement instrument is key to developing an understanding of how the human eye functions. Gaining an understanding of how the perceptions of a subject change with aberrations, the functioning of accommodation, the dynamics of eye-movement-induced aberrations, along with a way to quantify many of these effects is critical to advancing this science. As an example, instruments for measuring accommodation are beginning to provide quantitative feedback on whether certain new surgical techniques are effective.

quantity sphere(0) cylinder(0) axis

I

]value X X

+0.28 0.

-1.06 D 127:

I value

quantity sphere(0)

X

cylinder(0) axis

X

c

-1.31 0.. -0.89 0 121'

Figure 3 - Variation in refraction as a function of pupil size.

223

-

Figure 5 Accommodation measurement with an objective aberrometer. (a) aberrometer with external dynamic binocular target, (b) example data showing both defocus response along with change in coma.

As the general population ages, understanding and correcting for presbyopia is becoming an increasingly important topic. There are numerous innovations (multi-focal contact lenses, IOLs, laser refractive surgery, scleral surgery number among the more common. To assess the efficacy of these different techniques, it is very important to be able measure the objective changes in the lens, and separate those data from multi-focal, depth-of-field, and neurological effects. To this end we have developed a sequence of instruments aimed at the measurement of accommodation. To make this measurement with the wavefront sensor involves careful presentation of targets to the subject while simultaneously recording the full dynamic ocular response. The wavefront sensor is ideal for this since it provides a means, inherent in the data, for distinguishing between the various affects. Figure 5 shows one of these instruments and an example of a measurement. In Figure 6, the measured accommodative range is plotted as a function of the subject's age. The accommodative range is derived from the change in sphere as measured in Figure 5(b). However, the stimulus for this data set was fixed at 6 Diopters and the natural accommodative range of some of the younger subjects exceeds this amount. Therefore, the trend is likely actually steeper than is presented in the figure. There is a likelihood that the red triangles (labeled Optana) are more indicative of the true instrument performance, since we have excluded those younger than 30 from the study. This data is a good match to the expected results from the push-up test.

224

However, accommodation is a very complicated phenomenon. The DSA tool was designed to give an unambiguous visual stimulus to the subject to eliminate the possibility of various subjective factors (instrument myopia among others). The required stimulus includes apparent size of an object near the subject’s face, ability to discern the target with both eyes, duration and motion of the target, size of the target features, and deviation of the stimulus from the subject’s objective range. While the DSA solves many of these problems with a realistic view of a target with full binocular presentation, the binocular view introduces another problem. If a subject has different refraction between left and right eyes, the non-dominant eye does not get an accurate reading because the brain responds to the dominant stimulus. Thus the accommodative range would be under-predicted. In addition, a subject with a small pupil or large spherical aberration may have an extended depth-of-focus. Thus the subject may be able to fixate on the target well out of their objective range. The wavefront aberrometer also gives a lot of other information. In addition to the spherical accommodative range, the higher order aberrations (coma, spherical aberration, and others), pupil size, and other information can be directly derived from the wavefront data. Thus we can measure some of these effects directly. In fact, some of the outliers seen in Figure 6 are subjects that have a very large amount of spherical aberration.

Figure 6 - Some accommodation range measurements using the DSA tool. Note that the data generally follow the reduction-of -range-with-age curve. However, note also the outliers.

225

1

I

Accommodatlvechange in spherical aberration

0

10

20

30

40

50

80

Aee

Figure 7 - The change of spherical aberration also decreases with age. (similar to the accommodative range itself).

In Figure 7, the change in spherical aberration has been plotted as a function of subject age. Note that in this study the amount of spherical aberration change decreases dramatically with age. Although they are different subjects from the first study, this is an expected result because of the normal model for presbyopia-that one mechanism includes a gradual hardening of the crystalline lens. So as the subject ages, the lens naturally has less ability to change shape, which affects both the accommodation (focus) and the spherical aberration. The development of ocular Shack-Hartmann measurement systems has improved our ability to make detailed measurements of the eye facilitating improvements in methods to correct the optical errors of the eye, including laser refractive surgery, contact lenses and fittings, and spectacles. The wavefront aberrometer is already one of the largest applications of the Shack-Hartmann wavefront sensor. Already today it can be credited with improving the vision of many LASIK patients. With the development of more customized treatment modalities (such as customized contacts) it is likely to be increasingly used in the diagnosis and treatment of visual defects.

eferenees 1. D. R.

Neal, “Shack-Hartmann sensor engineered for commercial measurement applications,” SPIF! AM 100-20 (2004).

226

2. J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and highresolution retinal imaging through adaptive optics,” J. Opt. SOC.Am. A 14, 2884-2892 (1997). 3. T. 0. Salmon, L. N. Thibos and A. Bradley, “Comparison of the eye’s wavefront aberration measured psychophysically and with the Shack-Hartmann wave-front sensor,” J. Opt. Soc. Am A, 15 (9), pp. 2457-2465 (1998).

NT SEN SIN^ OF AN OPTICA THE HELP OF BI FEDOR STARIKOV, GENNADI KOCHEMASOV, STANISLAV KULIKOV, ALEKSEI MANACHINSKY, ANDRE1 OGORODNIKOV, STANISLAV SUKHAREV Institute of Laser Physics Research, Russian Federal Nuclear Center - VNIIEF, Mira ave. 37, Sarov, N. Novgorod reg. 607190, Russia ALEXIS KUDRYASHOV Adopt Ltd. &Moscow State Open University, Moscow, Russia VALERI AKSENOV, IGOR IZMAILOV, FEODOR KANEV Institute of Atmospheric Optics, Siberian Branch of Russian Academy of Sciences Akademicheskii ave. 1, Tomsk, Russia VIKTOR ATUCHIN, IVAN SOLDATENKOV Institute of Semiconductor Physics, Siberian Branch of Russian Academy of Sciences, Academician Lavrentiev ave. 13, Novosibirsk, Russia The reconstruction of phase front of the vortex laser beam is conducted with usage of the Hartmann-Shack wavefront sensor. The vortex beam in the form of the LaguerreGaussian LGo' mode is generated with the help of spiral phase plate. New reconstruction technique on basis of measured wavefront gradients allows one to restore the singular phase surface with good accuracy whereas the conventional least-squares approach fails. The vortex phase correction (removing the singularity) is carried out in a close-loop adaptive system with a bimorph deformable mirror.

1. IntrQ~uctiQn One of key trends in the development of modern adaptive optical systems is connected with the correction of scintillation effects arising in laser beams at propagation through inhomogeneous medium. They decrease the efficiency of light energy transportation and distort the information carried by laser beam. It is urgent to create the wavefront sensors with high measurement accuracy as well as the adaptive systems for correction of wavefront with screw dislocations acquired in the regime of strong scintillations. * This work was supported by ISTC under the project #263 1 .

227

228

The interferometric wavefront sensor was applied for reconstruction of phase surface of the higher-order Laguerre-Gaussian modes LG," [I] and in high-speed adaptive optical system for compensation of phase distortions under conditions of strong scintillations in atmosphere [2]. However, it is necessary to note that the Hartmann-Shack wavefront sensor is more widespread in adaptive systems but it generally operated with the regularly distorted wavefronts only. After the registration of the vortex-like structure of displacements of spots in hartmannogram of the Laguerre-Gaussian modes 13, 41, the reconstruction of singular phase surface of the LGo' mode by Hartmann-Shack sensor was performed [5] using new reconstruction technique. In the present paper we consider the reconstruction of singular phase surface as well as its correction in a close-loop adaptive system with a bimorph deformable mirror.

2. Vortex generation and wave front sensing Among the considered approaches of wavefront reconstruction the Fried's algorithm [6] is one of the best algorithms (with respect to accuracy, effectivity and stability to noises) of recovery of phase surface S(x, y) from its gradient VS, distribution in the presence of vortices. Its modification [7] allows one to increase the precision by 10-15%.Limitations of the technique show themselves under the reconstruction of phase surfaces including the screw dislocations of higher orders. In numerical simulations one succeeds in reliable phase front recovery of vortices up to forth order. To test the algorithm's accuracy and efficiency in actual experiment, it is necessary to form a reference optical vortex with maximally predetermined phase surface. We generate a Laguerre-Gaussian LGol mode using a spiral phase plate [ 5 ] manufactured with the help of etching the fused quartz substrate by kinoform technology. The plate has large working diameter, 2 cm. The break height agrees an ideal value with the accuracy of 1%.

I

2

3

4

5

6

Figure 1 . Scheme of the experimental setup for characterizationof optical vortex.

229

Experimental setup for comprehensive registration of optical vortex (Fig. 1) consists of a system of collimated laser beam formation, a Mach-Zehnder interferometer and a Hartmann-Shack wavefront sensor connected with a computer. The system of formation of collimated beam includes a He-Ne laser 1, a variable power attenuator 2 and a collimator 3. The collimator forms the reference basic Gaussian beam with the diameter of 1 cm and wave front close to plane one. The interferometer includes two optical wedges 4 and two mirrors 6 . The spiral phase plate 5 is interposed into one of interferometer's arms. Its working surface is completely covered by the beam. After passing through the spiral phase plate the Gaussian mode turns into an optical vortex @Go1 mode) in the focal plane 8 of the lens 7 with high conversion coefficient. The wavefront sensor consists of a lenslet array 10 and a CCD camera 11. Under the registration of laser beam intensity distribution in the far field, the focal plane 8 of the lens 7 with focal length 7 m is transferred (for the purpose of magnification) by an objective 9 in the conjugated plane 8' onto the CCD camera (the lenslet array is removed and the CCD camera screen is situated in its place). At blocking the reference beam in the second arm of interferometer the CCD camera registers the vortex intensity distribution, at opening the reference beam the interference pattern of the vortex beam with an obliquely incident Gaussian beam (plane wave) is registered. Tlie experimentai distributions of vortex beam intensity and interference pattern are shown in Fig.2. The beam intensity has a doughnut-like shape. The phase front singularity appears by fringe branching in the beam center with forming a "fork" typical for the screw dislocation with unity topological charge. It should be noted that the vortex quality (similarity to LGo' mode) is very good. This gives us grounds to believe that the vortex wave front to be reconstructed by Hartmann-Shack sensor has to be close to ideal LGol wave front.

Figure 2. Experimental distribution of intensity of the vortex beam in far field and its interference pattern with obliquely incident plane wave.

230

Under direct registration of phase front of the optical vortex by the Hartmann-Shack wavefront sensor, the complete experimental setup shown in Fig.1 is used. The reference beam in the second arm of interferometer is blocked, and in the conjugated plane 8’ the lenslet array with size of microlens d=0.3 mm, focal length +25 mm is arranged. It is the kinoform raster of 8-level Fresnel lenses fabricated of the fused quartz at accuracy of etching profile depth not worse than 2%. On the CCD camera screen the picture from 8x8 focal spots is registered. In Fig.3,a we present the wave front surface of optical vortex reconstructed by the Hartmann-Shack sensor with software incorporating the code of restoration of singular phase surfaces [7] based on the modification of Fried’s algorithm [6]. Experimental data show that the wave front surface is restored by the actual Hartmann-Shack sensor with good quality. The reconstructed wavefront has the characteristic spiral form with the break about of 2n size (PV=0.61 pm).The reconstruction accuracy is about of 220 and rises with increasing measurement grid. For comparison in Fig.3,b we demonstrate the result of vortex wavefront reconstruction using standard least-squares technique in the Hartmann-Shack sensor. The conventional approach obviously fails. z. w 06

z, cum 06

04

04

02

02

-

0

24

0

24 24 y,mm x, mm

y, mm

a)

b)

Figure 3. Experimental vortex phase surface reconstructed with using special Fried‘s (a) and conventional least-squares (b) procedure.

3. Vortex wave front correction We use a close-loop adaptive system (Fig.4.a) to perform the needed correction of vortex wavefront. A reference laser beam is formed using a He-Ne laser 1, a power attenuator 2, a collimator 3, and a square pinhole 4, which restricts the beam aperture by 10x10 mm2 size. An optical vortex formed by a spiral phase plate 5 passes through a fourfold telescope 6 and comes to an adaptive deformable mirror 7, which is arranged at relatively large distance from the phase plate. The radiation reflected from the adaptive mirror is directed by a plane mirror 8 through a reducing telescope 9 to a Hartmann-Shack sensor

231

including a lenslet array 11 (d=0.2 mm, &I5 mm) and a CCD camera 12. The planes of adaptive mirror and lenslet array are optically conjugated. The beam part is derived by a dividing plate 10 to a CCD camera 15 for intensity registration in the far field. The bimorph adaptive mirror (Fig.4b) on the piezoceramic base has the quadratic greed of 5x5 control elements, the size of the element is 9 rnm. Working aperture of the mirror is 55x55 mm, corrector thickness is 4.5 mm, substrate material is glass LK-105. The wavefront has no singularity at removing the spiral phase plate from the scheme and at switching off the adaptive mirror, so the picture of diffraction at the square diaphragm 4 takes place in far field (Fig.5a). After inserting the phase plate and at switching off the adaptive mirror, the wavefront acquires the spiral form with typical break (Fig.3), and the far-field intensity has the doughnut form (Fig.5b). Then, using results of wavefront measurement, the phase correction is implemented. The mirror is deformed to maximally reproduce the vortex wavefront and to obtain the wavefront after reflection from the mirror close to a plane one. The first experiments have demonstrated the capability to remove the wavefront singularity and increase the optical system resolution (Fig.%).

a)

b)

Figure 4.The setup for optical vortex correction (a) and deformable mirror (b).

a)

b)

c)

Figure 5. Far field intensity: reference beam (a) and beam before (b) and after (c) correction

232

a)

b)

Figure 6 . Phase surface of reference beam (a) and beam after correction (b) in the near field.

Each superposition of response functions of the bimorph mirror is the smooth function, and the mirror is not able to completely reproduce the phase discontinuity of 2rdepth. The reference beam phase surface is shown in Figha. Phase surface after correction in Fig.6b (the difference between the measured vortex phase surface and mirror surface) is close to the reference one except for narrow region at the break line (PV=0.5 pm). But the radiation from this part of the beam is scattered to large angles and its portion in the beam is relatively small, therefore the far-field intensity picture after correction (Fig.%) is closer to the reference beam (FigSa) rather than the vortex before correction (FigSb).

. Conclusions In conclusion, we have formed the vortex laser beam (the Laguerre-Gaussian LGo' mode) with the help of spiral phase plate. Intensity distribution and picture of interference of the beam with the obliquely incident plane wave testify to good quality of generated optical vortex. The singular phase front has been properly reconstructed by the Hartmann-Shack wavefront sensor with special novel software whereas the conventional least-squares technique fails. Using the close-loop adaptive system on basis of a bimorph deformable mirror we have experimentally demonstrated the capability to correct the wavefront singularity.

AcknQwledgment The work was supported by International Science and Technology Center (ISTC) under the project #263 1.

eferences 1. C. Rockstuhl, A. A. Ivanovskyy, M. S . Soskin et al. Optics Communications 242, 163 (2004).

233

2.

K. L. Baker, E. A. Stappaerts, D. Gavel et al., Optics Letters 29, 118 1 (2004). 3. F. A. Starikov, V. V. Atuchin, G. G. Kochernasov et al., Proc. SPIE 5894, 58941E (2005). 4. J. Leach, S. Keen, M. Padgett, C. Saunter and G. D. Love, Optics Express

5. F. A. Starikov, G. G. Kochemasov, S.M. Kulikov et al., Optics Letters, ID 80921, in print (2007). 6. D. L. Fried, Opt. Communications 200,43 (2001). 7. V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev and F. A. Starikov, Proc. SPIE 5894,589407 (2005);Proc. SPIE 6341,634133 (2006).

C

CENT A ~ ~ A N C EINS LAS TION OF HIGH ~ ~ E R SIN^ ~ ~ A ~ ~ - W A ~ E

BENOIT WATTELLIER, IVAN DOUDET, WILLIAM BOUCHER PHASICS S.A XTEC, Campus de I’Ecole Polytechnique, 91 128 Palaiseau, FRANCE Email :[email protected] We present a new scheme to measure and correct the wave front of high numerical aperture focusing optics without any re-collimation optics. This scheme is based on the ability of Lateral Shearing Interferometry to sample wave fronts with short radius of curvature, Combining a SID4 interferometer close to the focal region with a deformable mirror leads to diffraction limited spots. Wave front correction is also done with a parallel beam line using the corrected beam as a reference. This avoids keeping the wave front sensor in the interaction area. In both cases, no difference in far-field patterns was observed.

Adaptive optics for high power lasers aims to optimize the laser pulse intensity in the laser-matter interaction volume. A lot of projects now consider light interaction in volumes as small as h3,where h is the pulse central wavelength. This is achieved when all photons arrive in the interaction zone exactly in phase. This is achieved spatially if the beam wave front is perfectly spherical after the final optics, which is in general the focusing optics. Adaptive optics loops use wave front sensors to evaluate the wave front shape and compare it to a spherical wave front. The difference, called wave Eront aberrations, serves as an error signal to control the shape of a deformable mirror. Until now, wave front sensors were limited in terms of analyzed beam numerical apertures to the numerical aperture of the optics used to sample the wave front. An additional optics were consequently required to reduce the beam numerical aperture and make it compatible with the wave front sensor numerical aperture. The alignment and quality of this additional optics change the aberrations measured by the wave front sensor and the actual wave front cannot be perfectly spherical though the wave front sensor indicates so. Removing this additional optics is a challenge to get the highest intensity possible. 234

235

Because 4-wave lateral shearing interferometry uses a very simple diffractive optics to sample the wave front, the acceptable numerical aperture is much larger than other wave front sensors. This diffractive optics (an Modified Hartmann Mask or MHM) is made of a Hartmann plate, that is a grid of holes, and a phase mask, which role is to clean the MHM diffraction spectrum. When a flat wave front beam travels through the grid, its projection in a CCD plane placed a few millimeters away is a pure sinusoidal interference pattern which spatial frequencies are equal to the MHM spatial frequencies. If the beam wave front is spherical, the interference pattern is still a pure sine but with different spatial frequencies than the MHM. The ratio between the MHM frequencies and the spherical wave front frequencies is directly related to the sphere radius of curvature in the MHM plane. Aberrations are just deformation of this grid. Interferogram deconvolution by Fourier analysis is done not at the MHM frequencies (as it is done for conventional 4-wave shearing interferometry) but at the shifted frequencies. Using this method leads to aberration measurements with an sensitivity of All00 RMS for spherical waves which radius of curvature is below 3 mm. For instance, we were able to characterize lenses with f# as low as 1.5. We applied this new scheme to the correction of focusing optics. The SID4 wave front sensor is located after focus in the plane image of the deformable mirror by the focusing optics (see the right part of Figure 1). The loop then converges to a spherical wave front. The wave front sensor is then replaced by a conventional CCD with an imaging system in order to record the corrected farfield. In practical situations, it is not possible to keep a wave front sensor on the way of the laser because this has to interact with matter. Wave front measurement has to be done on a parallel beam line, supposed to be equivalent to the beam line that focuses the beam. A lot of effort is made about the way to characterize with high fidelity the wave front after the final optics with a parallel beam line. Our strategy is to create this high fidelity in two steps. We first create a perfect spherical wave after the final optics, using the method mentioned above. Since the wave front sensor has to be removed for physics experiments, we use a parallel beam line that shares the deformable mirror with the laser back-end. When the deformable mirror is set to create a perfect beam, we record the wave front in the parallel beam line. This wave front is subsequently used as a “perfect beam” reference for further loops with the second wave front sensor. In this strategy, the second beam line does not need to be equivalent to the final optics in term of optical paths. Its aberrations and those of the final optics are automatically subtracted with the new reference for the wave front sensor.

236

Figure 1 - Experimental set-up for wave front correction of a high power laser including the final focusing optics.

We implemented this experimental process in conjunction with the high numerical aperture correction experiment presented above (see Figure 1). A beam splitter was introduced in the experimental set-up and a parallel beam line was created with a reducing telescope that images the deformable mirror onto a second SID4 wave front sensor. The procedure described above was then applied. We checked the far-field after the second loop and saw no difference with the one recorded after the first loop (see Figure 2). We will present in details high numerical aperture beam characterization using Lateral Shearing Interferometry, together with adaptive optics in this extreme regime. Examples of practical implementations with various focusing optics (lenses, objectives, off-axis parabola) will be given. The authors thank Julien FUCHS and Raphael MARQUES for providing various high numerical aperture focusing optics, such as off-axis parabola.

Povbon (urn)

Figure 2 - Far-field pattern line-outs measured (a) after a loop with the SID4 after the focusing optics. (b) after a loop with the parallel beam line. As a reference, (c) represents the estimated Airy pattern. This data was generated with a fcJ.6 achromatic doublet, as the focusing optics.

OPTICAL ~ E T R O L O G USING ~ P~NCIPLES A V E ~ R O SENSING ~ ANI) I ~ E ~ E

~

DAVID M FAICHNIE, ALAN H GREENAWAY School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh, UK IAN BAIN Scalar Technologies Ltd, 5 Bain Square, Livingston, Edinburgh, UK Thin film metrology is an important quality control mechanism used in many industrial processes. Conventional techniques of Ellipsometry and Spectral Reflectance are limited in applicability to in situ measurements during film manufacture. This paper considers the measurement of wavefront shape reflected from interfaces within a laminate for determination of layer thickness and profile. For thick layers a wavefront sensor can provide the requisite wavefront shape data, for thin layers the interference between reflected wavefronts is used to retrieve wavefront shape.

1. Introduction Previous work [ 1-21 investigated the applicability of a film thickness monitor based on measuring the spatial separation of reflections from each surface interface. When a plane-parallel film is illuminated with a converging laser beam additional higher order aberrations are introduced which have a dependency on the film thickness. Monitoring of such higher order aberrations will allow the simultaneous measurement of film thickness and interface profile on multi-laminate film structures in real-time for in situ industrial process control. The inclusion of a wavefront sensor to monitor higher order aberration modes to measure film thickness and surface profile simultaneously has been investigated. Simulations have been carried out with the aid of Optalix [3] to determine the most prominent aberrations introduced by the film structure and determine their behaviour under changing system conditions. Experimental tests are used to verify simulated data and an appropriate thickness retrieval algorithm is developed. Experimental results taken of film layers c100pm thick where wavefront interference is utilised are reported. 237

N

238

erration ~ o d e l l i n g

A commercial ray tracing package called Optalix was used to determine the aberration mode strengths induced by film structures and how these vary under conditions of changing thickness, refractive index and surface tilt. These simulated results are used to formulate an appropriate thickness retrieval algorithm based on the Moore-Penrose pseudo-inverse.

2.1. Simu~tionR e s u ~ s A model of the experimental system was used as a basis for the simulated results. A plane-parallel film of thickness 0-100pm with a refractive index of 1.5, illuminated with a convergent beam (f-number=2.5) was modelled, and the most prominent aberration modes shown in figure l(a). Simulations are also carried out where the refractive index is varied (figure l(b)), and the relative surface tilts are varied (figure l(c) and (d)).

Figure 1 Aberration mode strength variation with (a) thickness (b) refractive index (c) horizontal tilt (d) vertical tilt.

These simulated results form the basis of the analysis required to formulate a thickness retrieval algorithm. Linear relationships exist between the aberration

239

mode strengths and the film thickness and surface tilts (both in the horizontal and vertical plane, plane orientations defined in [ 11). A thickness retrieval algorithm can now be formulated based on the gradients shown in figure 1. 2.2. Thick~ess~ e t ~ e v a l It would be extremely desirable to have the ability to measure thickness and horizontal tilt simultaneously in a single measurement. In previous work [l] the thickness and horizontal tilt were disentangled by making two orthogonal measurements on the same sample point. This obviously complicates the measurement procedure and requires either two separate sensors or a sample rotation during measurement, neither of which are ideal for in situ applications. The aberrations affected by film thickness and horizontal tilt have a linear relationship with both. For each of these aberrations the aberration coefficient can be written as a combined linear function, thus

o,,, = amdiP,,,t

(1)

where a,,, is the coefficient (strength) of the mth Zernike coefficient aberration and a,,, Is the linear coefficient that describes how changing film thickness d affects the strength of the mth aberration mode and P , is the linear coefficient ribes how changing tilt t affects the strength of the mth aberration mode. ect various Zernike coefficients we can write a matrix equation in the form: C=MU,

where:

and u =

M =

[:]

As many modes as required can be used in this equation and, provided that the equations are linearly independent the thickness and tilt may be found using the Moore-Penrose pseudo-inverse matrix M :

u=M+C.

(3)

240

The use of such an approach allows film thickness and surface tilt to be retrieved simultaneously from a single measurement. Information of layer thickness, surface tilt and refractive index are encoded in the aberration mode strengths and can be used to give robust measures film thickness and surface tilt. 3. Thin Film Metrology Using Wavefront Sensing

A system was constructed in the laboratory to verify the simulated results. The sample was illuminated with a converging beam produced from a point source and lens combination (the point source is generated by launching a He-Ne laser into a single mode optical fibre) as shown in figure 2(a). The reflected fields are then imaged and analysed using a defocus-based, phase-diversity wavefront sensor [4], the data from which is shown in figure 2(b). The +I diffraction orders appear along the top and bottom of figures 2(b) and 2(c) detailing the defocused planes used in phase retrieval.

(4

(3)

(c)

Figure 2 (a) Experimental layout (b) lmm slide data (c) 2mm slide data.

A 1mm thick microscope slide was used as a sample due to its good quality optical surfaces. Figure 2(b) shows the experimental captures where the front surface reflection appears on the left of the image and the back reflection on the right of the image. The influence on the back reflected fields can be observed by the asymmetric nature of the defocused fields suggesting a strong astigmatic component being introduced by the film layer as expected from figure l(a). A second slide was added (to produce a 2mm thick laminate structure) with the results shown in figure 2(c). The fringed orders which appear are a consequence of the air-gap between the two slides. Reflections from such closely-spaced interfaces overlap with a thickness-dependent shear. The interference fringe shapes encode the relative wavefront phases and this information which can be

241

processed to measure the air-gap thickness if required. Measurements of the thickness of all layers in the laminate are possible using such an approach. For the 1 m case simulated and experimental data were processed using a phase retrieval algorithm based on decomposition into Zernike coefficients [5]. The retrieved phase difference between the front and back reflections are shown in figure 3 for both the simulated and experimental data which detail the aberration modes strengths introduced by the thin layer. Work continues on matching the expected aberration modes strengths generated using the Optalix analysis software and the experimental measures. Decomposition of the retrieved phase into zkrnike coefficients will allow each mode of interest to be monitored and utilised for film thickness and tilt measurements.

Figure 3 (a) simulated phase difference associated with lmm layer (b) experimental phase difference associated with 1mm layer. [z scale in units of waves]

. Film ~ h i c ~ n eUsing s s Wavefront Interference When film layers decrease in thickness it becomes increasingly difficult to spatially separate the surface reflections for analysis by the phase diversity wavefront sensor. In cases where thin layers are measured, the reflected wavefronts can be interfered and a measure of the phase difference gained from the resultant interferogram. Initial experimental results are shown in figure 4.

(a) (b) (0) (4 (el Figure 4. Experimental data from resist samples of thickness (a) 1 4 . 5(b) ~ 2 4 . 5 (c) ~ 2 7 p (d) 4 6 p (e) 6 2 p .

242

Use of a suitable phase retrieval and phase unwrapping algorithm allows the difference in wavefront shape to be calculated and a Zernike fit carried out to identify the constituent aberrations of this difference. Phase retrieval is based on use of the FET [6] to isolate a sideband in the transformed experimental data to gain a measure of the wrapped phase. An unwrapping stage is then required to gain a measure of the absolute phase difference introduced by the film structure. A Zernike coefficient fit is then carried out on the unwrapped phase to decompose the wavefront difference into individual mode strengths. Initial experimental results indicate that a linear relationship between film thickness and retrieved mode strengths exist. This technique extends the dynamic range of the thickness monitor and allows very thin laminate layers to be measured. 5. Future Work It is hoped that further development of the wavefront sensor based thickness monitor will allow thickness measurements and surface form metrology to be carried out on multiple layer laminate structures. With the appropriate phase retrieval algorithm measurements on discontinuous and rough surfaces should be possible, extending the applicability of the sensor.

Ac~owledge~en~ This work was carried out as part of the OMAM (Optical Manipulation and Metrology) Smart Optics Faraday Partnership. D.M.F. would like to acknowledge EPSRC for their Engineering Doctorate sponsorship, the STFC and Scalar Technologies Ltd for their continued support.

References 1. D.M. Faichnie, K. Karstad, I. Bain and A.H. Greenaway, J. Opt. A - Pure Appl. Opt., 7(6), S290-297 (2005). 2. D.M. Faichnie, A.H. Greenaway and I. Bain, SPZE Proc. 6018, 6018OT-1 (2005). 3. Optenso Optical Software Engineering, Herbstweg 9, 86859 Igling, Germany, http://www.optenso.de. 4. P.M. Blanchard, D. Fisher, S. Woods and A.H. Greenaway, Appl. Opt., 38(32), 6692-6699 (1999). 5. T.E. Gureyev, A. Roberts and K.A. Nugent, J. Opt. Soc. Am. A , 12(9), 1932-1941 (1995). 6. M. Takeda, H. Ina and S. Kobayashi, J. Opt. Soc. Am, 72(1), 156-160 (1982).

I F F ~ C T I V EIMAGE S I ~ U L A T I ALEKSEY P. MARYASOV’ Institute of Applied Optics National Academy of Science of Ukraine, 10-G Kudryavska St. Kyiv, 040.53, Ukraine NICOLAY P. MARYASOV Institute of Electronics and Control Systems National Aviation University, I Kosmonavta Komarova Ave., Kyiv, 030.58, Kyiv, Ukraine We present direct diffractive approach and modeling results of test object image simulation under focusing. It provides to get image shape in presence of arbitrary wave front aberrations and different segmentation geometries. Test objects of different forms were illuminated by monochromatic plane wave and image simulation after passing through elementary focusing system have been performed. The simulation results show image degradation under given aperture segmentation and its modifications that cannot be derived by just PSF studies and ray tracing methods.

1. Introduction For the centuries optical science interest concentrated on how to built precision imaging system and have achieved considerable success. Although many optimized methods were developed for characterization of quality imaging system such as point-spread function (PSF), Encircled Energy (EE), Strehl ratio (SF) etc., but direct diffractive image simulation remains developed much less. Importance of it increases when going to more complicated active segmented mirrors and multi-conjugate adaptive optical systems (MCAO), where physical optics propagation (POP) analysis has to be exploited. Precision PSF calculations of segmented telescope mirror by means Modified Sommerfeld Diffractive Integral (MSDI) method was demonstrated in previous work [ 1,2]. Good coincidence of the numerical modeling with the NSOM experimental distributions in the focus of high NA(0.9) microscope objective was shown as well [3].

E-mail: [email protected]

243

244

Here we consider using direct diffractive analysis approach for image simulation from a test object, and will show how it changes when using segmented aperture and non-ideal segments phasing.

o d i ~ e dS o ~ e r f e l d Diffractive Integral (MSDI) ~ e t h o d We used method direct integration of Modified Sommerfeld Diffractive Integral (MSDI) as the core of our C++ program for calculation optical field distribution at different image planes. The integral is based on the general form of diffractive integral expression for potential distribution at propagation through the arbitrary hole [4]. The form of modified integral [ 5 ] :

Here the “modified” integral means that we do not uses Fresnel-Fraunhofer approximation. It main distinction from traditional one is that kr = ( 2 z / A ) r is not supposed to be much greater than 1 and bracket (1 + l/ikr) remains; Cos(n,r )is not considered close to 1 and, hence, the ratio of Cos(n,r)/r is not a constant, so the method is not restricted of constraint type kr>>l. Moreover, the value r in exponent is not cut after linear (Fraunhofer) or quadratic (Fresnel) components of power series expansion and the series expansion do not carried out, that can additionally improve accuracy. We performed image simulation via two steps, as shown in Figure 1.

Figure 1. Schematic representation of image simulation.

245

At first, the diffracted field distribution was obtained in the aperture plane by calculation diffraction of homogeneous plane wave on selected test object at distance L. And at second, we compute image at the image plane ( F + fl by calculation diffraction of convergent spherical wave in combination with aperture field distribution from first step

iffraetive Image Simulation Diffraction-based computations are very CPU intensive and require high performance computers (computer cluster). For simulation purposes we have performed calculations for test object in form of annular square with outer size of 2a = 0.72 mm and width of a/4 = 0.09 mm (see Figure 2a) for wavelength 632.8 nm. Such small dimensions were selected for calculation time decreasing reasons which allows to take less points number in both object and aperture planes (800x800 pts). In the Figure 2 (b,c) shown corresponded simulated dis~ibutionsin 2 planes: the aperture plane at L, and the image plane, at F + f =F + F 2 / ( L - F ) for ideally focused wave front under NA=0.4.

Figure 2. Simulated distributions at different planes: a) test object in form of annular square 0.72x0.72 mm, b) log. distribution of diffracted test object in the aperture plane 1.2x1.2 mm at L-2.8mm. (N~=73);c) simulated log. distribution in image plane 1.2x1.2 mm at F+f =3.23 mm (NF =176); h=632.8 nm, F=lSmm, NA=0.4.

The simulated size of square is equal to 0.415 mm and well agrees with size predicted by geometrical approach. The simulated image shows a diffractive propagation effect, which depends from an aperture and shape, a focal distance and wavelength of the incidence light.

246

The image simulation with accounting segmented mirror was performed as well. In Figure 3(a-c) shown Keck-like mirror segmentation with 2 different gaps: A/25 and A/5 were A=0.2 mm is side of hexagonal element. The simulated distributions shows influence of certain gaps on PSF and corresponding image degradation.

8)

-

1

-

2 gap=A/5

0,1

0,Ol

u0) a. 1E-3 u) 0 I E-4 1 E-5

1E-6

-10

-8

-6

-4

-2

0

2

4

6

8

10

lim Figure 3. Keck-like aperture segmentation with two sizes of intersegment gaps: A/25 and A/5 (a,d); calculated PSF (b,e) and corresponding simulated images (c,Q and calculated PSF for both cases (g); Aperture:800x800 pts., Image:200x200, F+f =3.23mm, F=lSmm

247

4. Conclusions The direct diffractive image simulation performed for test object in form of annular square. Different gape sizes considered for Keck-like segmentation with central obscuration. The simulation results show image degradation under given segmentation and its modifications. Such precision diffractive simulation will help to account different effects caused by focusing system construction and which cannot be reduced by A 0 system (for example obscuration by the secondary mirror and its supports) by accounting their physically position in respect to the aperture. Furthermore, we show that the quality of simulated image strongly dependent from the distance between an object and aperture plane. And ever for ideal PSF of focusing system, under high distances we will collect only the central diffraction lobes, which gives information only about object direction.

References 1. A. P. Maryasov. and N. P. Maryasov, ”Numerical modeling of influence telescope segment placement at aperture and its quality on focusing radiated field”, in Modeling, Systems Engineering, and Project Management for Astronomy 11, ed. by Martin J. Cullum, George 2. Angeli, Proc. of SPIE, 6271,6271 lB, (2006). 2. A.P. Maryasov and N. P. Maryasov, Journal of Electronics and control systems at Nat. Aviation Acad., 2(8), 66-71, (2006), in Ukrainian. 3. A P. Maryasov and N. P. Maryasov The numerical calculation of converging light beam diffraction on apodized aperture, Proc. of 3-rd International Conference on Laser Optics for Young Scientists (LOYS2006), Saint-Petersburg,Russia. 4. A. Sommerfeld, Optics. Moskow, “Inostrannaja Literatura”, 1953, Chap. 5, in Russian. 5. A. P. Maryasov and N. P. Maryasov, “Modeling the fine structure of focused optical field at diffraction on a hole with arbitrary shape”, in International scientific Conference on Advanced Optoelectronics and LASERs’2005, Yalta, Ukraine, Proc. of IEEE, pp.181-184, (2005).

S ~ E SMAKT E ~ CMOS SENSOR FOR A ~ A ~ T ~0V E T.D. RAYMOND AND DANIEL R. NEAL AMO/Wavefront Sciences, 14820 Central Ave., SE, Albuquerque, NM, USA A. WHITEHEAD AND G. WIRTH Southern Vision Systems, Inc., 8215 Madison Boulevard, Madison, Alabama, USA We describe the design and experimental performance of a smart Shack-Hartmann wavefront sensor based on a high speed CMOS imager chip and a Field Programmable Gate Array (FPGA) capable of full frame operation at 500 frame& and operated via simple USB2.0 interface. Two FPGA firmware designs are described. The serial version is most suited to modest speed (100 framesh) high precision (2 micro radian) optical metrology applications. The parallel version provides an on-board wavefront decomposition and is most suited to high speed (500 frameski) modest precision (5 micro radian) applications. Both versions provide high density spatial sampling with greater than 2300 ienslets analyzed.

1. Introduction Many industrial and ophthalmic applications can benefit from the implementation of high speed, high precision wavefront sensors for metrology and closed loop adaptive optic (AO) correction. Unfortunately, the cost and engineering complexity of such systems has prevented their widespread use. A major impediment to the implementation of high-speed adaptive optic (AO) and optical metrology (OM) methods is the high specialization and cost associated with the hardware and cabling necessary for high-speed sensor readout and data processing. Therefore, high-speed A 0 has historically been relegated to astronomy, where the substantial development costs are warranted by need. The high degree of customization, as well as the complex interconnection of elements in such systems deter their application in other areas, and make them decidedly non-portable. To broaden the accessibility of high speed A 0 and OM components, we have undertaken the development of a smart Shack Hartman sensor. The smart sensor incorporates an on-board dedicated processor capable of executing the complex, numerically intensive operations required to measure a wavefront or determine signals for an A 0 element or metrology tool. By processing the vast raw-image data on board the sensor, the data transmission 248

249

bandwidth requirement is substantially reduced, so that the data may be ported via conventional interconnection. Further, with the data so pre-processed, the host computer is freed to deal with other system components such as A 0 elements or motion control and data tora age'.^. The system interconnections become particularly simple when smart A 0 elements are used, e.g., USB driven A 0 elements like the MultiTMmirrors (AgilOptics, Albuquerque, NM, USA. The characteristics of this sensor are distinctly different from those typically developed for light-starved astronomy A 0 and from previous FPGA based Shack-Hartmann sensors. In this work, the precision and spatial resolution of the sensor is improved at the expense of light sensitivity to provide a sensor more suitable to industrial A 0 and OM applications. By sampling the focal spots with more pixels this sensor operates with high dynamic range and excellent wavefront precision.

2. ~escriptionof the Hardware The smart sensor is based on the Specterview camera (Southern Vision Systems, Inc., Madison, AL,, USA). This commercially available unit incorporates a 10-bit, CMOS imager chip comprising 1280 X 1024 12 pm square pixels (Micron MI-MV13). The data may be read out 10 columns at a time, and the full-frame data may be read at 500 frame& (for integration times less than 150 ps); higher frame rates can be achieved for sub aperture readout. Provision has been made for temperature stabilization of the imager chip. Two custom-designed lenslet square grid arrays, with 0.24 and 0.280 mm square lenslets, respectively, have been used with this camera; the arrays have 3038 (62 by 49) and 2322 (43 by 54) lenslets, respectively. The arrays are produced using a 32-level gray scale lithography process resulting in best form lenses that operate near the diffraction limit. The lenslets map onto either 20 X 20 or 23.3 X 23.3 pixel areas of the imager. The lenslet focal lengths are 24.46 and 28 mm, respectively. The central lobes of the Frauhaufer diffraction-limited spots illuminate about 100 or 150 pixels. As demonstrated below, the large number of illuminated pixels ensures precise spot location and excellent slope linearity within the dynamic range of the sensor. A Field Programmable Gate Array (FPGA) controls the basic chip functions as well as the wavefront calculations. The FPGA (Xilinx Model # XC2W30) has 3,000,000 gates and operates at a clock rate of 66 MHz. The FPGA firmware is developed off line and uploaded to the unit via USB2.0 interface upon camera initialization. Control of the camera is via dynamic link library on a host personal computer. Two versions of the smart camera have been designed. The first, which we will call the serial version, is most appropriate to OM and modest speed A 0

applications where very high precision is necessary. The firmware is designed to operate with the 0.280 mm lenslets with the 28 mm focal length and larger spots. The firmware for the serial version applies a locally adaptive threshold method specifically designed for the square Fraunhofer intensity distribution produced by the lenslets and calculates partial sums required to locate the spots precisely. The partial sum values (three per lenslet) are downloaded via the USB interface to the host computer, which then divides the sums by the appropriate local intensity normalization and geometric factors to yield the local phase gradient and then reconstructs the wavefront. This method of spot location is accurate to the 0.01 pixel level, which corresponds to less than 2 micro radians of slope uncertainty on the overall wavefront. The extensive FPGA resources required for the spot location algorithm, and the fact that each lenslet maps onto a column width that is not an integer multiple of 10 columns, requires that the image data be processed serially by the FPGA (one column at a time), limiting the smart sensor speed to about 100 framesls. The second version, which I will refer to as the parallel version, is appropriate to applications where high speed is of greatest importance and where a slight compromise in spot location precision is tolerable, e.g., atmospheric A 0 correction. This version uses a lenslet array with lenslets that cover 20 columns each to exploit the parallel readout capability of the Micron imager chip. In this case, the R G A data processing resources are allocated to handle the high speed parallel data stream. A user definable spot location reference vector may be uploaded to the FPGA. In contrast to the serial firmware, the parallel firmware provides full on-board calculation of the spot displacements relative to the reference locations and is also designed to carry out a matrix multiplication suitable for wavefront reconstruction or direct communication to an A 0 element control without burdening the host computer with these arduous calculations. The user may elect to either download the 6076-element spot displacement vector or to internally multiply this vector by a user definable 6076 X 78-element matrix that yields a downloadable output vector as long as 78 elements. This vector length is sufficient to produce polynomial wavefront fit with 78 coefficients (e.g., a Taylor or Zernike decomposition complete to 10" order) or to directly drive a medium density A 0 element. As the resources required to achieve this level of data processing are substantial, the sophistication of the spot location algorithm is limited to simpler methods that require less resources than used in the serial version. As is the case with the serial firmware, an adaptive threshold is applied to the raw image data, but the spots are then located using a simple centroid method that does not take advantage of apriori knowledge of the spot intensity distribution. This firmware version is capable of operation at 500 framesls.

251

Both firmware versions have extensive features and diagnostic capabilities that facilitate sensor setup and enable firmware validation. These include the ability to electronically shift the portion of the image analyzed and to simultaneously download the raw image and the corresponding processed data information. In the parallel version, the user is also allowed to upload a userdefined raw image for firmware processing; this feature greatly aids in the infield validation of new firmware releases.

3. Experimen~IResults The Micron MI-MV13 imager chip was tested for use in a Shack-Hartmann sensor with collimated light at precisely controlled tilt angles. The serial processing firmware was used in these tests. A single mode fiber from a fiber-coupled 785 or 635 nm diode laser was attached to an XYZ translation stage with computer controlled linear actuators. The light from the fiber was collimated using either a 750 or 400 mm focal length lens; collimation was tested using a shear plate. The optical path was shielded from drafts in the room. When the fiber was translated orthogonal to the optic axis a collimated wavefront with well-defined tilt angle was created. The wavefront tilt could be controlled to better than +1 microradians within a range of several milliradians.

I

-1.5

.$

-0.5

0

05

1

WavefmntTllt in X Dlrectlon (mR)

1.5

0

0.7

0.2

0.3

0.4

0.5

0.6

Time (sac)

Figure 1 The tilt response of the smart sensor with the serial firmware is quite linear. The triangles are the residuals from the linear fit and represent a standard deviation of 1.4 microradians. The chart on the right shows the tilt measured at 100 frames/second with the wavefront tilt nominally static.

252

1000

10000

Exposure (usec)

Figure 2 Shows the speed of the scnsor with the parallel firmware. The peak frame rate is 511 frameslsecond and rolls off only for exposure times in excess of 2 milliseconds.

Figure 1 shows the sensor response when operating with the serial firmware. The chart on the left shows the sensor tilt response to wavefront tilt. The sensor response is highly linear over the rt1.25 milliradian scan range; the residuals from the best fit are randomly distributed with a standard deviation of 1.4 microradians. In the chart on the right, the fiber source is held at a static location. The average wavefront tilt is plotted for a series of 80 images captured at the maximum frame rate of approximately 100 frames per second. Figures 2 and 3 show the sensor responses with the parallel firmware. Figure 2 shows the frame rate of the camera versus the exposure time. As the calculations are done in parallel to the chip exposure, the frame rate is above 500 frameslsecond for exposure times less than 2 msec. Figure 3 is analogous to Figure 1. The linearity is once again excellent over the 5 milliradian range with an RMS deviation from fit of 5.2 microradians, a value consistent with the simpler spot-locating routine used in the parallel firmware. The chart on the right shows the average tilt data acquired over a one second interval with an exposure time of 300 microseconds and frame rate of 500 frames/second. Clearly the atmospheric turbulence is well sampled in this case.

. ~QnclusiQns We have demonstrated that this high speed, smart sensor has high linearity and low noise floor and is thus a promising candidate as a component to adaptive optic system and high speed metrology systems. In either configuration, the smart sensor represents an advance in the packaging of high speed ShackHartmann sensors. Because of the improved packaging, the cost of such systems

253

1

-5-4-3-2-10

1

2

3

4

Wavefront Tilt in X Direction tmR)

5

0

0.1

0.2

0.3

0.4

0.5

0.6

Time (sec)

Figure 3 The sensor response with the parallel firmware is also highly linear; in this case the residuals have a standard deviation of 5.2 microradians. The chart on the right is analogous to that in Figure 1. With the parallel firmware, the tilt may be sampled at 500 framedsecond; the data clearly show that the sensor is capable of resolving the high frequency atmospheric components.

is lower than competitive technologies, and is especially attractive when the smart sensor is coupled to a smart deformable mirror.

Acknowledgements The authors would like to thank the state of New Mexico Technology Research Collaborative and the Center for Industrial Adaptive Optics (CIAO) for fundingt and Dennis Mansel and Harvey Packard at AgilOptics, and Professor Gary Loose at the Magdalena Ridge Observatory for their insightful technical contributions and project oversight, Phil Riera and Mike Kinney at AM0 for their technical contributions in collecting these data.

eferences 1. Goodsell S.J., Dipper N.A., Geng D., Myers R.M., Sunter C.D., “DARTS: a low-cost high-performance FPGA implemented real-time control platform for adaptive optics”, SPIE 5903,2005. 2. Fedrigo E., Donaldson R. Soenke C., Hubin N., “The ESO adapative optics real time computer platform: a step toward the future”, SPIE 5490. 3. Goodsell S.J., Fedrigo E., Dipper N.A., Donaldson R., Geng D., Myers R.M., Saunter C.D., “FPGA developments for the SPARTA project”, SPIE 5903,2005. 4. Rodriguez-Ramos L.F., Viera T., Gigant J.V., Gag0 F., Herrera G., Alonso A., Desharmes N., “FPGA adaptive optics system test bench”, SPIE 5903, 2005.

~EABLE A§TIGMATI§M MEA WAVEFRONT §ENS

ME

IT

S . D. KNOX,S . R. G.HALL, R.F. STEVENS Optical Technologies & Scientgc Computing,National Physical Laboratory, Teddington,Middlesex l W l 1 OLW, UK

The increasing use of wavefront sensors for metrology in industrial, medical and scientific applications, in particular those of the Shack-Hartmann type, has driven the need for consistent measurements between commercial instruments spanning the full range of measurement configurations. To fulfill this need a traceable calibration method is essential. At the National Physical Laboratory (NPL) we have developed measurement traceability for wavefront sensors using artefacts that generate prescribed levels of wavefront aberration. In the work described here we concentrate on astigmatic wavefront measurements. The artefacts have been designed using reflective optics to enable the same value of aberration to be generated at both visible and infrared wavelengths.

1. ~ a v e f r o nArtefact t An astigmatic wavefront is generated by the artefact shown schematically in figure 1. The artefact uses two spherical mirrors operating off-axis and is illuminated by a spherical wavefront from an optical fibre. Astigmatic wavefront

Laser source

optical fibre Figure 1. Design of astigmatic wavefront generator.

* This work was supported by the Department of Trade and Industry’s National Measurement System Directorate (NMSD) under contract number GBBWUI 1/12

254

255

A small aperture is located between the mirrors and is conjugate with the plane in which the wavefront sensor under test is placed. This aperture limits the diameter of the wavefront to that appropriate to the test device. The geometry and position of the mirrors control the level of astigmatism introduced and three artefacts of this design have been produced to offer a range a wavefront astigmatism values, typically 3 pm to 10 pm. A photograph of one artefact is shown in figure 2.

Figure 2. Photograph of wavefront generator.

2. Veri~cation Measurement traceability for the artefacts has been achieved by comparison against the NPL primary interferometer system at a wavelength of 632.8 nm. The artefact was illuminated in double pass with the collimated beam from the NPL Fizeau interferometer. The wavefront from the artefact was amplitude divided at a beamsplitter and measured simultaneously with the NPL interferometer and the Shack-Hartmann (SH) wavefront sensor. The wavefront aberration generated by the artefact in single pass was deduced from the double pass value and used to

256

verify the SH system under test. Because the artefact uses reflective optics the aberration is assumed to be constant with the wavelength of illumination. The lack of refractive elements in this artefact and the use of surface coated mirrors produces a constant aberration over the wavelength range of interest.

3. Initial check

A first check was made by measuring the collimated wavefront generated by the Fizeau interferometer and reflected from a flat mirror. Astigmatism was then introduced by inserting a weak cylindrical lens as shown in figure 3.

Figure 3. Test arrangement for simultaneous measurements.

The values measured by both the SH sensor and the phase-stepping interferometer showed agreement at the 0.2h level using a wavelength of 632.8 nm and typical measurements are shown in figure 4. M*im(i

(0)

m1IB35

(b)

Figure 4.Measurements on wavefront transmitted by cylindrical lens and mirror (a) interferometer measurement, (b) SH wavefront measurement.

257

To ensure the same wavefront shape was measured by both systems the interferometer camera was focused on a plane conjugate to the measurement plane for the SH sensor. A graticule was positioned in this plane and used to measure the magnification of the imaging optics of the interferometer and the pixel pitch values of the detection CCD. This enabled us to measure over the same dimensions of wavefront with each system.

. A s t i g m a t i ~artefact ~ u b lpass e measurement The lens and mirror shown in figure 3 was replaced with the astigmatism artefact shown in figures 1 and 2. To enable the collimated beam from the interferometer to illuminate the artefact in double pass, the optical fibre was removed from the artefact and replaced with a co-locatable plane mirror to give a cat's-eye reflection. In practice we inserted into the fibre holder a neodymium YAG laser rod with the same diameter as the fibre ferrule and used the optically flat end surface as the cat's-eye mirror. The artefacts were measured with different sized apertures to give a range of beam widths and astigmatism values suitable for a diverse selection of wavefront sensors. Figure 5 shows typical results.

Figure 5. Measurements on wavefront transmitted by astigmatism artefact in double pass (a) Interferometer measurement,(b) SH wavefront measurement.

258

4.2. Single pass measurements at two wavelengths For single pass measurements the artefact is illuminated with a laser and optical fibre as the source. The wavefront aberration generated by the artefact in single pass is calculated as 50% of the value measured in double pass. Figure 6a shows the result for a SH measurement using the artefact in single pass at a wavelength of 632.8 nm. Figure 6b shows a similar measurement using a different SH ins~rumentat a wavelength of 1550 nm.

Figure 6a. Wavefront from astigmatism artefact measured in single pass at 633 nm with SH system. Figure 6b. Artefact measured in single pass at 1550 nm with a different SH system.

5. Conclusion We have designed a wavefront aberration artefact using simple reflective optics working off-axis to generate astigmatism. It is suitable for verifying the performance of wavefront sensors at visible and infrared wavelengths. Initial trials with an artefact that generates 5h of astigmatism at 632.8 nm have shown agreement between a Shack-Hartmann system and the NPL Fizeau interferometer at the 0.2h level. Using a different Shack-Hartmann system at a wavelength of 1550 nm agreement was at the O.lh level.

259

~c~owledgment This work was supported by the Department of Trade and Industry’s National Measurement System Directorate (NMSD) under contract number GBBK/C/l 1/12

eferences 1. S. D. Knox, S. R. G. Hall, R. I;. Stevens, “Traceable Measurements with Wavefront Sensors”, SPIE Proceedings 5965,2005. 2. J. M. Geary, “Introduction to Wavefront Sensors”, SPIE Optical Engineering Press 7718,1995. 3. R. S. Longhurst, “Geometrical and Physical Optics 3rdEdition”, Chapter 16, p. 406, Longman, 1973.

Contacts [email protected] simon.hal1 @nd.co.uk [email protected]

This page intentionally left blank

This page intentionally left blank

~ A L - C O N ~ ~ G AADAPTI~E TE OPTICS I N § T R ~ E N TFO ~ I D E - F I E L D~ T I N A L I~AGING JORGEN THAUNG Department of Ophthalmology, Goteborg University, SU/Molndal Molndal, SE43180, Sweden thaung @of.gu.se METTE OWNER-PETERSEN Telescope Group, Lund Observatory, Lund University, Box 43 Lund, SE22100, Sweden ZORAN POPOVIC Department of Ophthalmology, GBteborg University, SU/Molndal Molndal, SE43180, Sweden

To date only conventional single-conjugate adaptive optics (SCAO) systems are used to correct ocular aberrations. A major shortcoming of SCAO is the severely restricted corrected field of view. This can be solved with multi-conjugate adaptive optics (MCAO), a solution that is costly and gives bulky instruments. Another problem, especially in the study of the human eye, is unwanted light from parasitic source reflections and light from unwanted object regions. We present a dual-conjugate adaptive optics (DCAO) demonstrator that will enable wide field high resolution imaging of the human retina in vivo, implementing five retinal guide stars, two O K 0 micromachined membrane deformable mirrors; a 15 mm 37 channel pupil conjugate mirror, and a 40 mm 79 channel mirror conjugated to a plane in the vitreous body approximately 3 tnm in front of the retina. The A 0 system runs with a closed-loop measurement wavelength of 835 nm. It incorporates an array of collimator lenses to spatially filter the light from all guide stars using only one adjustable iris, and a single camera to image the Harhnann patterns of multiple reference sources. Optical simulations in Zernax indicate an increase of the retinal isoplanatic patch from a radius of 0.5 degrees using SCAO to approximately 3.5 degrees or more using DCAO. The advantage of this is a clinically useful imaging area that is approximately 50 times the size of an SCAO system. This is corroborated by measurements on a mode1 eye while performing SCAO, ground layer adaptive optics (GLAO), and DCAO correction..

* This work is supported by Swedish Research Council Grant No. 2003-6254, The Gtiteborg

Medical Society, De Blindas VXnner in Gtiteborg, Kronprinsessan Margaretas ArbetsnXmnd ftir synskadade.

263

264

1. Introduction Clinical retinal imaging is limited by the wavefront aberrations of the human eye. The introduction of adaptive optics (AO) in retinal imaging has been successful in correcting for most aberrations and enabling diffraction limited imaging, albeit only over small fields of view (FOV). This is due to the fundamental limitation of conventional single-conjugate A 0 (SCAO) with only one retinal guide star (GS) and one deformable mirror (DM), which enables good correction close to the GS, the ‘isoplanatic patch’. Full correction is not achieved as one moves away from the retinal position of the GS, thereby decreasing image quality. Beckers [ 11 introduced the concept of multi-conjugate adaptive optics (MCAO) as a means of increasing the size of the isoplanatic patch. The principle of astronomical MCAO is to accomplish this by optically conjugating several DMs to different altitudes in the atmosphere. In ophthalmology this is equivalent to conjugating the DMs to different planes in the eye. The technique of MCAO is just emerging. There have been a few reports on laboratory test bench MCAO systems for astronomy [2-41 and only one paper on MCAO for the eye [5]. The first physical implementation in a large-scale astronomical observatory was recently demonstrated when the Multi-Conjugate Adaptive Optics Demonstrator (MAD) achieved ‘First Light’ at the ESO Very Large Telescope (VLT). Corrected images were obtained over the full 2x2 arcminute FOV, substantially larger than the 15x15 arcsecond FOV of conventional A 0 systems - an increase in FOV area by a factor of 64. We present a closed-loop dual-conjugate adaptive optics (DCAO) demonstrator for wide-field high resolution imaging of the retina with a comparable increase in corrected FOV. 2. ~ e t h o d s Our DCAO demonstrator (Figure 1) uses five retinal GSs and two DMs; one 15 mm 37 channel pupil conjugate mirror and one 40 mm 79 channel mirror conjugated to a plane in the vitreous body approximately 3 mm in front of the retina, both O K 0 MEMS mirrors (Figure 2). Continuous relatively broadband near-infrared light (835+14 nm) from a super-luminescent diode (Superlum Ltd, St. Petersburg, Russia) is fed through five single-mode fibers to form five separate collimated rays. These are relayed over the DMs and a Badal system into the eye. The periferal GSs are symmetrically placed 0.62 mm [2.2 deg] from the central GS. Reflected light passes back through the system and into the WFS

265

arm, where a novel spatial filtera filters the light from the five GSs with only one adjustable aperture (Figure 3). All five Hartmann patterns are imaged on a single wavefront sensor ( W S ) camera (Figure 4). Optical simulations were performed with the Zemax optical design software using the Navarro 99 eye model [6].

Laser Guide star

EYE

.'".'.t;-

:

..........2 Badal

focus

carreftor

Figure 1. Schematic diagram of our DCAO demonstrator.

Figure 2. Conjugate planes in the eye, and corresponding DM footprints. M. Owner-Petersen, J. Thaung, and 2. Popovic. Multi-object wavefront sensor with spatial filtering. USPCT patents pending.

266

Figure 3. Through focus images at the WFS spatial filter plane.

..

* .

" "

...*.*. . .. t *

4 1'..1

+ . . * I + .

.*+..'*'

1.

*+*tt+r.

I +

+*.*++.

fill...

t. . . l f . .

'.....+..** .'.. *. . * '..*.*.*... I+

..I

111.1

+ I + .

+.*+.

.*+*.*.

....* 1 . 1 1 . .

I * * +

Figure 4. Zemax simulation (left) and actual image (right) of the five GS Hartmann patterns on the WFS camera.

3. Results The system runs with a closed loop correction frequency of approximately 12 Hz in DCAO mode and 14 Hz in SCAO mode. Averaging 5 WFS images lowers the correction frequency to approximately 4 Hz. Simulated estimates of DM stroke (full Badal defocus correction) was 3.75 pm PTV for the pupil conjugate mirror and 20 pm PTV for the second mirror. Zemax simulations indicate an increase of the retinal isoplanatic patch from a radius of about 0.5 degrees using SCAO to approximately 3.5 degrees using DCAO (Figure 5). Real images of a model eye with a fiber bundle as a retina are shown in Figure 6 together with insets showing GS positions. The corrected FOV corresponds well to predicted Zemax results.

267

‘DIFfRACTtON LlYI

LI DIII(tXj -cDY2(+Y)

0.00

Fiaid angle (deg)

Figure 5. Plot of simulated image plane Strehl ratio vs. radial field angle at 830 nm in the upper vertical, lower vertical, and horizontal hemimeridians, using single DM and DCAO correction with five active GSs.

Figure 6 . Real images from initial tests with model eye. Left image uncorrected, right image with MCAO and three out of five active guide stars (whiteactive, gray=inactive). The center and left field of the right image are corrected.

Actual correction is currently slightly less due to the eye’s relatively large longitudinal chromatic aberration (LCA), approx. 2D over the visible spectrum. The measurement wavelength is 835 nm and an imaging wavelength would be in the visible spectrum. Simulations in Zemax show an axial path length difference of 18.6 mm between the 830 nm and 570 nm focal planes in the imaging arm and also a decrease in Strehl ratio (Figure 7). The introduction of a chromatic aberration corrector into the imaging arm slightly lowers the on axis Strehl ratio. However, the corrected FOV radius increases approximately by an additional 0.5 deg.

268

Fleld angle (deg)

Figure 7. Plot of simulated image piane Strehl ratio vs. radial field angle in the upper vertical, lower vertical, and horizontal hemimeridians at wavelengths of 830 nm (measurement) and 570 nrn (imaging).

iscu§§ion The main advantage of a DCAO system is a clinically useful corrected FOV, i.e. imaging area, that is approximately 50 times larger than in SCAO. In our system a 2x2 mm’ (7.2x7.2 deg’) retinal field roughly corresponds to 15.7x15.7 mm”2 on the science camera. The Airy radius at 570 nm is roughly 13 pm in the image plane, so the pixel size should be around 6.5 pm and the camera format should be 2415x2415 pixels in order to satisfy the Nyquist sampling criterion. Enlarging the pixel size to 7.5 pm will provide a slight undersampling at 570 nm and a slight oversampling at 830 nm. For a 2048x2048 camera format the field will be 15.4x15.4 mm’, closely matching a 2x2 mm’ retinal field which should potentially be well corrected and unvignetted using DCAO.

eference§ 1. J. M. Beckers, Large Telescopes and Their Instrumenta~~o~ (European Southern Observatory symposium, Garching, Germany), 693 (1988). 2. P. A. Knutsson and M. Owner-Petersen, Opt. Exp. 11,2231 (2003). 3. M. Langlois, C. D. Saunter, C. N. Dunlop, R. M. Myers, and G. D. Love, Opt. Exp. 12, 1689 (2004). 4. A. V. Goncharov, J. C. Dainty, S. Esposito, and A. Puglisi, Opt. Exp. 13, 5580 (2005). 5. P. A. Bedggood, R. Ashman, G . Smith, and A. B. Smith, Opt. Exp. 14,8019 (2006). 6. I, Escudero-Sanz and R. Navarro, J Opt Soc Am A Opt Image Sci Vis. 16, 1881 (1999).

LAURENT VABRE, FABlUCE HARMS,NICOLAS CHATEAU Imagine Eyes Orsay, France M O L I N N E MAIA ROCHA Federal University ofS&oPaulo Siio Paulo, Brazil RONALD R. KRUEGER Cole Eye Institute, Cleveland Clinic Cleveland, OH, USA This study assessed the visual effects of correcting and modifying higher-order ocular wavefront aberrations in a group of subjects using an adaptive optics system based on electromagneticdeformable mirror technology. The results showed that the correction of higher-order aberrations significantly improved visual performance compared to best sphere and cylinder correction. The introduction of single Zemike aberrations of same RMS magnitude and different mode numbers led to similar decreases in visual acuity when the applied aberration was relatively low (up to 0.3 pm). With larger amounts of pure Zemike aberrations (0.9 pm),rotationally symmetric modes led to more pronounced decreases in visual performance than non symmetric modes.

1. Introduction Adaptive optics technologies have found several applications in clinical and investigational ophthalmology. Wavefront aberrometers based on ~ ~ m a n n Shack sensors are now routinely used by eye surgeons to perform customwavefront corneal ablation procedures. Adaptive optics instrumentation has enabled several research groups to image the retinas of living eyes with a resolution of a few micrometers and made it possible to visualize cone photoreceptors and other retinal microstructures in vivo (Liang et al. [ 11, Carol1 et al. [ 2 ] ) . Adaptive optics systems have also been used by to modify the aberrations that affect the vision of human subjects and to assess the effects of 269

270

such optical changes on visual performance (Liang et al. [l], Fernhdez et al. [3], Yoon et al. [4]). As human eyes may suffer from a variety of aberrations, including sometimes higher-order aberrations with a RlMS amplitude of several micrometers, ophthalmic applications are very demanding. In particular, these applications require wavefront modulators able to generate a wide range of wavefront shapes and amplitudes. Fernhndez et a]. [5] demonstrated that a deformable mirror technology based on electromagnetic actuators was suitable for correcting monochromatic aberrations in a majority of human eyes, including eyes that suffer from large wavefront errors due to corneal pathology. In the present investigation, the magnetically actuated adaptive optics technology was used to correct and modify wavefront aberrations in the eyes of several subjects. An objective of the study was to measure and compare the effects of various single Zernike aberrations, including large wavefront errors, on visual performance.

etho We used a crxl adaptive-optics visual simulator (Imagine Eyes, France), as shown in figure 1, to measure and introduce wavefront aberrations in nine subject eyes, including seven normal eyes and two eyes previously diagnosed for moderate keratoconus. The crxl simulator is based on a 1024 lenslet ShackHartmann wavefront sensor, a 52 actuator magnetic deformable mirror[5] driven in a closed-loop system and an 800x600 pixels micro-monitor. After an initial measurement of the subject's ocular aberrations, we programmed the device to compensate for the eye's wavefront error, first for the second order only (sphero-cylinder correction), then up to the fifth order. We also successively applied several pure Zernike modes. These single Zernike aberrations were generated through a 5 mm artificial pupil and included defocus astigmatism, coma, trefoil and spherical aberration ranging from 0.1 to 0.9 pm. The different Zernike modes were presented in randomized order. We assessed monocular visual acuity using Landolt C optotypes generated at the device internal micro-monitor using a PEST staircase method. The psychophysical procedure was driven by the Freiburg Acuity Test software (Bach [6]). For each subject, the changes in visual acuity were computed by subtracting a baseline visual acuity value, measured with the best possible wavefront correction, from the visual acuity findings obtained while adding individual Zernike aberrations.

271

Figure 1. Photographic view of the crxl adaptive optics simulator.

3. Results The adaptive-optics correction of the aberrations present in the subjects' eyes up to the fifth order improved their visual acuity by roughly one optotype chart line (-0.1 LogMAR) in average, when compared to their best spherocylinder spectacle correction (see figure 2). Small amounts of single Zernike aberrations (0.1 pm RMS) resulted in a limited decrease in visual acuity, by less than half a line (+0.05 LogMAR) in average (figure 3). Medium amounts of Zemike aberrations (0.3 pm RMS) induced visually significant acuity losses that averaged to 1.5 optotype line (+0.15 LogMAR), without showing any clear dependence on the Zernike mode number (figure 4). Large aberrations (0.9 pm RMS) resulted in higher acuity losses that were more pronounced with spherical aberration (+0.64 LogMAR) and defocus (+0.62 LogMAR), while trefoil (+0.22 LogMAR) appeared to be better tolerated than other Zemike modes (figure 5).

272

0.2 I

'

-0.3

Y

SC SC+HOA Correction

Figure 2. Visual acuity (VA) of the study subjects measured with two different configurations of the adaptive optics system. SC: correction of spherical defocus and astigmatism. SC+HOA correction of all wavefront aberrations up to order 5. LogMAR units are interpreted as follows: a decrease of 0.1 LogMAR corresponds to an improvement in the subject's reading ability of approximately one line in a letter chart.

Figure 3. Statistics of the changes in VA induced by the application of individual %mike aberrations in an amount of O.1pm RMS. An increase of 0.1 LogMAR corresponds to a degradation in the subject%reading ability of approximately one line in a letter chart.

273

RNS = 0.3 urn

Figure 4. Statistics of the changes in VA induced by the application of individual Zemike aberrations in an amount of 0.3pm RMS.

Figure 5. Statistics of the changes in VA induced by the application of individual Zemike aberrations in an amount of 0.911mRMS.

274

. Conclusion The electromagnetic adaptive optics technology was able to correct and generate relatively large amounts of second to fifth order aberrations. The correction of higher-order ocular aberrations generally improved visual acuity compared to best-spectacle correction. As observed in previous investigations using computer simulated retinal images (Applegate et al. [6]), the effect of large single Zemike aberrations on visual acuity appeared to be strongly dependent on the mode number, with lower azymuthal orders being more detrimental to visual performance. Ac~owled~ents We gratefully acknowledge the help of Franck Martins and Xavier Levecq in designing and building the adaptive optics system. eferences

1. J. Liang, D. R. Williams and D. T. Miller, J. Opt. SOC.Am. A 1 (1997). 2. J. Caroll, D. C. Gray, A. Roorda and D. Williams, Optics and Photonics News, 36 (January 2005). 3. E. J. Fernandez, S. Manzanera, P. Piers and P. Artal, J. Refract. Surg. 1 S634 (2002). 4. G. Y. Yoon and D. R. Williams, J Opt SOCAm A 19,266 5. E. J. Femandez, L. Vabre and A. Hermann, Opt. Express 6. M. Bach, Optom. Vis. Sci. 73,49 (1996). 7. R. A. Applegate, C. Ballentine, H. Gross, E. J. Sarver and C. A. Sarver, Optom. Vis. Sci. 80,97 (2003).

IG

SOLUTION F I E L ~ - O F - V I E~ ~~ E N I NING EYE RETINA IMAGING

AN

ALEXANDER V. DUBININ, TATYANA W. CHEREZOVA Physical Department, Moscow Lornonosov State University, Vorobiovy Gory bld. 1/62, 1 19899, Moscow, Russia

ALEXEY V. KUDRYASHOV Moscow State Open University, Sportivnaya 9, 140700, Shatura, Moscow Region, Russia In this paper we investigate methods of widening high resolution area in fundus cameras equipped with adaptive optics. We first considered average phase correction method. It was found out that this method leads to isoplanatic patch increasing but residual error of correction between the reference sources increases. We also investigated the performance of an adaptive system with five reference sources and two correctors. For optimal corrector and reference sources positions we obtained approximately two times enlargement of isoplanatic patch area.

1. ~sopIanaticpatch d ~ ~ n i t i o n To get high quality of human retina image adaptive optics approach is often applied' and new generation of fundus-cameras are suggested to equip with adaptive correctors. But even in the case of ideal corrector, retinal image is still degraded by the effect of anisoplanatism'. That means we can get high-resolution image quality only within a finite area around the reference source - the isoplanatic patch. In this paper we discuss possible ways to enlarge isoplanatic patch size. We define the residual mean-square error of correction as:

1 u2(a)= - J&2(@, ?)d2r'

SS where E ( a , i") = q(a,r') - p(0, i") , cX is angular distance between the beacon position and the imaged point on the retina (we assume initial angular coordinate of the beacon to be O"), r' -is coordinate-vector in the pupil plane, (%(a, r') - wavefront from imaged point on the retina, p(0,r') - beacon wavefront, S is the pupil area. We define isoplanatic patch size as area where residual mean-square error of correction is less than 1 rad'. In the paper we 275

276

consider only ideal wavefront corrector that can ideally compensate for the aberrations of the wavefront from the reference source.

ethods of isoplanatic patch widening

2.1. Average phase correction method There are several methods of isoplanatic patch widening known from adaptive optics for astronomical applications such as for example average phase correction method and multiconjugate correction. These methods can be also applied for human eye isopianatic patch widening. First of all we investigated average phase correction method when average phase coming from different sources is calculated and applied to one corrector. On the basis of experimental measurements of human eye aberrations for different retinal eccentricities we estimated the efficiency of this method3.Figure 1 demonstrates the residual rootmean-square error of correction vs. angular distance between reference source and the point being imaged for subject AD.

angle, deg

Figure 1. Result of average phase correction method application for subject AD. Squares represent RMS error of correction using I reference source. Circles iilustrate the case of average phase correction using two reference sources placed at -1" and 1". Corresponding values of isoplanatic patch size 00 are also shown.

277

Isoplanatic patch size in the case of correction using one reference source for subject AD was found to be 2.6". It is shown that when this method was applied isoplanatic patch size was increased from 2.6" to 4.2" for this subject. Similar results were achieved for other subjects (isoplanatic patch enlargement from 2.4" to 3" for subject AB and from 1.7" to 2.3" for subject RL). However application of this method leads to image quality degradation within the isoplanatic patch. It can also be seen in figure 1. This is the main disadvantage of the method.

conjugate correction method We also considered multiconjugate correction method. Our goal was to investigate a system with two correctors and several reference sources and to find optimal number and geometry of sources and optimal corrector positions in order to increase isoplanatic patch area. Application of multiconjugate adaptive optics (MCAO) for human eye was considered in ref. 4 but for a larger number of correctors. Modeling of the system was performed using ZEMAX software. The system consisted of an eye model (suggested by Navarro' ), a telescope and two thin phase screens representing the correctors (see figure 2).

,..

Telescope

"".-*."".*"....f"""4__.1.""".

:...............................' Figure 2. Scheme of the model experiment.

We used several reference sources positioned on the model surface representing the retina. Measurements of wavefront aberrations for each reference source were performed in the plane conjugated to the pupil of the model. Then we minimized residual error of correction for all reference sources. We used Zernike coefficients for the phase introduced by the correctors as variables and built-in ZEMAX optimization algorithm. When residual error of

278

correction for all reference sources was minimized we estimated isoplanatic patch size. Then we repeated the optimization procedure for different corrector positions and different numbers of reference sources and distances between them. Results of MCAO correction for different configurations of reference sources are shown in fig. 3. Fig. 3(a) represents conventional correction using one reference source in the center of the retina and one corrector, conjugated to the pupil plane. Isoplanatic patch size is approximately 3.2" and isoplanatic patch area equals 1.02 mm2. Result for two correctors and two reference sources 3" apart is shown in figure 3(b). Although isoplanatic patch size is significantly enlarged in vertical direction, its area is only 1.3 times enlarged. Then we considered symmetrically positioned five reference sources. In figure 3(c) you can see the result of MCAO correction when distance between reference sources is not optimal (3" in horizontal and vertical directions). Isoplanatic patch has cross-like shape and that is not optimal if we want to obtain a uniformly corrected image. Optimal result was obtained for distance between reference sources approximately equal 2 degrees. We also optimized positions of the correctors. It is well-known that conjugating correctors to different turbulent layers is essential in MCAO for astronomical applications. For our system it has been found out that no significant increase in isoplanatic patch size occurs when correctors are conjugated to for example corneal surface, internal and external lens surfaces. For our system distance between correctors and corrector positions with respect to the pupil plane are more important. Figure 3(d) represents the optimal system configuration when one corrector is conjugated to the pupil plane and distance between correctors is 6 mm. The other corrector in this case is conjugated to a plane outside the eye. Isoplanatic patch area increases 2 times if compared with the case of conventional correction. Thus, application of multiconjugate correction with two correctors can significantly increase isoplanatic patch area and this method can be used for widening the corrected field of view of fundus cameras equipped with adaptive optics.

3. Con~lusions In this paper we considered two methods of widening high resolution field of view of fundus imagers equipped with adaptive optics. It was shown that when the phase, averaged over two beacons is compensated by the corrector, the portion of retina imaged with high resolution is increased by a factor of 1.25 1.7 for the measured subjects. However when this average phase correction

279

-4

“2

0

i

4

-4

.2

0

i

k

Figure 3. Results of conventional and multibeacon correction. (a) - one reference source and one corrector; (b) - two reference sources and two correctors. (c), (d) - five reference sources and two correctors. Positions of reference sources and level of 1 rad of residual RMS error (that corresponds to isoplanatic patch border) are also marked.

method is applied residual error of correction within the isoplanatic patch increases. This is the main disadvantage of the method. Also performance of an adaptive optics system with five reference sources and two correctors was considered. Optimization of positions of the two correctors was performed and distance between reference sources was also optimized. For optimal system configuration we obtained two times enlargement of isoplanatic patch area for Navarro ideal eye model. Unlike the previous method no increase of residual error of correction within the isoplanatic patch

280

was observed. The results presented in the paper may be used in widening the field of view of contemporary fundus-cameras.

eferences 1. J.Liang, D.Williams, D.Miller, J. Opt, SOC.Am. A 14,2884-2892(1997). 2. D. L. Fried, J. Opt. SOC.Am. 72,52-61 (1982). 3. Dubinin, T. Cherezova, A, Belyakov, A. Kudryashov, Proc. SPIE 6138, 260-266 (2006). 4. P. A. Bedggood, R. Ashman, G . Smith and A. B. Metha, Opt. Express 1 8019-8030(2006). 5. Escudero-Sanz, R. Navarro, J. Opt. SOC.Am. A 16, 1881-1891 (1999).

Psychophysical experiments on visual performance with an ocular adaptive optics system E. Dalimier* and J. C. Dainty Applied Optics Group, Department of Experimental Physics, National University of Ireland, Galway, Ireland * E-mail: eugenie. d a l i ~ i e r ~ n u i g a l w a y . ~ e

3. L. Barbur Applied Vision Research Centre, City University, London, UK An ocular adaptive optics system was used t o investigate the effects of higherorder ocular aberrations on everyday functional vision. The system comprised a Shack-Hartmann wavefront sensor, a Badal optometer and cylindrical lenses t o statically pre-correct refractive errors, and a 35 element bimorph mirror from AOptix t o dynamically compensate for higher-order aberrations. Measurements of contrast acuity with and without correction of higher-order aberrations were performed in a large range of light levels and pupil sizes. The results showed that the visual benefit is limited at all light levels due to the combined effects of light level on pupil size and neural sensitivity. Keywords: Adaptive Optics; Ocular aberrations; Functional vision

1. Introduction

Adaptive optics (AO) techniques have demonstrated the possibility to dynamically compensate for ocular aberrations beyond sphero-cylindrical refractive errors. This correction has led to significant improvement in retinal imaging and opened new research areas in vision science, in particular in the quest for ‘Lsuper-vision”.lThe possibility of a diffraction-limited correction holds promise in terms of ophthalmic applications. However, some important environmental factors must be taken into account when dealing with everyday vision. In particular, the ambient light affects both the ocular pupil size, hence the ocular aberrations, and the neural contrast sensitivity. It was the aim of this project to investigate how the higher-order aberrations affect visual performance in everyday vision under natural conditions 281

282

of light level and pupil size. An A 0 vision simulator was used for this purpose. We will describe the ocular A 0 system before giving details on the psychophysical experiments carried out and the results. 2. Ocular AO system

The A 0 vision simulator is illustrated on Figure 1. The human eye is aligned

Psychophysics WavefrontSenring

lens mirror beamspiitter Rotating

cythders

I

coidmirror diaphragm

Fig. 1. Schematic of the A 0 vision simulator, adapted from Hampson et aL2

in front of the instrument with the help of a bite bar fixation system, and an infrared removable pupil imaging arm. The measurements presented in this paper were performed on dilated pupils. The ocular wavefront error is measured at a wavelength of 825 nm, using a Shack-Hartmann wavefront sensor with a 0.6 mm sampling in the pupil plane. The sensor is calibrated with an external source, as shown on Fig 1. A special feature of the system is the scanner that helps removing speckle noise on the Shack-Hartmann spots.2 The wavefront error data given in this paper were calculated from a modal reconstruction using 30 Zernike polynomials. Ocular refractive errors can be statically pre-corrected in the system with a Badal optometer for a subjective correction of defocus, and with cylindrical lenses for a correction

283

of astigmatism controlled by the Shack-Hartmann;2 both corrections are performed within 0.1 D. The remaining second-order and the higher-order aberrations (in this paper, we will include the former in the latter term) are corrected with a 35 element bimorph mirror from A O p t i ~ The . ~ closed-loop correction is carried out at a sampling rate of 10-13 Hz, and the closed-loop bandwidth was evaluated to 2 Hz typically. Figure 2 illustrates the typical correction protocol and results for a human subject, over a pupil of 5.4 mm diameter. The wavefront error rms

3

Fig. 2. Ocular aberrations correction over a 5.4 mm pupil: (a-c) wavefront error maps (the scale is in microns), respectively before any correction: wavefront error rms = 0.71 pm, after sphero-cylindrical correction: rms = 0.32 pm, and during dynamic higher-order correction: rms = 0.065 pm; (d) wavefront error rms temporal behaviour before and during the dynamic A 0 correction.

at each stage of correction is given, as well as it’s temporal behaviour before and after A 0 correction. firthermore, the performance of the A 0 system was assessed for the seven subjects who participated in the psychophysical experiments. For four of them, the experiments were carried out with a pseudo-dynamic correction whereby the A 0 correction was refreshed during the visual test. For the other three subjects, the visual test was carried out for a fixed or static correction. The dynamic correction yielded a typical residual wavefront error rms of less than 0.1 pm (mean 0.071 pm over the 7 subjects, standard error 0.010 pm), while the residual for a static correction was 0.133 f 0.016 pm rms.

284

Subject

Fig. 3. Wavefront error rms over a 6 mm pupil, before and after A 0 correction for the 7 subjects who participated in the psychophysical experiments. The measurements were carried out after sphero-cylindrical correction as detailed above.

3. Psychophysical experiments on visual performance Two displays, namely a CRT monitor and a DLP projector, were implemented in the system for the psychophysical experiments. They were used alternatively, along with neutral density filters to set different stimulus light levels. An artificial pupil was placed in the psychophysical path to set the size of the visible beam independently from the wavefront sensing beam and control exactly the retinal illuminance. Non-common path errors were carefully assessed: they did not exceed 30 nm wavefront error rms over a 6 mm pupil; the chromatic focus shift between the wavefront sensing wavelength and the stimulus wavelength was also corrected. Seven young healthy subjects were tested. The research was approved by the National University of Ireland, Galway, Ethics Committee, and followed the tenets of the Declaration of Helsinki. The pupils were dilated with Ropicamide 1%and the protocol included a static pre-correction of sphero-cylindrical aberrations, as described above, as well as a correction of the aberrations of the system. The test chosen to assess functional visual performance was the contrast acuity test.4 It consists of measuring the contrast threshold needed to discriminate the orientation of a 15 minutes of arc Landolt C (the gap subtends an angle of 3'). This stimulus comprises a range of spatial frequencies important in normal visual tasks. More details on the protocol can be found in Reference 5. The A 0 benefit was defined as the ratio of contrast sensitivity (inverse of contrast threshold) with A 0 correction of higher-order (HO) aberrations, to the contrast sensitivity without A 0 correction. Figure 4 shows the results obtained for the first four subjects for a fixed

285

pupil of 6 mm diameter and an A 0 correction refreshed intermittently during the visual test. The graph highlights the drop in A 0 benefit as the light

A

1

0.5

1.5

25

2

3

3.5

Retinal Illuminance(log Td)

Fig. 4. Measured impact of higher-order aberrations on visual performance, in terms of A 0 benefit for the contrast acuity test, for four subjects and a pupil size of 6 mm diameter. The error bar represents f l standard error of the mean.

2.5

25

- f typical error -bar

-

-

~

~

20

2

E l 5

5 1.5

.

6

..........

0 10

g 1

05

0.5

jcotopic 00

~

~

--

c

L)

.*...---*

~

photopic

rnesopic

0 0

1

2

Retinal illuminance (log Td)

3

1

0

1

2

3

4

Retinal illuminance (log i d )

Fig. 5. (a) Measured impact of HO aberrations on visual performance for one subject for several pupil sizes and light levels. The typical error bar represents f 1 standard error of the mean. (b) Data fitted to typical pupil size at each light level, from Ref. 6.

level is lowered. It shows that the decrease in neural contrast sensitivity moderates the impact of higher-order aberrations on visual performance. Further measurements were performed with three other subjects, over a range of artificial pupils sizes and a larger range of light levels. The protocol was here based on a static correction of higher-order aberrations. Figure 5(a) gives the results obtained for one subject. For this particular

286

subject, a comparison between the visual performance with a static correction and that with a pseudo-dynamic correction yielded no statistically significant difference. As expected, the amount of HO aberrations increases with the pupil size, and so does the A 0 benefit. The graph also confirms the previous results: the measured A 0 benefit decreases at low light level because of the drop in neural sensitivity. The data were fitted to typical pupil sizes at each light level.6 The resulting expected A 0 benefit remains limited in all light regimes, due to the combined effect of light level on pupil size and neural contrast sensitivity. For the three subjects tested, it did not exceed 0.15 log unit. 4. Conclusions

The study illustrates the usefulness of adaptive optics tools to study the optical limitations of human vision. The A 0 system showed a very good performance in terms of dynamic correction of ocular aberrations, typically yielding a wavefront error residual of X/8 rms. It was found that the effect of HO aberrations on functional visual performance is moderated by the neural contrast sensitivity, implying that a higher-order ophthalmic correction would not have great impact for young healthy subjects in everyday vision. This conclusion is based on a functional visual test, and on typical pupil diameter values found in the literature, which are highly subjectdependent. The expected visual benefit may be larger for subjects presenting abnormally high wavefront error, such as patients with keratoconus.

Acknowledgements This research was funded by Science Foundation Ireland under grant number SFI/Ol/PI.2/B039C and by a European Union EU Research Training Network, contract number HPRN-CT-2002-00301 “SHARP-EYEY.

References 1. G. Y. Yoon and D. R. Williams, J. Opt. SOC.Am. A 19, 266 (2002). 2. K. M. Hampson, I. Munro, C. Paterson and J. C. Dainty, J. Opt. SOC.Am. A 22, 1241 (2005). 3. E. Dalimier and C. Dainty, Opt. Express 13, 4275 (2005). 4. C. M. Chisholm, A. D. B. Evans, J. A. Harlow and J. L. Barbur, Aviat. Space Environ. Med. ‘74, 551 (2003). 5. E. Dalimier, C. Dainty and J. L. Barbur, J. Modern Optics In press. 6. S. G. de Groot and J. W. Gebhard, J. Opt. SOC.Am. 42, 492 (1952).

Does the Accommodative Mechanism of the Eye Calibrate Itself Using Aberration Dynamics? K. M. Hampson*, S. S. Chin and E. A. H. Mallen Dept. of Optometry University of Bradford UK *E-mail: K. M. HampsonQBradford.ac.uk Kotulak and Schor have suggested that the accommodative mechanism of the human eye can determine the required response from the changes in retinal image contrast associated with the microfluctuations of accommodation. As other aberrations also display dynamic behaviour, they may too have an input in this self-calibration mechanism. An adaptive optics system with separate measurement and manipulation channels was developed to investigate this possibility. A rotating diffuser is used t o reduce laser speckle. The light hits the 37-element piezoelectric deformable mirror twice t o increase its effective stroke. The accommodation response to 0.75 D step changes in target vergence whilst inverting selective aberrations during the latency period was studied in three subjects. In two subjects, inversion of astigmatism and spherical aberration showed the greatest effect; suggesting that for these subjects the eye potentially calibrates itself using information obtained from the aberration dynamics. One subject could not accommodate even with the aberrations left unchanged, and so may require chromatic aberration to guide the accommodative mechanism. Keywords: adaptive optics; accommodation.

1. Introduction

The accommodative mechanism of the human eye is like an adaptive optics system. Light from an object falls onto the retina (sensor), and the brain (controller) determines the adjustment in the power of the lens (corrector) required to bring the object into focus via the contraction or relaxation of the ciliary muscle (actuator). Correction of monochromatic aberrations during the dynamic accommodation response can adversely affect the response of some subjects, which suggests that the accommodation control system uses information from these aberrations for its response.lf2How the accommodation control system extracts information from the aberrations 287

288

is not known with certainty. Kotulak and Schor have suggested a potential accommodative calibration mechanism based on the microfluctuations of accommodation that occur during steady-state ~ i e w i n gThey . ~ propose that by measuring the changes in retinal image contrast associated with these fluctuations in lens power, the eye can determine the correct response required to focus a blurred image. This is illustrated in Fig. 1. If the eye is over-accommodated the derivative of the changes in lens power and the derivative of the changes in contrast will have the opposite signs as these two signals will be out of phase; and vice versa for an under-accommodated eye. Hence the required direction of the response can be determined from the comparison of the signs of these derivatives. As the change in contrast with the power fluctuations will depend upon the amount of defocus present, comparison of the magnitude of the derivatives yield the amplitude of defocus change required. Although this theory is based upon the microfluctuations in accommodation, it is well known that all aberrations fluctuate during steady-state viewing* and so they can be incorporated into this model. Over-Accommodated

Under-Accommodated

Lens Power Fluctuations image Contrast Fluctuations

@ -

Fig. 1. Kotulak and Schor model of the error detection of the accommodative mechanism. For an over-accommodated eye the fluctuations in lens power and the corresponding retinal image contrast fluctuations will be out of phase, and in phase for an under-accommodated eye.

Potentially, this calibration mechanism takes place during the accommodation latency period which is around 360-380 ms (see for example, Campbell and We~theimer).~ If this model holds true, the inversion of certain aberrations during this period could misguide the accommodation system owing to a disruption of the association between lens power and retinal image contrast changes. We have constructed an adaptive optics system to

289

investigate this possibility. Three subjects were used. 2. Adaptive optics system

The adaptive optics system constructed is shown in Fig. 2. All optical components are mounted on a 600 mm by 900 mm breadboard.

Eadal Focus Correct

Wavefront Sensing Target Both

Fig. 2.

Adaptive optics system.

2.1. Eye illumination The eye is illuminated by a 817 nm laser diode. The beam is focused onto a rotating diffuser to reduce speckle.6 The use of a diffuser overcomes the non-common path error that results from the use of a scanner conjugate to the pupil (see for example Hampson et d7).After passage through the diffuser, the beam is re-collimated and passes through a Badal optometer so that the accommodation level at which the experiments are carried out can be adjusted. 2.2. Aberration measurements

After passing back through the eye’s optics, 50% of the light is reflected by the cube beamsplitter and directed onto the Shack-Hartmann sensor.

290

The lenslet array has a focal length of 7 mm and samples the pupil at 0.4 mm intervals. The camera is a Retiga Exi Fast 1394 monochrome CCD type (QImaging) which samples the aberrations at 11 Hz. This channel enables the measurement of the eye's aberrations directly rather than obtaining them from the sensing measurements that pass via the aberration manipulation channel containing the deformable mirror. 2.3. Aberration man~pulation

50% of the light from the eye passes onto the deformable mirror which a 37-actuator piezoelectric deformable mirror from OK0 Technologies. The maximum stroke of the mirror is 8 pm. The light hits the mirror twice to increase its effective stroke,8 which is a relatively low cost way of amplifying the stroke of the deformable mirror. A neutral density filter is included in the measurement-only channel to ensure that the brightness is equal for both channels. Measuring the aberrations from both channels on one camera reduces the system cost and complexity. The split of the two measurement channel paths at the cube beamsplitter is illustrated in Fig. 3.

T

To SH

ToIFrom DM

Fig. 3.

(a) Aberration measurement path, (b) Aberration manipulation path.

2.4. Target

The target is a Maltese cross subtending 1 minute of arc on the retina. It is illuminated with green light centred at 568 nm with a 10 nm bandwidth. The target vergence was 3 D. Light from the stimulus is prevented from reaching the sensor with an IR filter.

291 2.5. E ~ p e ~ ~ eprocedure ~ t a l Data were collected on three subjects. We used the deformable mirror to step defocus by either or - 0.75 D and dynamically invert selective aberrations during the accommodation response latency period (370 ms). These aberrations included astigmatism (Z3), vertical coma (Z7), trefoil (ZS), secondary astigmatism ( Z l l ) and spherical aberration (212). Measurements were made over a 5 mm natural pupil. Each measurement run lasted 4 s with the step introduced after 2 s. Ten repeated measurements were taken for each condition. A bite-bar was used to stabilise the subjects. The accommodation responses were obtained from the defocus term (24) as measured on the measurement-only channel.

+

3. Results

Figure 4 shows typical accommodation responses for two of the subjects. Subject 3 could not accommodate at all even when only a step change in target vergence was introduced. The time traces on the left are examples of the accommodation response to a negative step for subject 1. Responses to a positive step for subject 2 are shown on the right. The inversion of astigmatism and spherical aberration showed the greatest effect on the accommodation response for both subjects. The traces for trefoil (Z9) and secondary astigmatism (211) were similar to that of coma (27) for both subjects. 4. Discussion & Conclusion

Subject 3 could not accommodate at all and so may require chromatic aberration to guide the accommodative mechanism. For the other two subjects, inverting astigmatism and spherical aberration resulted in the failure of the accommodation system to respond to the step change in target vergence. Based on the Kotulak and Schor model,3 one might expect the accommodation response to have stepped in the wrong direction. However only one aberration mode was inverted at a time and the remaining aberrations would have an influence on any calibration mechanism. F’uture work will include predicting the accommodation response based on the Kotulak and Schor model with the inclusion of the knowledge of the aberration dynamics. These predictions will then be compared with results obtained using the adaptive optics system. In conclusion, we have developed an adaptive optics system to investigate the role of the aberration dynamics in the self-calibration mechanism

292 Subject 1

Subject 2

- 0.75 D Step

+ 0.75 D Step

invert Spherical(Z12) Step c

. 1

4 seconds

Fig. 4. Typical time traces of the accommodation response for two subjects.

of the human accommodation system. Inversion of certain aberration modes during the accommodation latency period can adversely affect the response suggesting that the eye potentially calibrates itself using aberration dynamics during this period for some subjects.

5. Acknowledgements The authors acknowledge support of the research by Engineering and Physical Sciences Research Council grant EP/D036550/1 from the UK.

eferences 1. L. Chen, P. B. Kruger, H. Hofer, B. Singer and D. R. Williams, JOSA A 23, 1-8 (2006). 2. E. J. Fernhndez and P. Artal, JOSA A 22,1732-1738 (2005). 3. J. C. Kotulak and C. M. Schor, Biol. Cybern. 54, 189-194 (1986). 4. H. Hofer, J. L. Aragbn, D. R. Williams, P. Artal and B. Singer, JOSA A 18, 497-506 (2001). 5. F. W. Campbell and G. Westheimer, J . Physiol. 151, 285-295 (1960). 6. K. M. Hampson, S. S. Chin and E. A. H. Mallen, J. Mod. Opt. (in press). 7. K. M. Hampson, C. Paterson, E. A. H. Mallen, JOSA A 23,1082-1088 (2006). 8. R. H. Webb, M. J. Albanese, Y . Zhou, T. Bifano and S. A. Burns, Appl. Opt. 43,5330-5333 (2004).

Y OF FIELD ABERRATIONS IN THE AN EYE A. V. Goncharov*, M. Nowakowski*, E. Dalimierc, M. Sheehan**, and J. C . Dainty* *Applied Optics Group, Department of Experimental Physics, National University of Ireland, Galway, Ireland ie E-mail: ale~~arider.noiicharov~ni~i~alwav. **Optometry Department, School of Physics, Dublin Institute of Technology, Dublin, Ireland A study of ocular aberrations and their field dependence is the main objective of this paper. We present off-axis measurements of wavefront aberrations for five fixation points in the horizontal meridians up to 5 degree in the periphery of the field. The effect of the tear film on wavefront measurements is analyzed in relation to the variability of the low-order and high-order aberrations. The idea of estimating the isoplanatic angle is outlined.

1. Introduction The nature of aberrations occurring in the human eye is complex mainly due to the lack of rotational symmetry of the eye, irregular shape of the cornea and gradient index structure (GRIN) of the crystalline lens. The aberration theory of rotationally symmetric optical systems is not always applicable here, yet one could still benefit from it when studying the young eyes with some minor asymmetry in their optical structure, which can be regarded as perturbations and misalignment. This approach is useful for prediction of the aberrations occurring in the eye at the periphery of the visual field. One the other hand, measuring field aberrations in the eye may help to identify their origin and reveal those properties of the optical structure that are significant to image formation. Ultimately, one should get deeper undersigning of optical factors limiting the retinal imaging, which in turn could lead to better imaging techniques. It is also expected that with more accurate knowledge of optical structure of the eye, one could possibly achieve vision correction over larger field. As a first attempt to measure field aberrations in connection with possible vision enhancement, we investigate only central visual field. Wavefront measurements of the ocular aberrations at far periphery of the field, which are more relevant for designing new optical instruments to improving retinal imaging, will be the subject of our future study. 293

294

2. Experimental Setup For measuring ocular aberrations in the central field we have designed and built a versatile Shack-Hartmann (SH) wavefront sensor (WFS) [l]. Due to the relatively recent development of HS-based aberrometers for the human eye [ 11, there have been only a few attempts to study off-axis aberrations in eyes using this technology [2-51. The SH aberrometer, shown schematically in Fig.1, enables us first to measure the wavefront aberrations (within the central 10 deg) and then construct a wide-field schematic eye model featuring a GRIN lens by optimizing one of our generic eye models [6] so that the resulting subject-specific model fits the wavefront data. The latter model makes it is easy to analyze the variability of ocular aberrations across the central visual field in a continuous manner. However, here we present the analysis of field aberrations using discrete wavefront data obtained for one subject in the right eye.

MASK Figure 1. Optical layout of the aberrometer imaging the SH spots and the pupil on a single CCD.

295

3. The tear film effect on repeatability of wavefront measure men^ At the beginning of the experiment, we adjust the position of the Badal stage (see Fig.1) in order to compensate the defocus term and then six wavefront measurements are obtained on axis to estimate the repeatability of the instrument, as well as the stability of the paralyzed accommodation in the eye. The latter is analyzed by comparing first six measurements (n=1.. .6) with other six measurements (n=7.. .12) taken at the very end of the session. Figure 2 shows the variability of the wavefront aberration represented by Zemike terms at these twelve data points. We grouped Zernike terms as slightly decreasing, increasing and relatively stable over time. Figure 3 depicts the variation of the total RMS wavefront error as a function of time elapsed from the start of the experiment. The twelve phase maps and the corresponding PSFs (based on Fourier transform) are presented as well. The pupil diameter is 6 mm and the reference wavelength is h=677 nm. 0.4

1

Zernike coefficientslmicrons

Figure 2. Variability of the Zemike coefficientsin the wavefront measurements obtained onaxis.

296

RMS, microns

12

8

t , min 10

30

50

n=7

n=2

n=8

n=9

n=10

n=l 1

n=12

Figure 3. The RMS wavefront error and phase maps (with PSFs) for on-axis measurements.

297

A single measurement represents an average value of Zernike coefficients estimated from 20 consecutive frames collected over 2 seconds after a single blink. The standard deviation (SD) of each Zerinke coefficient shown in Fig.4 includes not only the errors of the SH sensor but also the effect of the tear film evolution within the period of 2 seconds. The SD of the Zernike coefficients estimated over the full session (12 blinks) is about twice the amount of the single-measurement SD. This indicates that the changes in the tear film profile from blink to blink are not negligible, especially for astigmatism and trefoil coma terms. To reduce the tear film contribution in the wavefront error we averaged two measurements for the same direction taken after different blinks. SD, microns = multiple blinks

m

8

I

.

.

.

.

.

.

single blink

.

.

.

.

.

.

z; zi: z;" z; z-; z;" zi: z: z: z-: z: z: Figure 4.Standard deviation of the Zernike coefficients estimated for a single blink and twelve blinks.

4.. Field dependence of ocular aberrations Following the definition of the isoplanatic angle (IA) used in astronomy, we estimate it as the angle for which the change of the RMS wavefront error does not exceed 1 rad. In our case, this is equivalent to W2.n = 0.108 microns. Figure 5 shows how the total RMS error varies across the horizontal field. We applied a cubic spline to find the direction at which the RMS error reaches its minimum (2 degrees to the nasal side on the retina). The IA at this field point is about 2.5 and 4 deg to the nasal and temporal side respectively. Our results are comparable with an earlier study [7]. Similarly, one could analyze contributions from different Zernike terms and find their typical IA. We can see from Fig.5 that some terms (e.g. spherical aberration and coma) do not show much variation, whereas defocus can undergo significant changes across the field (due to the retina shape). A large variation (small IA) indicates that the aberration OCCUTS at some distance from the pupil (e.g. corneal contribution)

298 microns

* Figure 4.Variation of the RMS wavefront error and Zernike coefficients across the horizontal field.

Acknowledgment This research was supported by Science Foundation Ireland under Grant No. SFI/Ol/P1.2/B039C eferences 1. M. T. Sheehan, A. V. Goncharov, and J. C. Dainty, “Design of a versatile clinical aberrometer,” Proc. SPE 5962, 59620111, in Optical Design and Engineering II,L. Mazuray and R. Wartmann Eds. (2005). 2. L. Lundstrom, J. Gustafsson, I. Svensson, and P. Unsbo, “Assessment of objective and subjective eccentric refraction,” Optom. Vision Sci. 82, 298306 (2005). 3. R. Navarro, E. Moreno, and C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eye across the visual field,” J. Opt. SOC. Am. A 15,2522-2529 (1998). 4. D. A. Atchison and D. H. Scott, “Monochromatic aberrations of human eyes in the horizontal visual field,” J. Opt. SOC.Am. A 19,2180-2184 (2002). 5. D. A. Atchison, D. H. Scott, and W. N. Charman, “Hartmann-Shack technique and refraction across the horizontal visual field,” J. Opt. SOC.Am. A 20,965-973 (2003). 6. A. V. Goncharov and C. Dainty, “Wide-Field Schematic Eye Model with Gradient-Index Lens,” accepted for publication in J. Opt. SOC.Am. A (2007). 7. A. Dubinin, A. Belyakov, T. Cherezova, and A. Kudryashov “Anisoplanatism in adaptive compensation of human eye aberrations”, in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein Eds., Proc S P E 5572,330-339 (2004).

Dual wavefront corrector ophthalmic adaptive optics: design and alignment Alfred0 Dubra* and David R. Williams Center for Visual Science, University of Rochester, Rochester, NY 14627-0270, USA * E-mail: adubraacvs.rochester .edu This work studies how to match a wavefront sensor with a single and multiple wavefront correctors by minimizing the condition number and mean wavefront variance in the presence of photon, background and electronics noise. It is also shown that the minimization of the wavefront variance provides a simple experimental procedure for aligning the wavefront sensor. The particular choice of deformable mirrors suggests that a sequential closed-loop control of the adaptive optics, BS opposed to simultaneous control, would be more stable, given the condition number is lower by an order of magnitude. Finally, the effect of beam displacement at the pupil plane, a consequence of poor optical design in ophthalmic scanning systems with adaptive optics is discussed.

The design or selection of a wavefront corrector for an adaptive optics (AO) system is based on the spatial and temporal characteristics of the aberrations to be compensated for.lS2 Once the wavefront corrector is selected, a matching wavefront sensor should be designed. The matching can be achieved by minimizing the condition number of the A 0 response matrix and the noise propagation coefficient of the A 0 control matrix, provided the noise in all sensing elements is equal and ~ n c o r r e l a t e d . ~However, -~ the former is not always a valid hypothesis. For example, in Shack-Hartmann (SH) wavefront sensors, the lenslets over the pupil boundaries will collect a smaller average number of photons than the ones inside the pupil. In this work, we use the condition number and mean wavefront variance to design a Shack-Hartmann (SH) wavefront sensor with square-packing geometry matching two deformable mirrors (DMs), accounting for noise differences across the wavefront sensor signals, as described in our previous work.* The DMs are the Multi-DM from Boston Micromachines (U.S.A.) and the Mirao52 from Imagine Eyes (F’rance), with 144 and 52 actuators respectively. The SH parameter space explored i s defined by the number of SH lenslets across each wavefront corrector element, the relative orientation and lateral 299

300 Hypothetical Multi-DM

Mirao52

Multi-DM

Hypothetical Mirao 52

(broad influencefunction)

harrow influencefunction) 1000 BOO

600 400 200 0 1

2

3

4

2

3

4

lenslets B C ~ S Seach aotuator

1

1

2

3

4

lentiletsacross each actuator

-2

1

lenslets across each aduator

2

lenslets~

3 C ~ each S S

4 aduator

1

2 5 4 ~. lenslets across each actuator

1

2

3

1

4

1

lenslets across each actuator

100

100

ao

ao 60

N B 40

40

20

20

P

3

4

2

3

4

lensletsacross each actuator

60

1

2

lenslets across each acbator

0

0

1 2 3 4 Ismlets acrosseach actuator

1

2

3

4

lsnsletsacmss each aduetor

1 2 3 4 lensletsacross each actuator

1

2

3

4

Im3Bts across each actuator

Fig. 1. Condition number and mean wavefront variance (E2) plots for A 0 systems using a SH with square-packing geometry in combination with a Mirao 52 or a MultiDM. The areas between the blue solid lines comprise the range of values for all possible SH orientations and alignment with respect to the DMs.

displacement with respect to the DMs. The results, shown in the central two columns of Fig. 1, indicate that there are optimal lenslet size ranges for each DM, and that these depend on the dominant source of noise. Interestingly, there is no single configuration that has an outstanding performance, suggesting that off-the-shelf SH lenslet arrays and/or magnification optics can be used with similar performance to that obtained using customized elements. In order to understand the origin of the difference between the DMs, the calculations were repeated for a hypothetical Mirao52 with the influence functions that correspond to the Multi-DM, and viceversa. The resulting plots shown in the outermost columns of Fig. 1 suggest that the narrower the influence functions the lower the condition numbers, as would be expected. Also, a comparison of the plots in the first and fourth, and the second and third columns, seems to indicate that the noise curves are mostly determined by the influence

301

8

40000

9

30000

1s 20000 c

f:

10000

0 -40

-20

0

20

40

-40

-20

0

20

40

Fig. 2. These plots show the condition number, the maximum and minimum singular values respectively for all the possible relative orientations of the DMs. The optimal value, i.e. the lowest condition number, occurs at 38.5 degrees.

function width, rather than the number of actuators across the pupil. The dashed curves in the condition number plots of Fig. 1 correspond to the SH configurations that produce the lowest wavefront variance for all three sources of noise, and the dashed curve in the wavefront variance plots correspond to the configurations with lowest condition number. From these, it is clear that the configurations that minimize the condition number also minimize the wavefront variance and vice-versa. Therefore either of these two metrics can be used for optimizing the optical alignment of the SH array. Simply by using the experimentally measured A 0 response matrix, one can obtain the condition number or, in combination with the light intensity detected on each SH sub-aperture, the impact of the dominant source of noise could be estimated through the wavefront variance. It is important to note that if one was to align the system using the wavefront variance, only relative comparisons are required, thus greatly simplifying the calc~lations.~ The particular selection of DMs takes advantage of the large stroke of the Mirao52 and the high number of actuators and narrow influence function of the Multi-DM. The first step when combining the DMs in a single A 0 system is to minimize the overlapping of modes between them, by rotating one with respect to the other. Both DMs are kept centered with respect to the optical axis of the system in order to maximize the number of actuators within the pupil. As a measure of mode overlapping we calculate the condition number of the influence function matrices corresponding to all the relative DM orientations. The condition number plot in Fig. 2 shows that the preferred orientation is 38.5 degrees, assuming 6 Mirao52 actuators across the pupil and 10 Multi-DM actuators. By looking at the corresponding maximum and minimum singular value curves, it can

302

Fig. 3.

be seen that the lower condition number is due to increased sensitivity of the higher spatial frequency modes. We can therefore be confident that by orienting the DMs using the prescribed angle, we gain sensitivity in some modes without sacrificing it in others. Once the DMs are correctly oriented, we study the matching of the DM combination with a SH sensor by once more calculating the condition number and mean waveffont variance. The resulting plots are shown in Fig. 3. The most striking result is in the condition number plot, where the values are more than one order of magnitude larger than in Fig. 1. This is an important result, already observed experimentally by Chen et al.,lo and indicates that driving both DMs simultaneously in closed-loop will lead to a more unstable system. Therefore, a sequential closed-loop control is preferable. The reason for the large condition number of the simultaneous control of the dual-DM A 0 lies in the mode overlapping, which is determined by the packing geometry of the actuators and their influence functions. Another point to consider when designing a scanning ophthalmic system with AO, is the pupil displacement at the subject’s eye due to the scanning and imperfect axial alignment of the subject. Given the very low optical signal from the eye, most systems to date rely on off-axis reflective optics to reduce the effect of reflections in the beam entering the eye. In such systems, unless particular care in the optical design is used, the beam entering the eye does not pivot around a stationary point in the pupil plane of the eye, but wanders, sometimes by as much as 7%11 and 10%,l2which is the width of a full actuator in the Multi-DM. This beam displacement at the pupil plane results in the wavefront sensor seeing a spatial average of the laterally displaced aberrations. Therefore, the A 0 can only detect and correct a low-pass filtered version of the eye’s aberrations, leaving aberrations with high spatial frequency content uncorrected. Even though this is not

303

desirable, the success of both the instruments developed in Berkeley" and Rochester12 despite the mentioned beam wandering, suggests that a large number of actuators or a narrow influence function (< 30% width) such as those provided by the Multi-DM might not be required for diffractionlimited imaging in the human eye. In summary, the matching of one and two deformable mirrors to a single SH sensor have been presented, and the results indicate that a sequential control system should give a more stable closed-loop performance. This result is consistent with previous experimental evidence.'* Careful consideration must be given to the optical design of scanning ophthalmic imaging instruments equipped with AO. In most cases all the effort is placed in making sure the imaging of the retinal plane is diffraction-limited. This is correct and necessary, but great attention should also be paid to the pupil plane, where the scanning beam can wander. This will result in a spatial low-pass filtering of the aberrations of the eye at the wavefront sensor, resulting in an underestimation of the aberrations and therefore a poor A 0 correction.

Acknowledgments This research was supported by the NIH grant BRP-EY014375 and the NSF, Science and Technology CfAO, managed by UC Santa Cruz under cooperative agreement AST 98-76783.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

C. Paterson, I. Munro and J. C. Dainty, Opt. Exp. 6, 175 (2000). E. Dalimier and C. Dainty, Opt. Exp. 13,4275 (2005). R. Ragazzoni, Journal of Modern Optics 43,289 (1996). A. Dubra, C. Paterson and J. C. Dainty, App. Opt. 43,1108 (2004). M. E. Furber, Opt. Eng. 36, 1843 (1997). W. Jiang, Y. Zhang, H. Xian, C. Guan and N. Ling, Proc. Znd Internat. Workshop on Adaptive Optics f o r Ind. and Med. , 8 (2000). C. Paterson and J. C. Dainty, Opt. Lett. 25, 1687 (2000). A. Dubra, Opt. Exp. 15,2762 (2007). F. Roddier, Adaptive optics in astronomy (CambridgeUniversity Press, Cambridge, U.K., 1999). D. C. Chen, S. M. Jones, D. A. Silva and S. S. Olivier, J. Opt. SOC.Am. A 24, 1305 (2007). Y. Zhang, S. Poonja and A. Roorda, Opt. Lett. 31,1268 (2006). D. Gray, W. Merigan, J. Wolfing, B. Gee, J. Porter, A. Dubra, T. Twietmeyer, K. Ahamd, R. Tumbar, F. Reinholz and D. Williams, 14,7144 (2006).

IG

MICHAEL PIRCHER', ROBERT J. ZAWADZKI~,JULIA EVANS^, JOHN s. WERNER~ AND CHRISTOPH K. HMZENBERGER' 'Centerfor Biomed. Eng. & Phys., Medical Universityof Vienna, Vienna, Austria. 'Dept of Ophthal. and Vision Science, Univ. of California Davis Med Ctr., Sacramento, CA We present a new adaptive optics (AO) enhanced high speed imaging system that is capable of recording scanning laser ophthalmoscope (SLO) and optical coherence tomography ( 0 0 images, simultaneously. A superluminescent diode (SLD) with central wavelength at 841nm and a bandwidth of 51nm is used for imaging. The closed loop A 0 system consists of two deformahle mirrors (one bimorph mirror and one MEMS mirror) and a Hartmann-Shack wavefront sensor with a frame rate of 16Hz.Using a fiber-based Mach Zehnder interferometer provides equal power returning from the eye for the SIX) and OCT channels and a pixel-to-pixel correspondence between both channels. The time domain OCT system is based on a fast transverse scanning of the sample and incorporates a resonant scanner operating at -14kHz. The instrument currently records S M and OCT images consisting of -700x500 pixels at a frame rate of 28fps. A quantitative comparison of the human cone mosaic imaged with S M and OCT at different eccentricities from the fovea is presented.

1. Introduction Imaging of the living human retina with cellular resolution is still challenging. Scanning laser ophthalmoscopy (SLO) is an imaging technique that provides high transverse resolution and moderate depth resolution [ 11. To further enhance transverse resolution, aberrations of the eye have to be corrected, which can be achieved by the use of adaptive optics (AO) [2, 3,4]. On the other hand, optical coherence tomography (OCT) represents a unique imaging technique that is capable of recording images of the retina with high depth resolution but with rather poor transverse resolution [ S ] . Recently, a combination of OCT with A 0 has been described that permits the human cone mosaic to be imaged in vivo [6, 71. Because of a sensitivity advantage of Fourier-domain (ED) OCT compared to time domain (TD) OCT, most groups implemented FD-OCT into their A 0 system. However, FD-OCT in combination with A 0 suffers Erom some drawbacks. A high-transverse resolution results in a very small depth of field 304

305

(DOF), i.e., the plane of best sharpness. For the eye the maximum numerical aperture is fixed and the DOF is on the order of tens of micrometers. FD-OCT records the whole imaging depth (the thickness of the retina is in the order of several hundreds of micrometer) simultaneously; therefore, only a small portion of the recorded data will be in focus and will appear sharp. Sometimes structures of interest (e.g., human cone mosaic) are best observable in the en-face imaging plane. Since the fast (or priority) scan direction of FD-OCT is in the depth direction, a whole 3D volume has to be recorded to extract en-face information. This is rather time consuming and therefore motion artifacts in the transverse direction are most likely. In contrast to FD OCT, transversal scanning (TS, or en-face) OCT can overcome these problems. Another advantage of TS-OCT is the possibility of simultaneous recording of SLO images.

2. Methods We introduce a new high speed en-face imaging system equipped with A 0 with the ability to record SLO and OCT images simultaneously. Our system is -20 times faster than a previously reported instrument [S]. The experimental setup is shown in Fig. 1. In brief, we used a superluminescent diode (SLD) emitting at 8411x11with a bandwidth of 51nm for imaging, which results in a theoretical depth resolution of -6pm in air. The light is coupled into an 80120 single mode fiber splitter where 20 percent of the light is directed via a closed-loop A 0 system to the eye and 80 percent of the light is directed to the reference arm of the OCT system. The power on the cornea of the eye was measured with 300pW, which is well below the safety limits for this wavelength region. Light backscattered from the eye uses the same path through the A 0 system and is back coupled into the same fiber splitter. One exit of the fiber splitter is connected to a 50150 fiber splitter which provides equal power returning 'from the eye for the SLO and OCT channels and a pixel-to-pixel correspondence between both channels. The A 0 system consists of two deformable mirrors (one bimorph mirror and one MEMS mirror) and a Hartmann-Shack wavefront sensor with a frame rate of 16Hz 191.The A 0 loop is first closed for the bimorph mirror which is then kept at a fixed position. Then the loop is closed for the MEMS mirror throughout image recording. A transversal scanning, time domain OCT setup [lo] is used which enables the use of a resonant scanner operating at -14kHz for a fast transverse scanning of the sample. Two acousto-optic modulators (AOM's) are placed in the reference arm to generate a carrier

306

frequency for the OCT channel of 2.5 MHz. The instrument currently records SLO and OCT images consisting of -700x500 pixels at a frame rate of 28fps.

Figure 1. Experimental setup. SLD superluminescent diode, AOM: acousto-optic modulator, M: mirror, DAQ: data acquisition board, PC:personal computer.

3. Results Figure 2 shows an example of images of the human cone mosaic in vivo recorded at 2deg. eccentricity (nasally) from the fovea. The measured Strehl ratio after AO-correction was 0.8 for this volunteer. Fig. 2a) and b) show en-face images retrieved from the SLO and OCT channel, respectively. Note that Fig. 2a) represents an average over 10 frames that were corrected for transverse motion [ 113. The scanning angle of the image was reduced from l"x1" to 0.9" x 0.9" by the motion correction algorithm. The imaging depth of the OCT image corresponds to the end tips of photoreceptors (ETPR) or sometimes called Verhoeff's membrane [7]. Clearly the cone mosaic can be observed in both images. (Note that each bright spot within the image corresponds to the reflection of a single cone.) To present a quantitative value of the correlation between SLO and OCT images we calculated from a subsection (omitting artifacts at the edges of the SLO image caused by the motion correction algorithm) the normalized cross correlation with Matlab 7.0 (Mathworks Inc.). From the result shown in Fig. 3a) we could retrieve a value of 0.37 for the correlation between SLO and OCT channel. The two dimensional FFiTs of Figs. 2a) and b) are shown in Fig. 3b) and c), respectively. Clearly visible in both

307

images are Yellott’s rings [I21 which are caused by a regular spacing of the cones. From these images we measured an average cone spacing at this eccentricity of 1.43 arcmin which is in good agreement with a cone spacing of 1.48 arcmin retrieved from histology [ 131.

4

b)

Figure 2. Human cone mosaic at 2deg. eccentricity. a) SLO image, b) OCT image (displayed on a linear scale) at end tips of photoreceptors (or Verhoeff s membrane).

a)

b)

c)

Figure 3. Evaluation of Figure 2. a) Cross correlation between SLO and OCT, b) Fast Fourier transformation (FIT)of SLO image, c) FFT of OCT image.

Figure 4 summarizes the cone spacing at different eccentricities measured with our system. Again a rather good correspondence between ow: measurements and histology can be observed.

308

++

0

2

4

6

8

10

12

I Figure 4. Cone spacing depending on the eccentricity from the fovea. SLO cone spacing retrieved from the SLO channel, OCT-ETPR cone spacing retrieved from an imaging depth corresponding to the end tips photoreceptors, OCT-IS/OS cone spacing retrieved from an imaging depth correspondingto the junction between inner and outer segments of photoreceptors.

Acknowlegments The authors gratefully acknowledge financial support from the National Eye Institute (grant EY 014743) and the Austrian FWF (grant P16776-NO2 ).

eferences 1. R.H. Webb, G.W. Hughes, IEEE Trans. on Biomed. Engineering 28, 488492 (1981) 2. J. Liang, D. R. Williams, and D. T. Miller, J. Opt. Soc. Am. A 14, 28842892 (1997). 3. F. Vargas-Martin, P. M. Prieto, and P. Artal, J. Opt. Soc. Am. A 15, 25522562 (1998). 4. A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T. J. Hebert, M.C.W. Campbell, Optics Express 10,405-412 (2002)

309

5. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178-1181(1991). 6. Y. Zhang, J. Rha, R. S. Jonnal, and D. T. Miller, Opt. Express 13, 479248 11 (2005) 7. R.J. Zawadzki, S.M. Jones, S.S. Olivier, M. Zhao, B. A. Bower, J. A. Izatt, S. Choi, S. Laut, J. S. Werner, Opt. Express 13,8532-8546 (2005) 8. D. Merino, C. Dainty, A. Bradu, A.G. Podoleanu, Opt. Express 14, 33453353 (2006) 9. R.J. Zawadzki, S. Choi, S.M. Jones, S.S. Olivier, J. S. Werner, J. Opt. SOC. Am. A 24,1373-1383 (2007) 10. M. Pircher, B. Baumann, E. Gotzinger, and C. K. Hitzenberger, Optics Letters 31, 1821-1823 (2006) 11. P. Thevenaz, U.E. Ruttimann, M. Unser, ZEEE Trans. on image Processing 7,7-41 (1998) 12. J. I. Yellott Jr, Vision Res. 22, 1205-1210(1982). 13. C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, J. Comparitive Neurology 292,497-523 (1990).

Characterization of an AO-06'1: system J.W. Evans'vtyt, Robert J. Zawadzkit, Steve Jones$, Scot S. Oliviert, John S. Wernert

t Vision Science and Advanced Retinal Imaging Laboratory, Department of Ophthalmology & Vision Science, University of California, Davis, Sacramento, C A 95817, USA * E-rnail:evans74 Qllnl.gov f

Lawrence Livermore National Laboratory,

7000 East Avenue, Livermore, USA 94550, USA

Adaptive optics (AO) and optical coherence tomography (OCT) are powerful imaging modalities that, when combined, can provide high-resolution, 3-D, in viva images of the retina. We will discuss general techniques for characterizing a vision science A 0 system, and we will describe the results of applying these techniques t o measure the residual wavefront errors for the UC Davis AOOCT system. Careful characterization of the A 0 system will lead t o improved performance and inform the design of future systems.

Keywords: Adaptive Optics; MEMS deformable mirror; OCT

1. Introduction

The Adaptive Optics (A0)-Optical Coherence Tomography (OCT) system at UC Davis has been under development for 2 years and has demonstrated the utility of this technology for microscopic, volumetric, in wiwo retinal imaging. Traditional OCT has excellent axial resolution, allowing individual layers of the retina to be imaged. The addition of A 0 improves lateral resolution, which can reveal individual structures within the retinal layers. Improved A 0 correction can increase image contrast making individual structures more visible. Developing an error budget is a common tool for improved performance and system design in astronomical A 0 s y ~ t e m sIn . ~general, ~~ an A 0 system error budget must include an analysis of three categories of residual wavefront error (WFE): errors in measuring the phase, errors caused by limitations of the DM(s), and errors introduced by temporal variation. Understanding the mechanisms and relative size of these errors is critical to 310

311

improving system performance. In this paper we discuss both the techniques for characterizing these error sources and our measurement of them for the AO-OCT system. 2. System Description

The AO-OCT sample arm is shown in Fig. 1. The major components of the A 0 system are the 22 by 22 Shack-Hartman wavefront sensor (S-H W S ) , and two deformable mirrors. Spherical mirrors (indicated by S1-S10 in the diagram) re-image the pupil. The system uses an AOptix bimorph (DMl) deformable mirror (DM) for low-order, high-stroke correction* and a 140-actuator Boston Micromachines DM (DM2) for high-order c ~ r r e c t i o n . ~ Like several other imaging modalities OCT requires the sample arm to scan the retina to produce the science image (indicated by horiz. and vert. in the diagram). For some characterization tasks we can use a model eye, consisting of a lens with a paper ‘retina’ at the focal plane. 3. Analysis of residual wavefront error

During closed loop operation of the AO-OCT the controller uses a singular value decomposition of the previously measured system matrix of each deformable mirror to determine the voltages to be applied. The wavefront is reconstructed from the centroid displacements during post-processing using a Fourier reconstructor.6 The individual components of residual error can be thought of as orthogonal and the rms WFE from each can be added in quadrature and compared to the total measured rms in an error budget. Fitting error is introduced by the fundamental limits of the wavefront corrector and is inversely proportional to the number of actuators of the DM. Wavefront errors with spatial frequencies greater than half the number of actuators across the aperture cannot be corrected. The AO-OCT system over-samples the wavefront, so to some extent, we can measure these outof-band errors directly. In-band errors (errors that can be corrected) are the true residual errors we wish to evaluate in the error budget. In an ideal system the residual error would be primarily out-of-band, indicating that the A 0 system is working well. Total residual WFE in the model eye case is 48 nm rms, with 36 nm rms being out-of-band. It is encouraging that most of the in-band error is being corrected, however there are still in-band errors that should be evaluated. In the case of a human subject total WFE is 154 nm rms, with 76 nm rms out-of-band. Clearly we need to investigate other in-band error sources.

312

Sample Arm

s3

Fig. 1. Layout of the AO-OCT sample arm. The system uses a 22 by 22 ShackHartmann wavefront sensor, a bimorph deformable mirror for low-order correction and a MEMS deformable mirror for high-order correction. Horizontal and vertical scanners axe used to scan the retina. The mirrors indicated by S1 - S10 are spherical mirrors used t o re-image the pupil plane.

In addition to fitting error, the DM will introduce errors based on the ability of each individual actuator to go to the position demanded by the control system. Generally this voltage step size is limited by the resolution of the drive electronics. The MEMS device has an actuator precision of 1%, which corresponds to W E of 12 nm rms. The bimorph mirror with its 16-bit electronics introduces negligible step size error. Measurement error includes calibration error, wavefront sensor (WFS) CCD noise, and sampling errors. The easiest way to estimate measurement error is to compare successive wavefront measurements when the system is stable (using the model eye for example). Measurement error is calculated by subtracting each converged reconstructed wavefront during a 20s measurement from the average converged wavefront and calculating the rms value of the differences. The average rms value is the measurement error, which in our system is 4 Ifr 2nm rms. This is lower than expected and is negligible in our error budget. Alternatively the measurement error can be

313

estimated from measured signal to noise. This is more complicated but will decouple measurement errors from system vibrations and will be done to confirm this initial finding of low measurement error. One significant flaw of this type of analysis is that the WFE measured by the WFS is a relative and not an absolute measurement. It is dependant on the calibration of the sensor. We are in the process of installing a far-field camera in the system to better evaluate calibration error and that error will be added to the WFE measured by the WFS. Temporal variations in the system can be introduced by the limited bandwidth of the AO system or by systematic variations such as vibration on the optical table. Data from the model eye were used to estimate the temporal variation of each pixel, or the stability of the system, to be 4 rt 2nm rms, which, like the measurement error, is negligible. For a human eye dynamic abberations will introduce bandwidth errors. These can be estimated in the same way that measurement error in the model eye is estimated. Figure 2 includes a sample of wavefronts used to calculate

Fig. 2. Sample of wavefronts used to calculate bandwidth error for a human subject. Left: Average wavefront from one 20-second measurement, Middle: Individual wavefront iteration, Right: Difference between average and iteration. The average rms of the difference between the average wavefront and each iteration is the measurement error plus the bandwidth error, because measurement error is small this value is dominated by the bandwidth error. In this case it is about 48 nm rms.

bandwidth error. On the left is the average converged wavefront from a particular dataset, the middle wavefront is a single iteration and on the right is the difference of the two. The error is the average of the rms differences for all of the converged wavefronts in the dataset. In this case we are actually calculating the combination of measurement and bandwidth errors, however because measurement errors are small this will be dominated by bandwidth errors. We exclude bandwidth errors that have out-of-band

314

spatial frequencies as we cannot correct them. Bandwidth error for human subjects is about 48 nm rms. This accounts for some of the increased error between the model eye and the human eye, but the remaining error is still unaccounted for. Error Source Out of Band MEMS step size Measurement/bandwidth Stability Total (calculated) Total (measured)

0

Model rms (nm) 36 12 4 4

38 48

Human rms (nm)

76 12

48 4 91 154

2 4 6 8 Frequency (cycles/aperture)

10

Fig. 3. Sample power spectrum of the averaged-converged reconstructed wavefront for a human subject and model eye. In both cmes in-band error is dominated by low order WFE, which should be correctable.

Table 2 summarizes the error sources we have identified so far. In both cases a significant portion of the error remains. The power spectrum of the reconstructed wavefronts can reveal the dominant spatial frequencies of the

315

residual error which could help identify the source. In Fig. 3 the power spectra calculated from the average converged reconstructed wavefront for the model eye and human eye are compared. In both cases in-band WFE is dominated by very low-order error. Note that during reconstruction tip/tilt is numerically removed, invalidating the zero point in both graphs. In the case of the model eye it is clear that correction is better at spatial frequencies of 3 and 4 than it is at 1 and 2. The total rms error from 0 to 2 cycles per aperture for the model eye is 21 nm, for the human subject it is 109. This error should be correctable. Most likely the wavefront controller is ill-suited to correcting this error because of the mirror modes it is using as a basis. The reconstructor can identify this error because it is using a Fourier basis instead of the mirror modes. More work is needed to confirm the cause, and to reduce this uncorrected low-order error. 4. Conclusions

A 0 system characterization is an iterative process. We have presented our preliminary error budget for an AO-OCT system. The uncorrected loworder error in our system needs to be better understood and reduced, perhaps by modifying the A 0 controller. We are also installing a far field camera to directly measure the point spread function of the system, and investigate calibration errors.

Acknowledgments This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. UCRL-PROC-233190. This research was supported by the National Eye Institute (grant EY 014743).

References 1. 2. 3. 4.

R. Zawadzki, et al, Optics Express 13, 8532 (2005). M. van Dam, D. Le Mignant and B. Macintosh, Applied Optics43,5458 (2004). J. W. Evans, et al, Optics Express 14, 5558 (2006). D. A. Horsley, H. Park and J. S. Laut, Sophie P. and Werner, Sensors and

Actuators A: Physical 134, 221 (2007). 5. T. Bifano, P. Bierden and J. Perreault, Micromachined deformable mirrors for dynamic wavefront control, in Advanced Wavefront Control: Methods, Devices and Applications 11, eds. J. D. Gonglewski, M. T. Gruineisen and M. K. Giles Proc. SPIE 5553 2004. 6 . L. Poyneer, D. Gavel and J. Brase, JOSA A 19,2100 (2002).

A

VE O ~ ~ I C OS ~ T I C ~COHE L

GUOHUA SHI The Laboratory on Adaptive Optics, Institute of Optics and Electronics, P . 0.Box 350, Shuangliu, Chengdu 610209, P.R. China ZHIHUA DING State Key Lab of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, Hangzhou, Zhejiangu 310027, P.R. China W N DAI The Laboratory on Adaptive Optics, Institute of Optics and Electronics, P . 0.Box 350, Shuangliu, Chengdu 610209, P.R. China XUNJUN RAO The Laboratory on Adaptive Optics, Institute of Optics and Electronics, P . 0. Box 350, Shuangliu, Chengdu 610209, P.R. China WDONG ZHANG The Laboratory on Adaptive Optics, Institute of Optics and Electronics, P . 0. Box 350, Shuangliu, Chengdu 610209, P.R. China When optical coherence tomography (OCT) is used to image human retina, its transverse resolution is limited by the aberrations of the human eye. To overcome this disadvantage, a set of high resolution imaging systems for living human retina, which consists of a time domain OCT system and an adaptive optics (AO) system that have been developed. The ~ A 0 closed loop rate is 20 frames per one second, and the OCT has 6 . 7 axial resolution. In this paper, this system is introduced and the high resolution imaging resolution results for retina are presented.

1. IntrQductiQn Optical coherence tomography (OCT) [l] is similar to ultrasound B mode imaging except that it uses light instead of sound. It has a high resolution * This work is supported by Innovation Foundation of Chinese Academy of Sciences

316

317

(1-15pm) , which is one or two orders of magnitude higher than the conventional ultrasound technique. OCT can also be used to perform real-time cross-sectional tomography imaging. The unique features of this technology enable a broad range of clinical applications. Human eyes is not a perfect optical system, it has wave front aberrations [2] which deteriorate the transverse resolution of OCT. Human’s aberrations are different from person to person and change with time, it is therefore difficult to correct the aberrations by a static way. Adaptive optics (AO) can correct the aberration in real time 131 but traditionally it has a bulky size, complicated configuration and high cost, and it was mainly used in astronomical telescope. With the development of low-cost components, A 0 has been applied in ophthalmic imaging [4, 5, 6, 7, 81. Recently A 0 combined with a spectral domain OCT succeed in the retinal cone mosaic imaging[6,7,8]. We set up a set of time domain AOOCT system. In this system, a novel type of 37 elements small PZT deformable mirrors are used as wave front corrector, and wave front errors are measured by a 16x16 array Hartman-Shack wave front sensors.In this paper, the experimental configuration of our AO/OCT system is described, and the current experiment results for pig retina are presented.

. S y § t e de§cription ~ The optical arrangement of the OCT system is shown in Fig.1. Light form a SLD (k840nm, Ak49nm) passes through an optical isolator and then is splitted equally by a fiber coupler into reference and sample arms. The Light of sample arm pass through the A 0 system and reflect back to fiber coupler, then interferes with light of reference arm which reflected buy a rapid scan optical delay line (RSOD) [9, lo]. The interference signal is measured by a detector and then processed by a computer. In order to compensate the polarization mode dispersion of the system, a fiber polarizer control is applied in the sample path to control the polarization. A phase modulator will be used to supply a carrier frequency, and the interference signal can avoid the l/f noise, this lead to enhancement of system SNR. The A 0 system is consist of a 37-element deformable mirror, a 16x16 array Shack-Hartmann wave front sensor, a beacon (k780nm) and a X-Y scan system. The beacon passes through the whole optical system and is focused on the retina, thereby it experiences the wave front aberrations of the eyes. The wave front sensor detects the back-reflected light and measures the displacements of light centroids in all sub-apertures. The wave front slope is reconstructed from the centroids displacements. The control signal calculated

318

from the wave front slope is amplified by a voltage amplifier and the used to control the deformable mirror to correct the wave front aberrations of eyes. This leads to a diffraction-limited resolution in the transverse direction of the OCT imaging. The A 0 closed loop rate is 20 frames per one second.

Figure 1. The schematic of AOOCT system. PM, phase modulator; PC polarization controller; H-S Shack-H~mannwave front sensor;DM small PZT deformable mirror; L1, focuing lens.

3. ~xperimentresolution We carry out experiment with pig eye, and it is fixed by an adjustable mount. Because the pig eye lose focusing ability, so the L1 function as a focusing lens to make sure the incidence light is focused onto retina, and the incidence beam diameter is 6mm with 325uw power. The phase modulator is purchasing, so at present the carrier frequency is supply by RSOD, and it’s schematic show as Fig.2 (A). In order to supply a carrier frequency the sanner pivot must offset from the optical axes. Fig.2 (B) show the relation between scanning mirror offset to carrier frequence while the scan rate is 500 Hz.

319

A

Figure 2. (A) is block diagram of rapid scan optical delay. (B) is the chart of the relation between scanning mirror offset and carrier frequence.

The benefit of RSOD[9,lO] is that it can compensate the material dispersion of the eye, combined with the polarization controller, the whole system’s dispersion (include material dispersion and polarization mode dispersion) could be compensate primely. Picture A and B in Fig.3 show the states without

MX

D

Figure 3. (A) show the state whitout material dispersion compensation. (B) show the state without polarization mode dispersion compensation, (C) show the state whit whole dispersion compensation, (D) is the FPT of interference signal.

320

dispersion compensation. The system interference signal show as picture C in Fig.3. The resolution of the OCT is about 6.7 um, it approach the ideal resolution (6.23um). The FFT of interference signal show the carrier frequency is 500 KHz. Fig.4 is the experiment results of pig eye. Image A express the aberration before and after compensation. Picture B and C are retina images in the same position with and without AO. In picture C, the vas of W E layer is distorted by the aberrations. But in picture B, it is visible. So it is obviously that the A 0 system could enhance the OCT transversal resolution effectively. After Comoensetion

RM

I

A vas

B

C

Figure 4. (A) is aberration before and after compensation. (B)is the retina image with A 0 and the (C) is the retina image without AO.

. Concl~io~ We set up a set of time domain AOOCT system, which consist of a 37 elements small PZT deformable mirrors which is used as wave front corrector, a 16x16 array Hartman-Shack wave front sensors, and a time domain OCT system. The

321

A 0 closed loop rate is 20 frames per one second, so that it can correct the aberration in real time. The current experiment results of pig eye show the A 0 can enhance both the transverse resolution of OCT effectively.

eferences 1. D. Huang, E. A. Swanson, C. P. Lin, et al, Science. 254, 1178 (1991). 2. Liang J , G r i m B , Goelz S et al, Opt. SOC.Am. (A). 11,1949 (199 3. Jiang Wenhan, Tang Guornao, Li Mingquan et al. 0pt.Engng. (1995). 4. Liang J ,Williams D R ,Miller D T, Opt. Suc. Am. ( A). 14,2884 (1997). 5. Ling Ning, Zhang Yudong, Rao Xuejun, et al, Chinese Optics Letter. 3, 225 ( 2005). 6 . Robert J. Zawadzki, Steven Mi. Jones, Scot S . Olivier, et al, Opt. Express. 13,8532 (2005). 7. Yan Zhang, Jungtae Rha, Ravi S . jonnal, Donaid T. Miller, Opt. Express. 13,4792 (2005). 8. David Merino, Chris Dainty, Opt. Express, 14,3345 (2006). 9. Tearney GJ, Bouma BE, Fujimoto JG, Opt. Lett. 22,181 1 (1997). 10. Andrei V. Zvyagin, Elwyn D. J. Smith, David D. Sampson, Opt. SUC.Amer.

EVE LOP ME^, CALIBRATION AND PERF0 E L E C T R O M A ~ ~ T MIRROR IC BASED ADAPTIVE OPTICS SYSTEM FOR VISUAL OPTICS ENRIQUE GAMBRA, LUCIE SAWIDES, CARLOS DORRONSORO, LOURDES LLORENTE & SUSANA MARCOS Instituto de CSptica, Consejo Superior de lnvestigaciones Cienttficas C/Serrano 121,28006 Madrid (Spain) Email: e.gambra @ io.cfmac.csic.es Adaptive optics is a promising technology to investigate the impact of optical aberrations on vision [I]. The ability to perform measurements under correction and accurate control of high order aberrations allows, among others, testing of research questions to understand the mechanism of accommodation. We have developed, calibrated and evaluated the performance of a new Adaptive Optics (AO) laboratory instrument for applications in visual optics, and we have performed measurements on real eyes, unaccommodated and as a function of accommodation with natural and closed-loop corrected optical aberrations.

1. Introduction An interesting question in vision is the understanding of the impact of ocular aberrations in the accommodative response and in visual function. Previous studies suggest that aberrations may play a role in determining the direction of accommodation [2], at least in some subjects, and also in the response accommodation time [31. Differences in accommodative lag between emetropes and myopes caused by the presence of increased aberrations in myopes have also been suggested [4, 51. Also the role of ocular aberrations in vision needs better understanding. Applications of an A 0 system in this context include: refractive and presbyopic corrections, visual adaptation and tolerance to blur.

2. Set-up We built an adaptive optics system for testing relationships between optical aberrations and vision. A photograph of the optical set-up is shown in Figure 1. It consists of five channels: 1) illumination channel, with a Super Luminescent Diode (central wavelength: 827 nm) entering the eye l a m off-centered; 2) a test channel, with a motorized Badal system and a microdisplay for stimulus 322

323

presentation; 3) a Hartmann-Shack wavefront sensor (HAS0 32 OEM, Imagine Eyes, 32x32 microlenses) for aberration measurement; 4) an electromagnetic mirror (MIRAO 52, Imagine Eyes) with 52 actuators on a 15mm effective diameter for aberration correctiodgeneration; 5) a pupil camera for pupil monitoring. There is a 2x magnification between the eye's pupil and the HS wavefront sensor, and 0.5X between the eye's pupil and the adaptive optics mirror. Figure 1: A 0 set-up.

3. Calibration

The system was calibrated using an achromatic doublet lens with a rotating diffuser at the focal plane. These measurements were used to ensure a flat wavefront and used as a reference. The stability of the system was also checked. Aberrations were measured and actively corrected on two aberrated artificial eyes (with significant values of spherical aberration, Eye #1, and astigmatism at 0" and horizontal coma, Eye #2, respectively). Aberrations were compared with those obtained with our Laser Ray Tracing (LRT) aberrometer and manufacturer values, in terms of individual Zernike coefficients and root mean square (RMS) wavefront error. The correction performance was evaluated in terms of RMS decrease, Strehl ratio increase and correction gain. The A 0 system stability was high, with less than 0.3% total RMS fluctuation over a three-hour measurement. Discrepancies between measurement and nominal values were 0.020 pm (5.3%) for spherical aberration and 0.052 pm (11%) for total RMS for Eye #1 (6.0-mm pupil), and 0.008 prn (1.0%) for astigmatism at O", 0.035 prn (7.7%) for horizontal coma and 0.047 pm (4.9%) for total RMS for Eye #2 (6.5-mm pupil). We achieved an active flatness of 0.015 pm. After 8 iterations of close-loop compensation, the RMS decreased from 0.783 pm to 0.052 pm in Eye #1 and from 0.960 pm to 0.033 pm in Eye #2. Figure 2 A shows a comparison of measured and nominal aberration terms for artificial Eye #2, and Figure 2 B shows aberrations before and after correction of aberrations with the deformable mirror on Eye #2.

324

22-2 22+2 23-3 23-1 23+1 23+3 24-4 24-2

240

24+2 24+4

Zernike aberration term

.-E r;

H

0.6

0.6 0.4

0.2

0 -0.2 -0.4

-0.6

Figure 2: (A) Aberrations measured with the wavefront sensor of our A 0 system compared with those provided by the manufacturer for artificial Eye #2. (B) Ey&2 aberrations before and after compensation with the deformable mirror.

4. Measurements on real eyes We measured 4 eyes from 4 young normal subjects (average age: 31t5, average spherical error: -1.8t2.9D), under natural viewing conditions. The studied met the tenets of the Declaration of Helsinki, with protocols approved by Institutiona~Review Boards, and signed informed consent provided by the subject. The patient is stabilized using a bite bar, and best spherical correction was achieved with the Badal system for the unaccommodated condition. Measurements were conducted at 0 D, and 3 and 5 D of accommodative stimulus. Aberrations were dynamically measured with natural aberrations (the deformable mirror only compensating for the aberrations of the system), and subsequently under correction of high order aberrations in closed loop. In real eyes, we observed significant amounts of corrections for all significant aberration terms, at all accommodation stimuli levels. Figure 3 A

shows Zernike terms in an unaccommodated eye before and after correction of aberrations with the deformable mirror (for 6.6 mm diameter). Aberrations were compensated from 0.307rt0.019 pm to 0.026rt0.003 pm for OD, from 0.372t0.046 pm to 0.037rt0.003 pm for 3D and from 0.379rt0.030 pm to 0.126t0.024 pm for 5D, in terms of 31d and higher order RMS, for a constant pupil diameter of 4.8mm (Figure 3 B). Measurement and compensation was achieved for dynamic pupil changes. We observed a decrease in pupil size with increased accommodative effort (as previously reported) with the pupil diameter systematically smaller when compensating aberrations with the deformable mirror (a reduction of 0.27 mm/D for the measurements under natural aberrations and 0.33 mxdD with the aberrations corrected).

(A)

-

S#1

0.4

0.3

;0.2 UI

f 0.1 v

E

;..

f

O -0.1

-0.2 -0.3

-0.4

Zernike aberration term

(a> 0.500

f

r

................................................

....I.. ............................................

...

............................................. .............................................

0.000

-1

0

1

2

3

4

5

6

Accommodatlve demand (D)

Figure 3: A. Real eye aberrations before and after compensating with the deformable mirror. B. Total aberrations rms with and without compensation for different accommodative efforts.

326

.I. Effect of a ~ e ~ a t i o on n saccommodative response We studied the effect of aberrations on accommodative response. It is well known that accommodative effort is not capable of equalling accommodative demand; difference is called accommodative lag. We tested to which extent the accommodation lag is affected by the presence of aberrations. The hypothesis is that the larger tolerance to blur produced by aberrations plays an impact in determining best focus. Three conditions were tested: 1) Natural aberration condition (i.e., with the deformable mirror correcting residual system aberrations only). 2) Static correction of all aberrations, except for defocus, i.e. with the mirror compensating astigmatism and high order aberrations of the unaccommodated condition; 3) Statistic compensation of all aberrations of the unaccomodated condition, except for spherical and defocus for OD. Measurements of ocular aberrations were performed for best spherical correction at 0 D, and 3 and 5 D of accommodative demand. The accommodation response was obtained from the defocus term of the Zernike polynomial expansion (see Figure 4). Changes in spherical aberration were also monitored.

i

0

I

S#l, Age: 35

1

2

3

4

Accommodative demand (0)

5

,

1

0

I

1

2

3

4

5

6

Accommodative demand (D)

Figure 4: Accommodative response for two different subjects. S#l shows worse response for the higher accommodative demand when only spherical aberration is not compensated. S#2 benefits from both correcting all aberrations and all except spherical.

.2. Thru - Luminance Visual Acuity: Snellen E In a second experiment, Visual Acuity of S#l was measured as a function of luminance. A 4 alternative forced choice paradigm (Snellen E) was performed using a QUEST algorithm for threshold estimation, using Psychtoolbox + MatLab. Each E was shown every 0.5 seconds and a measurement consisted of 50 trials per luminance position. Measurements were done with and without adaptive optics correction.

327

Results are presented in figure 5: VA increases with luminance along the considered range of luminance. On the other hand, when aberrations are corrected VA is significantly better for lower luminance. However, when the luminance increases, VA acuity decreases when aberrations are corrected, presumably due to the saturation of the image. 1 tNatural

1

I--.- Corrected (AO)/

S#l

0-6

0.5 0’01

0,l Luminance level (arbitraryunits)

1

Figure 5: Visual acuity of S#l with and without correcting his aberrations.

5. Conclusions In conclusion, our A 0 system allows us to highly reduce optical aberrations, and control aberrations with high stability and reliability. It is also capable of compensating optical aberrations on real eyes, at different accommodation levels. In the youngest subjects, accommodative response is better when correcting aberrations, while the other subjects seem to use other cues. For lower luminance VA improves when correcting aberrations. ~cknowledgmen~ The authors acknowledge funding from Ministerio de Educacicin y Ciencia, Spain (grant FIS2005-04382) CSIC (I3P grant to Enrique Gambra) and EURYI Award (EURHORCs) to Susana Marcos. References 1. G.-Y. Yoon and D. R. Williams, J. Opt. Soc. Am A. 2,266-275 (2002) 2. L. Chen, P. B. Kruger, H. Hofer, B. Singer and D. R. Williams, J. Opt. Soc. Am A. 1, 1-8 (2006).

328

3. E. J. FernClndez and P. Artal, J. Opt. SOC.Am A. 9, 1732-1738 (2005). 4. D. 0. Mutti et al, Inv. Opht. & Vis. Sci. 3,837-846 (2006). 5. J. C. He, J. Gwiazda, F. Thorn, R. Held, F. A. Vera-Diaz, Vis. Res. 45,285290 (2005) 6. D. H. Brainard, Spatial Vision 10,433-436 (1997) 7. D. G. Pelli, Spatial Vision 10,437-442 (1997)

APTIVE EYE ODE^ SERGEY 0. GALETSKIY Physical Department, Moscow State Lomonosov University, Vorobiovy Gory bld. 1/62, I 19899, Moscow, Russia ALEXEY V. KUDRYASHOV Moscow State Open University, Sportivnaya 9, 140700, Shatura, Russia

w Region,

We propose experimental adaptive eye model based on flexible 18-electrode bimorph mirror reproducing human eye aberrations up to 4‘h radial order of Zernike polynomials at frequency of 10Hz. The accuracy of aberrations reproduction in most cases is better than M I 0 RMS. The model is introduced to abemometer for human eye aberrations compensation to improve visual acuity test.

1. Intro~~ction A human eye is a very complicated optical instrument that possesses a rich variety of high-order aberrations. These aberrations vary significantly among subjects and that is why there are no two persons with the eyes being exactly alike. Traditionally, schematic eye models have fixed parameters representing the optical properties of the average human. In this paper we try to define the human eye model in terms of a wavefront aberration map. We propose experimental model of “live eye”, which can reproduce human eye aberrations in real time. It is capable to reproduce low order (defocus, astigmatism) as well as high order monochromatic aberrations of a human eye.

a ~ t i v eye e model scheme The model consists of 18 electrodes flexible semipassive bimorph mirror [ 11 and a telescope resizing beam diameter up to the mirror’s one (figure 1). Suggested model scheme and mirror electrodes configuration are shown in figure 1 (left and right figures correspondingly). 329

330

Figure 1. Adaptive eye model scheme (left) and grid of bimorph mirror electrodes (right).

It is known that amplitude of power spectrum of human eye aberrations at frequencies higher than 5 Hz is negligible [2,3].Our bimorph mirror has first resonant frequency about 1.5 kHz. So our model can reproduce aberrations at all significant frequencies.

3. Control algorithm In order to show the effectiveness of human eye reproduction by suggested eye model we built the experimental setup consisting of suggested eye model itself and S h a c k - ~ ~ t m a nwavefront n sensor placed at the conjugated plane. The algorithm of the flexible mirror control was following. First of all we measured the response functions of all actuators of the mirror, i.e. aberrations induced by the suggested eye model, when only one actuator of the mirror is active. These response functions form matrix R. The element (ij) of it represents the local tilt of the wavefront at j-th microlens of the Shack-Hartmann sensor, when unit voltage is applied to the i-th mirror actuator. While reproducing aberrations of the real eye the vector of voltages applied to the mirror actuators is calculated as: ... ... V , = V,-l (R 'R)

+

Here V, is vector of voltages applied to the mirror at moment t,, V,.1 is vector of voltages applied to the mirror at the previous moment tn-land t, - tn-l= 100 ms (to fully reproduce power spectrum of aberrations up to 5 Hz the system has to induce aberrations at least at frequency 10 Hz); Am, is calculated according to the following formula:

Where m, is the local tilt vector corresponding to the real eye aberrations at moment t, and m,.,* is the local tilt vector measured by the Shack-Hartmann sensor at time moment tn-l.

33 1

uman eye aberrations measurement The data on human eye aberrations was collected using aberrometer [4], which performs wavefront measurement based on Shack-Hartmann method. We considered the main error sources when measuring human eye aberrations using aberrometer: Eye pupil positioning error Camera resolution Camera noise Signal quantization Error due to intensity nonuniformity

-3% -1.3% -0.4% -0.2% 2-6%

Generally the wavefront reconstruction by means of Shack-Hartmann technique assumes intensity uniformity across beam aperture. We have developed a special program module, which estimates intensity distribution across eye pupil and eliminates the error caused by intensity distribution nonuniformity.

5. Aberrations reproduction results The measured and reproduced aberrations in terms of interferogramms are shown in figure 2. For this case the RMS error of wavefront reproduction is 0.07 pm.

Figure 2. The interferograms of measured (left) and reproduced aberrations (right) for patient BA.

332

For the most cases averaged FWS error of reproduction was less than UlO

(k780nm).This allows using adaptive eye for calibration and testing of optical devices. During reproduction of total human eye aberrations for each Zernike term we obtained RMS error less than U20 for most patients (figure 3). = 0.06

1

A

T

2

4

8

6

1

0

1

I

2

patientDAl patient LRr patiantGSr patient BAi

14

Zemlke polynomial

Figure 3. The average error of each Zemike term reproduction for different patients.

To analyze the dynamical properties of proposed model the power spectrum densities functions were calculated (figures 4 3 .

i52 -0

-reproduced aberrations spectrum

1

-

real eye eberradons spectrum

0.1

2

Hp

1._-

0.01

1E-3

1E-4

z 1E-5

.

Y

.., 0.1

1

5

Frequency, Hz

Figure 4. Power spectrum of fluctuations of real eye aberrations (solid line) and the ones induced by adaptive eye (dashed line) for patient GS.

333

-reproduced aberrations spectrum

.-

--._. real eye aberrations spectrum

._ VI

5

0.1 'i

z1

E

2

0.01:

i

1E-63 . . ,

1

0.1

5

Frequency, HZ

Figure 5. Power spectrum of fluctuations of real eye aberrations (solid line) and the ones induced by adaptive eye (dashed line) for patient LR.

. Aberratio~co~pensationresults We integrated the adaptive eye model into the aberrometer and used it to compensate eye aberrations of a patient in real-time. The adaptive eye model is positioned so that the surface of the flexible mirror is conjugated with the pupil of the patient. In this case the control closed-loop algorithm is phase conjugation. The effect of aberrations correction in terms of interferogramms for subject LR is shown in figure 6.

PV = 3.81 pm

PV = 0.49 pm

Figure 6. The interferogramms of eye wavefronts without (left) and with (right) correction.

In figure 7 Residual RMS error and Strehl ratio with and without correction are shown.

334 RMS, pm

-.-

I

RLL

I

RLR

/I

I

AD

I

A8

I

AK

I

Figure 7. Wavefront RMS (left) and Strehl ratio (right) with and without aberration correction for different patients.

The residual error of correction typically did not exceed 0.1 pm for the amplitude of aberrations up to 4.5 pm.

,~

"-

.""""".""lll_" l^l_.l

_._lll_.

-diffraction

J

,

o

.

,

n,

.

_"

___^_I

limited

,

.

40

,

. M)

,

Spatial frequency, cldeg

ao

.

___

,

Figure 8. Modulation transfer function for diffraction limited system and for patient LR with and without correction.

As it is shown in figure 8 the limiting spatial frequency of the system with adaptive correction is 85 c/deg. That corresponds to resolution of 4 pm for eye retina. So by using such compensator one can get resolution enough to discern neighbour photoreceptors.

7. Conclusions In the paper the performance of adaptive eye model is discussed. It is shown that the quality of human eye aberrations reproduction is typically better than 3J10 RMS for the whole wavefront and 3J20 for each Zernike term. The adaptive eye

335

model allows us to compensate eye aberrations so that the wavefront RMS with correction is 10 times less than without it. The impact of correction on the MTF was studied. The results show major improvement of the MTF with adaptive correction.

References 1. A.V.Kudryashov, V.I.Shmalhausen, Opt.Eng., 35, 11,3064-3073, (1996). 2. H. Hofer, P. Artal, B. Singer, J. L. Arago’n, D. R. Williams, J. Opt. SOC.Am. A, 18,497-506, (2001). 3. S . 0. Galetskiy, T. Yu. Cherezova, A. I. Belyakov, A. V. Kudryashov, Journal of Optical Technology, Vol. 73, Issue 7,491-493, (2006). 4. S. Galetskiy, R. Letfullin, A. Dubinin, T. Cherezova, A. Belyakov, A. Kudryashov, Proc. SPIE 6018,601806-1-601806-9, (2005.)

Adaptive optics system for retinal imaging based on a pyramid wavefront sensor S. CHIESA*, E. DALY and J. C . DAINTY Applied Optics, Dept. of Ezperimental Physics, National University of Ireland Galway, Galway, Ireland *E-mail: sabine.chiesa~nuigalway.ie http://optics.nuigalway.ie

S. R. CHAMOT Microvision and Microdiagnostics Group, IOA-STI-EPFL BM 4.126, Station 17, 1015 Lausanne, Switzerland E-mail: stephane. chamotQepft. ch Preliminary fundus images showing blood vessels in-vivo at lo off-axis of the fovea over a 2 O field of view have been obtained with an adaptive optics system using a 19 actuator piezoelectric mirror in a pyramid wavefront sensor system. The optical design is presented and key instrumental parameters are discussed. Keywords: Pyramid Wavefront Sensing; Adaptive Optics; Retinal Imaging; Instrumentation

yramid wavefront sensing for ophthalmology with i ~ a g i n gof retinal blood vessels Pyramid wavefront sensing1T2 has shown the ability to measure and to be integrated in a correction system for ocular aberrations of a 6mm diameter pupil of the human eye3>4.This system is schematically illustrated in Fig.1. The sensing of the aberrations of the eye is realized with a Helium Neon laser (633nm) backscattered from the retina to the pyramid prism. The focus error of the subject is previously characterized with a commercial instrument (ZywaveTM aberrometer , Bausch&Lomb) and corrected before sensing by modifying the optical path length of the imaging system with a Badal stage. The required displacement been calibrated3 with il diopter ophthalmic lenses in steps of 0.25 diopter. Circular modulation of the focusing wavefront around the tip of the pyramid is induced by a Newport fast steering mirror at 1OOHz resulting in 4 pupils 336

337

reimaged on the wavefront sensing camera. Custom Labview@ (National Instruments, Austin, TX, USA) software detects the wavefront aberrations after correction of the focus error and determines the mirror commands controls required to correct for the higher-order aberrations by singular value decomposition of the wavefront gradients.

Deformablemirror alibration closedloop

Mirror

-

Dichroic SS 632/680nm Dichroic SS 530/632nm R............ .. Retinal plane & conjugates P - - - - - Pupil plane & conjugates

.CI

open loop 635nm

Fig. 1. Scheme of the pyramid wavefront sensor for ophthalmic applications with fundus camera.

Adjusting the camera binning to get l6pixels across the 385pm pupil and the modulation radius to small values (7 X/D, where D is the diameter of the pupil image on the steering mirror) the typical residual wavefront error of the closed-loop mode typically reaches O.1pm root mean square (X/8) at 55Ez frame rate. As illustrated in Figure 2.a, when the subject does not have large values of initial wavefront error (6pm full-wavefront error for the 6mm pupil diameter as measured by the Zywave in this case), it is possible to correct fully the focus error with the Badal stage and the remaining aberrations with the closed-loop. This would tend to confirm the major influence of the low-order aberrations on the full-wavefront-aberrations for this range of pupil size.5

338

A 53Onm-pulsed illumination arm delivering 200ms flashes of 20mW power was added to the original system3. Its synchronization with the image acquisition camera (Retiga 1300C, QImaging Corp., http://www.qimaging.com) enabled repeated imaging of a single location in the eye. The optical design (ZEMAS Development Corp., WA, USA) for the imaging indicated in this case a diffraction limited point spread function diameter of 18pm at the camera. Considering that the point spread function of an aberration free diffraction limited 6mm pupil has a diameter of 3.6pm, we estimate that our imaging system has a 5 times magnification factor. A fixation target placed in a conjugated retinal plane in the illumination path enabled a quantified rotation of the eye's line of sight by use of the optical design parameters. For example in taking the Emsley reduced eye as model in the optical design, an eye's movement of 0.5" towards the line-of-sight on the temporal side was obtained with a right shift of the fixation target of 2.9mm the towards the illumination's optical axis. The combination of the quantified eye's rotation with the multiple frame recording of a single retinal region enabled post-processing of the images, such as presented in Figure 2.b. which is the image resulting of the average signal obtained for 10 images of 200ms exposure each. This set was recorded by asking the subject to fixate the target shifted of 3.8mm in the way previously explained, leading to estimate that the center of the field points the region at 1" off-axis of the fovea.

Fig. 2. 2.a. Root mean squared wavefront error evolution over time: the loop is closed after 8 seconds - 2.b. Eye rotated of lo, average over 10 images of 200ms exposure each, full field 3.6', arrow defining the blood vessel full-section, from which we calculate a full-width at-half-max (FWHM) of 20pm.

339

An adjustable diaphragm placed in a conjugate retinal plane allows adjustment of the imaging field of view, the optical design predicting a 0.6 magnification factor between them. The region of interest selected on the camera was defined to encompass this field of view, such as in Fig.2b1 where the internal disk highlights a 3.15'-diameter retinal zone (Nlmmdiameter). Using the inversion of the transverse magnification factor, we know a single CCD pixel of 6.7pm measures 1.34pm in the retina. Thus we get to estimate the diameter (40-50pm diameter, due to the blur) and the position (2-2.5' temporal side) of the blood vessel indicated by the white double arrow. In order to image smaller details of the retina, the system has to be modified. First, the long-exposure time (200ms) of the imaging integrates the eye's motion, thus blurring the image. Secondly, to reach the theoretical diffraction limit of the aberration free eye, the imaging magnification factor has to be increased to at least 7.5. It is also expected that the correction range of the system would benefit of the use of the high stroke of the magnetically actuated 52-actuator Mirao membrane mirror as presented in the next section. 2. Magnetic mirror features

The proposed deformable mirror for the second generation of pyramid wavefront sensing for ophthalmic applications is the Mirao52 magnetic mirror (Imagine Eyes, Paris). The suitability of this mirror for ophthalmic applications has been numerically assessed following a method previously used6>7. The influence functions of the mirror are recorded with a Fisba Twyman-Green interferometer to define a typical surface deformation. Assuming linearity of the deformation with the voltages sent, we can expect a membrane stroke of f50pm for a single actuator. The surface deformations created by single actuators constitute a basis of surface deformations that are used to state the shape of the membrane reproducing Zernike polynomials modes, as illustrated in Figure 3.a. A study of the root mean squared wavefront error of the simulated surface deformation towards the theoretical deformation highlights in Figure 3.b the quality of the mirror. For example, the O K 0 37 membrane mirror adds aberrations if more than 10 mirror-Zernike modes are used, as predicted by the increase in the wavefront error. The same study shows that using the full aperture of the Mirao 52 ( 15mm, 52 mirror modes, 0.069pm wavefront error) or a smaller aperture (12mm, 37 mirror modes, 0.074pm wavefront error) predicts a very good correction of the aberrations in both cases.

340

3.b)

0

10

20

30

40

50 60 S*mpl*

70

80

90

100

Fig. 3. 3.a. Simulated residual RMS wavefront error between deformable mirror surface reproducing Zernike modes and the corresponding theoretical modes. - 3.b. 37 Zernike modes reproduced by the Mirao52 over a 12mm diameter area. - 3.c. Ability of the Mirao52 to correct a set of 100 typical ocular aberrated wavefrontsh

The suitability of the mirror to correct for ocular aberrations is finally simulated over a set of of typical aberrated wavefront@. As shown in Figure 3.c. where the initial aberrated rms wavefront error is plotted against the final rms wavefront error after correction, we can estimate the quality of the correction using the appropriate number of modes (52 for 15mm, 37 for 12mm) by the residual O.Olpm remaining error reached after correction.

3. Conclusions The presented system has been designed so as to state on the feasibility of a coupling of a fundus camera with a pyramid wavefront sensor. Preliminary results have shown the possibility of imaging some blood vessels at 530nm, estimated to be at 2" off axis of the fovea. Improvements of the wavefront sensing are expected with the use of the high-stroke, highnumber and highly compact deformable Mirao mirror. In the meantime, improvements of the retinal imaging are expected from an increase of the imaging magnification factor. The use of a more powerful light source in the illumination path will help reduce the integration time of the imaging while improving the image quality.

341

4. Acknowledgements This research is funded by Science Foundation Ireland under grant No. SFI/Ol/PI.2/BO39C. and by the European Union Network HIRESOMI under grant MEST CT-2005-020353.

References 1. R. Ragazzoni, J. Mod. Opt. 43,289 (1996). 2. A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito and P. Stefanini, Laboratory characterization of a “Foucault-like” wavefront sensor for adaptive optics, in Proc. SPIE, 3355, March 1998. 3. S. R. Chamot, J. C. Dainty and S. Esposito, Opt. Express 14,518 (2006). 4. A. Burvall, E. Daly, J. C. Dainty and S. R. Chamot, Opt. Express 14,11925 (2006). 5. J. Porter, A. Guirao, I. G. Cox and D. R. Williams, J . Opt. Soc. Am. A . 18, 1793 (2001). 6. E. Dalimier and C. Dainty, Opt. Express 13,4275 (2005). 7. E. Daly, E. Dalimier and J. C. Dainty, Requirements for MEMS mirrors for adaptive optics in the eye, in Proc. SPIE, 6113, 2006. 8. L. Thibos, A. Bradley and X. Bong, Ophthal. Physiol. Opt. 22, 427 (2002).

MODELLING OF NONSTATIONARY DYNAMIC OCULAR ABERRATIONS C. LEAHY* and J. C. DAINTY Applied Optics Group, Dept. of Experimental Physics, National University of Ireland, Galway, Ireland *E-mail: conor.leahy~gmail.com The human eye is an optical system with its own characteristic aberrations. It has been well established that the aberrations of the eye are dynamic - i.e. that they vary over time. The goal of this work is t o develop methodologies for computer modelling and simulation of these dynamic aberrations. Dynamic aberrations can be measured experimentally using a wavefront sensor. Analysis shows that the time-series for the various aberration modes are nonstationary. This makes the goals of analysing and modelling the process more difficult. An Autoregressive Integrated Moving Average (ARIMA) modelling approach is described, and results are presented.

Keywords: Ocular aberrations; ARIMA Models; Nonstationary Processes

1. Introduction

As an optical system, the human eye has its own characteristic aberrations, which occur mainly due to the surface of the cornea and the lens. These take the form of both chromatic and monochromatic aberration types. In this research we are concerned with the latter. The dynamic nature of ocular aberrations has been widely investigated [l-41,for example by Hofer et al. [l],who presented results illustrating these dynamic effects, and suggested some of the possible causes. In particular, it has been shown that the tear film has significant dynamic effects on the overall aberration of the eye [5, 61. Other possible factors include, eye tremors, microfluctuations in accommodation, and retinal pulsation [3] A useful model of static aberrations in the human eye was developed by Thibos et al. [7, 81. This model established that in general, higher-order aberrations tend to be normally distributed around zero for a large population of eyes. This leads to a reasonable assumption that the aberration function for an individual eye can be modelled as a multivariate Gaussian 342

343

random variable with known mean, variance, and covariance. The paper suggested the use of a model to create a database of “virtual eyes”. The approach was based on a static model however, i.e. the dynamic nature of the eye’s aberrations were not taken into account. Our work aims to develop a modelling approach that also accounts for dynamic effects.

2. Measurements

To analyse the aberrations of the human eye, the concept of the wavefront aberration is often used. A wavefront is the locus of electric field points of equal instantaneous phase. The wavefront aberration of the eye can be estimated from measurements performed in the laboratory, for example using a Shack-Hartmann sensor [9].In the procedure, the test subject firstly has his/her head secured in place using a bite-bar. Tropicamide is normally used to paralyse the eye’s accommodation. The subject’s retina is illuminated using a near infra-red laser source, and the back-scattered light is then sensed using a Shack-Hartmann wavefront sensor. The length of dataset taken varies, but short datasets can be easier to work with as it is possible for the subject to avoid blinking for the duration of the test. Blinking introduces discontinuities and complicates the results, as can be seen in Figure l.(b). The Shack-Hartmann spot positions are read out to a PC through a CCD camera. In order to derive meaningful interpretations from the data, the local wavefront slopes are estimated from the Shack-Hartmann spot measurements. This in turn enables the calculation of the corresponding estimated wavefront. It should be noted that the presence of speckle and electronic noise has an adverse effect on these estimations. A method of performing these calculations is described in [lo]. A centroiding algorithm is used to define the exact position of each spot on the CCD. Each spot can be defined by horizontal and vertical shifts of its focal point. The local wavefront slopes can then be estimated, and used to determine the coefficients in a Zernike polynomial expansion, which can be described by Eq. (1):

k l

where # denotes phase, M is the number of terms used in the expansion, and u k are the Zernike coefficients.

344

Fig. 1. (a) Phase map of aberrated wavefront; (b) Dynamics of selected Zernike modes

3. Nonstationary Processes

It is important to consider stationarity when performing statistical analysis on a process. A process X ( t ) is said to be strictly stationary if for any delay T, the joint probability density of { X ( t , ) ,X ( t 2 ) ,...,X(t,)} is identical to the joint probability density of { X ( t , + T ) , X ( t 2 T ) , ...,X ( t , + T ) } . This

+

implies that the statistical properties of the process are independent of time. It was clear from analysis of the eye aberration data that this was not the case. Therefore it can be stated that the dynamic aberrations of the eye fail to meet the criteria for either strict stationarity or wide-sense stationarity (which places restrictions just on the first and second order moments). This result means that the dynamic ocular aberrations of the eye should be classified as a nonstationary process. This makes the analysis and modelling significantly more difficult [111. 4. Modelling

We proceed to develop a statistical model of the dynamic aberrations of the eye, based on observed data. It should be noted that ideally one should take a large number of observations from many different subject eyes as the basis for modelling. In this paper just one subject is used, to illustrate the procedure. The resultant model is specific to that subject.

4.1. Autoregressive Integrated Moving Average ~ A R I M A ) Models The ARIMA approach is a generalised case of the standard ARMA model as described by Box and Jenkins, which extends it to include certain classes of nonstationary processes [12]. In the stationary ARMA case, the aim is

345

to model a discrete process y as the output of a causal linear filter driven by white noise v as follows [13]: V

k=l

(I

k=l

The p and q limits determine the order of the model. a k and b k are the model coefficients and can be estimated by solving linear equations constructed from autocorrelation calculations of the process. This is known as the YuleWalker (or autocorrelation) method. For the ARIMA case, a level of differencing d is applied to the data to render it stationary. After differencing, the autocorrelation method can again be used to extract ARMA parameters, giving the completed model:

Often the choice of the model order and differencing is not straightforward. By looking at the sample autocorrelation (SAC) and sample partial autocorrelation (SPAC) functions, one can gain insights about the nature of the process and make a more informed choice of the ARIMA parameters. The partial autocorrelation of a time series at lag k can be thought of as the autocorrelation at lag k with the effect of intervening observations removed. Figure 2.(a) shows a measured dataset (in this case Zernike total RMS error with blink discontinuities removed), along with its SAC and SPAC as calculated using R. The slow decay of the SAC is a characteristic often observed in nonstationary processes. 4.2. Simulation of Models

Simulation is carried out by driving the completed model with a Gaussian white noise process. This converts the input sequence to a process with the same characteristics as the true process used to obtain the model. In the ARIMA case, after simulation the nonstationary data can be recovered from the ARMA simulated data by taking partial sums [14]. Figure 2 shows results from a simulation performed using R. In Figure 2.(a), an ARIMA (3,1,3) model was obtained from a set of measured data, then this model was simulated as described above. The resulting output, shown in Figure 2.(b), has similar characteristics to the original process, as can be seen both from the time series themselves, as well as the similar SAC and SPAC plots. It should be remembered that the simulated model output is not intended

346

tes

Fig. 2. Autocorrelation and partial autocorrelation functions of: (a) Measured aberration data; (b) Simulated aberration data.

to be identical to the original data, but merely to be statistically similar, i.e. their mean, variance and autocorrelation functions should be comparable. 5. Discussion

A procedure to model dynamic ocular aberrations and to simulate aberration data has been outlined. It is hoped that this technique could be useful in areas such as testing of optical designs, simulation of retinal image quality or visual performance, or for control design or prediction in adaptive optics systems. It should be noted that although it is assumed for the construction of the model that the various Zernike modes are independent of each other, there is some evidence that weak correlations exist between certain modes (71. It is planned to investigate these correlations further and to include their effect in the model if required. It has also been shown that there exists a weak correlation between the cardiopulmonary system and eye aberrations [4].Since aspects of this can be measured experimentally, it may be possible to include its effects in the model as an additional regressor. firther investigation is required. It is planned to improve on this modelling technique in the future. In

347 particular, it is hoped to collect a large database of aberration measurements to produce a more comprehensive model t h a t could take into account variations over sample population, as well as over time.

Acknowledgments This work is funded by the Embark Initiative under the Irish Research Council for Science, Engineering, and Technology (IRCSET), and Science Foundation Ireland (SFI).

References 1. H Hofer, P Artal, B Singer, JL Aragon, DR Williams. (2001). Dynamics of Am. A. 18 (3), 497-506. the eye’s wave aberration. J . Opt. SOC. 2. DR Iskander, M Collins, M Morelande, M Zhu. (2004). Analyzing the dynamic wavefront aberrations in the human eye. IEEE Dansactions on Biomedical Engineering. 51 (ll),1969-1980. 3. L. Diaz-Santana, V. Guriaux, G. Arden, and S. Gruppetta, ’New methodology to measure the dynamics of ocular wave front aberrations during small amplitude changes of accommodation,’ Opt. Express 15, 5649-5663 (2007) 4. K Hampson, I Munro, C Paterson, JC Dainty. (2005). Weak correlation between the aberration dynamics of the human eye and the cardiopulmonary system. J. Opt. SOC. Am. 22 (7), 1241-1250. 5. Gruppetta, S., Lacombe, F., Puget, P. (2005). Study of the dynamic aberrations of the human tear film. Optics Express. 13 (19), 7631-7636. 6. K. Y. Li and G. Yoon, ’Changes in aberrations and retinal image quality due to tear film dynamics,’ Opt. Express 14, 12552-12559 (2006) 7. Larry N. Thibos, Arthur Bradley and Xin Hong. (2002). A statistical model of the aberration structure of normal, well-corrected eyes. Ophthalmic and Physioiogical Optics. 22, 427-433. 8. L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, ’Statistical variation of aberration structure and image quality in a normal population of healthy eyes,’ J. Opt. SOC.Am. A 19, 2329-2348 (2002) 9. Carl Paterson (2004). Wavefront Reconstruction and Control. Imperial College, London. 10. W.H. Southwell. (1980). Wave-front estimation from wave-front slope measurements. J. Opt. SOC.Am. 70 (a), 998-1006. 11. Priestley, M. B. (1988). Non-linear and nonstationary time series analysis. London: Academic Press. 140-174. 12. Box, George E.P.; Jenkins, Gwilym M. (1970). Time Series Analysis, Forecasting and Control. San Francisco, CA: Holden-Day. 1-5. 13. R.M. Rangayyan. Biomedical Signal Analysis : A Case-Study Approach. IEEE Elsevier Press, 2002. Series on Biomedical Engineering. 14. Adrian Dunne. (1992). Time Series Simulation. The Statistician. 41 (I), 3-8.

Adaptive Optics Analysis of Visual Benefit with Higher-order Aberrations Correction of Human Eye Lixia Xu2 Yun Dai, Xuejun Rao, Cheng Wang, Yiyun Hu, Qian Liu, and Wenhan Jiang I,

Institute of Optics and Electronics, Chinese Academy of Sciences, P. 0.Box 3.50, ShuangLiu, ChengDu 610209, P.R. China Higher-order aberrations correction can improve visual performance of human eye to some extent. To evaluate how much visual benefit can be obtained with higher-order aberrations correction we developed an adaptive optics vision simulator (AOVS). Dynamic real time optimized modal compensation was used to implement various customized higher-order ocular aberrations correction strategies. The experimental results indicate that higher-order aberrations correction can improve visual performance of human eye comparing with only lower-order aberration correction but the improvement degree and higher-order aberration correction strategy are different from each individual. Some subjects can acquire great visual benefit when higher-order aberrations were corrected but some subjects acquire little visual benefit even though all higher-order aberrations were corrected. Therefore, relative to general lower-order aberrations correction strategy, customized higher-order aberrations correction strategy is needed to obtain optimal visual improvement for each individual. AOVS provides an effective tool for higher-order ocular aberrations optometry for customized ocular aberrations correction.

1. Introduction It is well known that human eyes suffer from different aberrations. Besides defocus and astigmatism that can be corrected by wearing spectacles or contact lens, there are also higher-order aberrations in human eye which influence the visual function. Many researchers have reported that correcting higher-order aberrations can acquire visual improvement. In 1997, Liang et a1 firstly found that correcting the higher-order aberrations can provide improvement in contrast sensitivity when view monochromatic grating through 6-mm pupil "I. Guirao et a1 calculated the contrast improvement when correcting higher-order aberrations of a large people and discovered that some people can acquire significant improvement, whereas others experience very small improvement "I. In 2002, Yoon extended monochromatic measurement including viewing conditions more closely approximate to normal viewing in white light. They also found the visual benefit *

[email protected]

348

349

of correcting higher-order aberrations in normal vision 13]. Patricia A. Piers et al used adaptive optics to simulate modified spherical aberration to study the influence of IOL to visual performance 14’. The result is correcting ocular spherical aberration can improves spatial vision. In China, the Laboratory on Adaptive Optics in the Institute of Optics and Electronics (IOE), Chinese Academy of Sciences, has developed the technique of retinal image with adaptive optical system 15’. After that, a system of higher-order aberrations correction and vision analysis for human eye has been developed. In this letter, after brief description of the system, the experiment procedure and test data are presented.

2. Methods 2.1. Adaptive Optics Vision Simulator The optical schematic is shown in Fig.1. A laser diode (LD) with output wavelength of 905nm is used as the beacon. The beacon is collimated as a parallel light after passing through a spatial filter and the beam expander, reflected by the mirror and the beam splitter, and injected into human eye. The backward scattering light from the human eye retina exists through the pupil, passes through deformable mirror (DM), pupil matching system, and project into the Hartmann wave-front sensor (WFS). The wave-front slope data measured by the WFS is acquired by a computer. By using the direct-slope algorithm and control algorithm 16’, the slope data set is transformed into voltage data and used to drive the DM to correct eye’s aberration or construct different aberration pattern. So, the eyes with different aberrations can be realized. Through measurement software, Contrast sensitivity or visual acuity under different conditions can be measured. The power into human eye is about 2uW, which is little than the standard of International Electrotechnical Commission (EC). The system was detailed described in another paper 17]. The main system specifications are listed here. The A 0 system consists of a 37-actuator piezo deformable mirror with a stroke of about 2 microns and a Hartmann-Shack wave front sensor with 97 lenslets operating at 25 Hz. In our experiment, the wave-front aberrations are reconstructed or filtered using the first 20 Zernike polynomials. The bandwidth of A 0 system is about 1Hz. It is well known that human eye’s aberration fluctuates according to time. In experiment, dynamic closed-loop was used to control the variation of human eye’s aberrations. The change curve of aberration of one subject is shown in Fig.2. According to the curve, abnormal data influenced by the subjective factors can be excluded from the original data measured from Hartmann sensor. For

350 example, aberrations variation of one subject is too large this time but little most of time, we consider that subject's status is not stable and exclude the data. 1 I

Fig. 2 Variation of aberration in dynamic closed-loop

Fig. 3 Visual control and analysis

2.2. Vision Test Design The visual stimulus was produced by software and projected by a DMD (Digital Micro-mirror Device) projector. The stimulus can randomly change its direction and contrast by software and the DMD was illuminated by a monochromatic light source with wavelength 550nm. A four-alternative, forced,-choice discrimination test was designed and the contrast acuity was measured using psychophysical method, the Quest procedure. Subjects pressed one of four buttons on a handle to indicate letter orientation following 1 second presentation. The choices of subjects were acquired into a computer through USB interface and processed by the analysis software. Each frequency was repeated six times. The 50% correction ratio was taken as the measure of visual acuity. The average i l l u ~ n a t i o nof stimulus kept constant during visual performance test and the retina illumination was about 61 Td.

351

2.3. Experiment Procedure Experiments were done on the right eyes of six subjects in dark room. The age ranged from 25 to 32 years old. Through normal ophthalmic check, all eyes were healthy. The entrance pupil of A 0 system was 6 mm, so, the subject's pupil was dilated with phenylephrine hydrochloride (2.5%). Comparing with reference [3] and [4], this drug dilated the pupil while kept accommodation function of eye so as to simulate normal physiological status to the fullest extent. Each subject's consent was obtained. Before experiment, subject was told firstly how to cooperate with operator in the test. Astigmatism and defocus were corrected firstly with trial lenses. The subject adjusted defocus and cylinder axis to optimize image quality. In test, residual defocus was below O.1D and residual astigmatism was below 0.2D. Because of accommodation, the values of defocus and astigmatism varied during the test process. To eliminate the effect of fluctuation of ocular aberrations with time, dynamic real time closed-loop was used in experiment. Five correction strategies were adopted in experiment, including open-loop of AO, correcting system static aberrations, correcting all aberrations with dynamic closed-loop, correcting higher-order aberrations with dynamic closed-loop, correcting low-order aberrations with dynamic closed-loop. The system static aberration was defined as the aberration from the beam splitter to the Hartmann sensor and was measured using a reference parallel beam injected into the system at the place the eye's pupil. The aberration was small, about 0.12pm rms. The influence was removed by saving the actuator voltages on the deformable mirror required to compensate for system itself and paying back to the DM when eye was in place. 3. Results and Analyze 3.1. Influence of Different Correction Strategy on Rsual Benefi Apply sphere aberretian

-:36 40

? 30

" 2 $20

. I 0

"k

16

3 10 ;S 0 -3.2

-a i

0.2

RYS of S p h e r e W

Fig. 4 Visual acuity of seven subjects with Fig. 5 Different sphere aberration on visual different strategy acuity

352 The visual acuity in different correction strategy was shown in Figure 4. From the result we can see the benefits greatly varies among eyes which consists with conclusion obtained by other researchers. Two subjects who were both higher myopia (-6.OD and -8.OD respectively) show almost no benefit for any correction strategy and even deterioration for one subject. Four subjects can obtain visual benefit with different extent when higher-order aberrations are corrected. Compared with open-loop, correcting static aberrations show obvious visual improvement. Although system static aberration is about 0.12pm rms, a little reduction in aberrations can acquire visual benefit. It suggested that eyes are more sensitive to out world aberration.

3.2. Znfluence of Single Higher-orderAberration on WuaE Benefit Different higher-order aberration has different influence on vision function. To analyze the influence of single higher-order aberration on vision function, single order aberration was simulated by adaptive optics. Through changing the reference data of closed-loop, single Zernike modal aberrations can be fitted by DM. Especially, the influence of single sphere aberration on human eye was firstly tested in experiment. The experimental result was shown in figure 5. From the result we can see that sphere aberration with different direction has reverse influence on visual acuity. Further experiment and analysis of influence of each single higher-order aberration on visual performance is being conducted.

4, Discussion and Conclusion This paper analyzed the visual performance after correcting aberrations of human eye with different strategy. Dynamic closed-loop can control the variance of eye's aberration. The results shown that individual has great different in performance. The reason can be considered from the following conditions. First, the experiment has some uncertain factors, such as the status of subject, cooperate well with the test. Second, the result has some relationship with the cause of vision. Object is imaged on retina by refractive system of eye, transferred to paliium by second nerve, recognized by brain. The vision function is determined by optics system of eye and second nerve. The correction strategy is only effective to the optics of eye. So, the reduction in aberration of eyes is not identical with visual improvement. The adaptation of eye to its own aberrations must be taken into consideration, The phenomenon in different subject can also suggest the idea that eye's adaptation is important. Static aberrations correction can acquire obvious improvement in visual acuity compared with open-loop even if the static aberration is about 0.12pm rms. The results showed that the out world aberration is not identical with the inner of eye event if they have equal number. This conclusion is somewhat identical with the result of Pablo Artal [81. He points that

353 the neural system of human eye is adapted to eye’s aberration. In addition, two subjects with high myopia have no change in all conditions. Perhaps, eyes are adaptive to their defocus and not sensitive to higher-order aberrations. More experiments are needed to support the view that higher-order aberrations correction is not effective to high myopia. Compared with correcting low-order aberrations, the contrast acuity of subject is not all improved when correcting higher-order aberrations. This result did not coincide with the conclusion of Yoon. Perhaps the main reason is the different drug used to dilate pupil. In our experiments, the drug has little effect on cycloplegia. The status with accommodation is most near to the natural view conditions. In the test, it represented that correcting static aberration can acquire more benefit than correcting higher-order aberration or low-order aberration in some subjects. But correcting static aberration has little effect on reducing eye aberrations measured by HS sensor. The reduction in ocular aberrations is not proportional to the visual benefit. Some aberration is good for vision, but some is bad. The next work is to find the influence of different aberrations. Therefore, relative to general lower-order aberrations correction strategy, customized higher-order aberrations correction strategy is needed to obtain optimal visual improvement for each individual. AOVS provides an effective tool for higher-order ocular aberrations optometry for customized ocular aberrations correction. acknowledge men^

This research is funded by National Nature and Science Foundation of China (No: 60438030) and the National “863” Program of China (2006AA02Z4D2). Corresponding author Lixia Xue’s email is [email protected].

References 1. 2. 3. 4.

5. 6. 7. 8.

J.Liang,D.R.Williams,and D.T.Miller, J.Opt.Soc.Am.A, 14(11), 2884(1997). A.Guirao, J.Porter, D.R.Williams, Ian G.Cox, J.Opt.Soc.Am.A,19(1),1(,2002). G Yoon, D.R.Willimas, J.Opt.Soc.Am.A,19(21),266(2002). P A.Piers, E J.Fernandez, S Manzanera, et al, Investigative Ophthalmology &VisualScience,45( 12), 4601(2004). Y. Zhang, N. Ling, X. Rao et al, The 3d International workshop on adaptive optics for industry and medicine, 97(2001). Xinyang.Li, PH.D paper, 91 (2000). Xue Lixia, Rao Xuejun, Wang Cheng, et al. Acta Optica Sinica (In Chinese), 27(5), 893 (2007). P.Artal, L.Chen, E.J.Fernandez, et al, Journal of Vision, 4,281(2004).

EX

E L E C T R O M A ~ ~ T D~FORMABLE IC MI ~ E ASSE ~ S S ~ EA~AND T FI~ APPLICATIO~S

IC

L. VABRE', E.J. FERNANDEZ2, F. HARMS', J. CHARTON3, B. HERMANN4, A. UNTERHUBER4, B. POV&AP, N. CHATEAU', W. DREXLER4 Imagine Eyes, I S rue Charles de Gaulle, Orsay, France. Laboratorio de Optica, Universidad de Murcia, Centro de Investigacidn en Optica y Nanotecnologia, Campus de Espinardo, 30071 Murcia, Spain. Laboratoire d'Astrophysique de Grenoble, CNRS Observatoire de Grenoble, Grenoble, France. Biomedical Imaging Group, Department of Optometry and Vision Sciences, Card@ University, Wales, UK Following are the key characteristics of the miraoTM52-d Electromagnetic Deformable Mirror (Imagine EyesTM,France) and our estimation its suitability for ophthalmic applications. This study demonstrates the device's high stroke, high linearity, and low hysteresis. Equally presented is an example of the correction obtained using the device in a closed-loop configuration an eye presenting aberrations.

e ~ o ~ bmirror l e description The mirao 52-d can be described as follows:

Figure 1. Schema of the mirao52-d Electromagnetic Deformable Mirror.

An array of 52 magnets is fixed under the reflecting deformable membrane. A corresponding set of coils creates independent magnetic fields for each magnet that either push or pull them depending on the polarity of the voltage applied to each coil. The ensemble of these components makes up the mirrors actuators. The produced force F is proportional to the magnetic field B which is also proportional to the current I through the coil. 354

355

2. ~ e f o r ~ bmirror le characterization To test the performances of this deformable mirror, we built a closed-loop adaptive optics system that combined the mirao deformable mirror with a 32x32 Hartmann-Shack wavefront sensor (HASOTM32-eye, Imagine Eyes, France). This system was used to evaluate the following criterion of the deformable mirror:

* 0

wavefront generation range linearity hysteresis surface quality stability

A stroboscopic illumination source was used to explore the temporal behavior of the mirror in an open-loop configuration in order to measure its bandwidth. A detailed study of mode coupling, up to the 5' Zernike order, was also performed.

2.1. Zn~uence~unctions The following figure shows the influence functions measured by applying the same voltage to each actuator.

Figure 2. Influence functions obtained for each actuator (+0.5V).

356

2.2. L i n e a ~ The following figure shows measured linearity curves. Linear fit demonstrated a linearity of 99 %

Figure 3. Linearity response of the deformable mirror as a function of the applied voltage (0 to 1V).

esonance frequency The resonance frequency of the deformable mirror was measured by plotting a Bode diagram. The measurement was performed by tuning the frequency of a sinusoidal signal sent on a single actuator. The resonance frequency was measured by plotting a Bode diagram using the deformable mirror. The measurement was performed by tuning the frequency of a sinusoidal signal sent on a single actuator. 10'

1

Figure 4. Bode diagram (top = amplitude, bottom =phase) of the deformablemirror's response.

357

This diagram shows that the first resonance frequency is 200-250 Hz.

3. Closed-loopcorrection Having assessed the measured performances, we concluded that the deformable mirror capable was capable of correcting for both lower and higher-order aberrations in human eyes. The following (figure 5 ) shows the Zernike coefficients of an aberrated eye before (in white) and after correction (in red) with the mirao 52-d Electromagnetic Deformable Mirror.

s3

Figure 5 . I0 white, the eye’s original measurement values. In black, residual values measured after correction. The Sthrel ratio increased from -0 to 0.7.

This deformable mirror can correct highly-aberrated eyes to obtain high Strehl ratio values.

4. Conc~usion~ s u ~ r ofy the performances Nearly no mode coupling was observed on a wavefront generation range that was found to be compatible with the statistics of aberrations measured in real eyes, including most pathological cases.

358 Table 1: Principal measurement characteristics of the mirao 52-d ElectromagneticDeformable Mirror. Parameter Linearity Hysteresis active flat wavefront quality RMS,maximum wavefront stroke Zmaximumgenerated Zernike aberrations (peak-to-valleywavefront) bandwidth

Measurement >95 % < 2% 10 nm 100 pm defocus +/-35 p ~ s t i g ~ t i s+/m 30 pm,spherical aberration +/- 8pm > 200 Hz

We can conclude that this electromagnetic deformable mirror combines large stroke with a high optical quality. These characteristicsmake it suitable for various adaptive optics applications as confirmed by the first closed-loop corrections.

eference 1. Enrique J. Fernandez, Laurent Vabre, Boris Hermann, Angelika Unterhuber, Boris Povazay, Wolfgang Drexler, Opt. Exp., 14,20, 8900 (2006).

C

CTING OCULAR A B B E ~ T I O N SIN 0 COHE~NCE T O ~ O G ~ P ~ Y

SIMON TUOHY*,ADRIAN BRADU~,ADRIAN GH. PODOLEANU Applied Optics Group, Photonics Centre, School of Physical Sciences University of Kent, CIZ INH, Canterbuiy, UK sgt3 @kent.ac.uk, a.bradu @kent.ac.uk, a.g.h.podoleanu Bkent.ac.uk NICOLAS CHATEAU Imagine Eyes, 91400 Orsay, France [email protected] CHRIS DAINTY Applied Optics, Dept. of Experimental Physics National University of Ireland, Galway, University Road, Galway, Ireland. c.dainty @ nuigalway.ie

The theoretical confocal profile of an ideal Optical Coherence Tomography (OCT) system is modeled and analyzed. The results of the analysis are used to determine the suitability of both Time Domain (TD-OCT) and Fourier Domain OCT (FD-OCT) in conjunction with Adaptive Optics. It is shown that for large depth ranges the interference signal from FD-OCT drops below the level of TD-OCT interference signal indicating that for larger depth ranges, TD-OCT is a more suitable system. A TD-OCT novel system design is presented as well. The system incorporates a high stroke deformable mirror (MIRA052 Imagine Eyes) and a Shack-Hartmann wave-front sensor. It is able to produce simultaneous en-face OCT and Scanning Laser Ophthalmoscopy (SLO) retinal images as well as OCT longitudinal images.

1. Introduction Novel technological advances in wave-front sensing and adaptive optics corroborated with well known, already clinically used techniques such as OCT and SLO have opened a new exciting and challenging research subject: measuring and correcting the optical aberrations introduced by the eye itself.

* Marie Curie training site MEST-CT-2005-020353 EPSRC support, grant GWS18120/01 Foundation.

359

360

OCT, which is a technique based on low coherence interferometry [ 11, has the potential of achieving high depth resolution. As the depth resolution is given by the coherence length of the optical source, its values can be as small as a few microns, OCT commercial apparatus able to produce longitudinal images being already available. Also, OCT has been reported as being able to produce en-face or transversal images generated by moving the beam across the object [2-51 The OCT technique applied to Ophthalmoscopy has evolved rapidly in the last few years as it can deliver a better depth resolution than a SLO. The achievable resolution of an SLO system is typically of around 300 pm in depth and 10 pm laterally [6].However when imaging the retina, the performances of the OCT and SLO systems in terms of their resolution are still limited by the aberration of the eye itself. Adaptive Optics (AO) has been demonstrated as a suitable method to correct for these aberrations and it has been used in combination with OCT [7] or SLO IS]. A combination of OCT and SLO using aberration correction via A 0 was also reported [9]. Here we demonstrate the superiority of using Time Domain OCT and present a novel simultaneous Time Domain OCT/SLO system with Adaptive Optic correction.

2. Profiles of different pupil sizes The sensitivity drop off of an AO/OCT system as we move away from the focus is dictated by the systems confocal profile. The graph in figure 1 represents ideal confocal profiles for 4 different pupil sizes constructed using a theoretical model [lo]. It was constructed from: exp(--)

C(z)=

?;

where z is the distance from the centre of the profile, 0.15 is the depth at half width at half maximum for a pupil size of 3mm and

a=

1 ln(0.5)

(0.15"1

361

/i /

Figure 1. Graph Gaussian confocal profiles.

An alternative theoretical way of representing the graphs is by using a sinc based model of the graphs [ 1I]: U

C(u) = sin c(-)

(3)

2

where

n

u =: ~ z - ( N . A ) ~ /zn

(4)

while z is the distance from the focus, NA is the numerical aperture of the eye + lambda and n!!

--.

3 mn pupil - - - 4mn

-5m t

08

06

04

02

I

0

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Figure 2. Sinc Confocal profile.

362

As can be seen from the diagram as the pupil size increases the confocal profile shrinks resulting in lower signal at the extremities of an image when using fixed focus. FD-OCT operates under fixed focus meaning that the central peak of the profile is stationary while in TD-OCT can operate under a non-fixed focus allowing the centre of the peak to be moved as the depth changes resulting in a more linear signal. A larger pupil size is desirable as it gives a better lateral resolution and the larger the pupil the larger the aberrations that will be corrected while the PSF enlargement due to diffractions is low. Graphing the values of the signal vs the pupil size at 150 pm from the centre in figure 3 below it can be seen that as the pupil size increases the difference between the signal from the EDOCT and the TD-OCT operating with non-fixed focus decreases and at a certain pupil size the signal from the TD-OCT system is greater then the signal from the ED-OCT system. 0 -5

-+-Sinc -+-'&assisin +-nme-Domain

-10

-

-15 -20 -25

1

1

I\

-50J

Figure 3. Graph of the signal in DB versus pupil size at 150 pm from the peak for Gaussian and Sinc representations.

As the objective of using Adaptive Optics is to bring the confocal profile down to the ideal confocal signal then a system that allows for the moving of the focus is required if imaging a wide depth range. In the next section we present a system operating in the Time Domain. The system is able to produce simultaneously OCT and SLO images and correct for the optical aberrations introduced by the eye itself, by incorporating within the system A 0 elements.

363

3. System The schematic of the simultaneous OCT/SLO system that incorporates Adaptive Optics elements is shown in figure 4. The source used in this system is a pig-tailed Super Luminous Diode (SLD) from SuperLum. It has an output wavelength of 830 nm and a coherence length of 17nm which dictates the resolution of about 13 pm in the eye.

Figure 4.Schematic of the system: L1-L6 lenses, M: flat mirrors, MO: Microscope Objectives, DM: deformable mirror, BS: beam -splitter, PDi: photo-detectors and APDi: avalanche photo-detector.

The light from the SLD injected into the system via Microscope Objective M01, (x30) is split via the beam-splitter BSl (70/30) into the reference and the object arm of the interferometer. In the object arm, light enters the eye via a pair of orthogonal galvoscanners and the telescope T1. Lenses L1 and L2 have been chosen such as the diameter of the beam entering the eye to be 2 mm. On the other hand, we have considered that the beam diameter leaving the eye is 6 mm. L3 and L4 are required to increase the size of the beam exiting the eye via the scanners to the size of the aperture of the deformable mirror, 15 mm. After this the light passes through lenses L5 and L6 which reduce the beam diameter from 15 mm to 2.25

364

mm so the light can be efficiently injected into a single mode optical fiber by means of a X20 microscope objective. Equally, a 2.25 mm beam diameter, will cover the lenslet array to give an array of spots on the CCD of the ShackHartman suitable for measuring the wavefront aberrations. One of the benefits of the design is that the non-common path between the imaging system and the wavefront sensor is reduced resulting in the wavefront measured by the wavefront sensor being more accurate. Our wavefront corrector is MIRAO52-D magnetic mirror, produced by Imagine Eyes. It has a large rt50 pm stroke and 52 actuators controlled by voltage levels from 0 to 1 volt. The deformable mirror is operated in closed loop with a Shack-Hartman wavefront sensor. The reference arm contains 2 flat mirrors (M2 and M3) mounted on a computer controlled mechanical translation stage that has a range of movement of 2.5 cm. It allows coherence matching for different lengths in the object arm and thus different depths in the subject’s eye. In order to create B-scan images, the frame galvo-scanner is switched off while the translation stage scans in depth We believe that this system is an improvement of the system developed in our group by Merino et la 191 which included an O K 0 deformable mirror with 37 actuators and a stroke of 3.5 pm. Due to the small performance of the OK0 mirror, they managed to achieve an improvement in signal-to-noise ratio, when the A 0 was turned on of only 4 to 6 dB. Due to high stroke of the MIRA052-D, we believe that much better improvement could be achieved. We also expect a large reduction of the depth resolution in the confocal channel. Consequently, in order to acquire large size B-scan OCT images, dynamic focus is required. Our system is ideally suited for dynamic focus. The rate of focus adjustment required is 2 Hz, which could easily be achieved mechanically for both en-face and Bscan regimes of operation. An elegant method to achieve dynamic focus would be the use of the MIRA052-D deformable mirror itself without the need of using extra optical and mechanical components.

. Conclusion We theoretically demonstrated the superiority of using TD-OCT over FD-OCT when imaging a large depth range with Adaptive Optics. A novel design of a TD-OCT retinal imaging system interfaced with A 0 elements is also presented. However, further work is required in order to fully demonstrate the suitability of the MIRAO52-D deformable mirror.

365

A~knowledgmen~ S.Tuohy and A. Podoleanu acknowledge the support of the Marie Curie training site MEST-CT-2005-020353, A. Bradu acknowledges EPSRC support, grant GWS 18120/01. efere~ces 1. D. Huang, E.A.S., C. P. Lin, J. S . Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto., Optical coherence tomography. Science, 1991.254: p. 1178-1181. 2. Podoleanu, A.G., G.M. Dobre, and D.A. Jackson, En-face coherence imaging using galvanometer scanner modulation. concern, 1998. 3. Podoleanu, A.G., et al., Coherence imaging by use of a Newton rings sampling~nction.Opt. Lett, 1996.21: p. 1789-1791. 4. Podoleanu, A.G., et al., Simultaneous en-face imaging of two layers in the human retina by low-coherence reflectometry. Optics Letters, Optical Society of America, Washington, US, 1997.22(13):p. 1039-1041. 5. Podoleanu, A.G., et al., Transversal and Longitudinal Images from the Retina of the Living Eye Using Low Coherence Reflectometry. Journal of Biomedical Optics, 1998.3( 1): p. 12-20. 6. Donnelly Iii, W.J. and A. Roorda, Optimal pupil size in the human eye for axial resolution. Journal of the Optical Society of America A, 2003. 20( 11): p. 2010-2015. 7. Hermann, B., et al., Adaptive-optics ultrahigh-resolution optical coherence tomography. Optics Letters, 2004.29( 18): p. 2142-2144. 8. Roorda, A., et al., Adaptive optics scanning laser ophthalmoscopy. Optics Express, 2002. lO(9): p. 405-412. 9. Merino, D., et al., Adaptive optics enhanced simultaneous enTface optical coherence tomography and scanning laser ophthalmoscopy. Optics Express, 2006.14(8): p. 3345-3353. 10. Kimura, S. and T. Wilson, Confocal scanning optical microscope using single-modefiber for signal detection. Appl. Opt, 1991.30: p. 2143-2150. 11. Izatt, J.A., et al., Optical Coherence Tomography and Microscopy in Gastrointestinal Tissues. IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, 1996.2(4): p. 1017. 12. Dalimier, E. and C. Dainty, Comparative analysis of deformable mirrors for ocular adaptive optics. Optics Express, 2005. 13(11): p. 4275-4285.

This page intentionally left blank

art

This page intentionally left blank

ICATIONS OF A L I ~ CRYSTAL ~ D ABE FOR THE OPTICAL DISC SY MASAKAZU OGASAWARA and MAKOTO SAT0 Corporate Research and Development Laboratories, PIONEER CORPORATION 6-1-2 Fujimi, Tsu~ga~hima-shi, Saitama, 350-2288,Japan An optical disc such as Compact Disc (CD) or Digital Versatile Disc (DVD) is one of the most familiar and indispensable storage media in our daily life, because of its better portability and lower production cost than other storage media. Recently there have been many approaches and studies to increase an optical disc capacity by employing a higher Numerical Aperture (NA) objective lens and a shorter wavelength laser. The problems of aberrations caused by a deviation from the disc standard and a dispersion of the quality of an optical pick-up head become morc serious when these high-density techniques are applied to an optical disc system. Applying an adaptive optics to these optical disc systems is believed to be the best solution to compensate for these aberrations. On the other hand, the consumer optical disc system requires the adaptive optics device to be low cost and simple, and to achieve high stability, easy controllability and so on. We believe the most suitable adaptive optics device having potential to meet these requirements is a Liquid Crystal Aberration Compensator (LCAC) 111. In this report we damental researches on the LCAC and introduce our application studies ur latest DVD drive.

f a n optical disc system disc system mainly three kinds of aberrations have made it difficult to guarantee stable recording and playing back on the marginal discs. The concerned aberrations here are coma, spherical and astigmatic aberration. 1.1. Coma a b e ~ a ~ ~ The coma aberration is caused by a disc tilt against the optical axis of an objective lens. Figure l(a) shows the calculated results of the beam spot profile caused by the disc tilt. The disc tilt causes the coma aberration and deforms the beam spot on the disc. In this situation, the read-out signal from the disc is degraded by the signal crosstalk from adjacent tracks. The DVD disc standard defines its angular deviation limit to prevent a circulation of the discs having the large tilt angle. However, actually, some of the discs on the market are out of this specification. 369

370

1.2. Spherical aberration The spherical aberration is caused by the cover layer thickness error. A certain amount of spherical aberration also deforms the beam spot and consequently the read-out signal is degraded by the signal crosstalk and inter-symbol interference (Fig. l(b)). There is a limit for the disc manufacturers to perfectly control the cover layer thickness under mass-production condition. In addition, the DVD disc standard defines a dual layer type disc that has two recording layers. The spherical aberration is generated when the objective lens changes its focusing point between two layers.

1.3. Astigmatic aberration The astigmatic aberration is mainly generated by distorted optical elements or an improper assembly of the pick-up head (Fig. l(c)). So, each optical pick-up head has the astigmatic aberration with the different direction. It is difficult to determine its direction in a production process of the optical pick-up head before the adjustment is finished. The ordinary techniques to correct the astigmatic aberration focus on choosing high accuracy optical elements and assembling the pick-up head carefully. However, these techniques have the limit to keep a stable good quality of the pick-up head.

Cover layer thickness

3 : sc tilt

I

I

(b) Spherical aberration

(c) Astigmatic aberration

1

Distorted optical element (a) Coma aberration

Figure 1. Aberrations in the optical disc system.

371

2. The basic s t r u c ~ r eof the LCAC We decided to adopt the liquid crystal device as the adaptive optics for the optical pick-up head, since it has the ability to meet some requirements for an implementation of it. The LCAC is composed of the Liquid Crystal (LC) molecule sandwiched by two glass substrates. We adopted a homogeneous alignment for the LCAC, and this structure gives large change of the refractive index and large phase shift modulation to the wave front of the transmission light. The transparent electrode formed on a surface of the glass substrate is divided into some areas to adjust the wave front distribution of one of concerned aberrations (Fig. 2). The number of the divided electrodes was chosen so that the LCAC have an enough aberration compensation performance and a simple electrode structure with easy algorithm for its control. Especially, in case of the astigmatic compensation, we adopted the electrodes divided at an equal angle interval and switched the applied voltage combination according to the direction of the astigmatic aberration (Fig. 2(c)).

(a) Coma aberration

(b) Spherical aberration

(c) Astigmatic aberration

Figure 2. WAC electrode patterns.

3. Experi~entalresults Figure 3 shows a structure of an experimental pick-up head for DVD. The LCAC is located beneath a quarter wave plate and the orientation of the liquid crystal is matched to the polarization direction of the laser beam. Ohjcctiva 1cns :NAO.

Photo detector

L l t w diode : 66Onm

)ttriz& &mi Splitter

Figure 3. Structure of the experimental DVD pick-up head.

372

3.1. Single function LCAC Figure 4 shows the readout radio frequency (RF) signals with the LCAC off-state and on-state. In case of (a), the DVD was intentionally tilted by 1.0 degree against the objective lens. We obtained a better quality RF signal by applying the optimum voltage to the electrodes. In case of (b), a dual layer DVD that is out of specification was used. The LCAC compensated for the spherical aberration and made the RF signal quality of the dual layer DVD almost the same as the single layer DVD's good one. In case of (c), the DVD was reproduced by using the optical pick-up head having a distorted optical element. Since the direction of the astigmatic aberration wasn't predicted beforehand, we selected the suitable electrode combination by try-and-error method to get better R F signal.

(a) Coma aberration (Disc tilt angle = 1.O deg.)

(b) Spherical aberration (Dual layer disc)

(c) Astigmatic aberration

Figure 4.Aberration compensation effect of the single function LCAC.

ualfunction LCAC In an optical pick-up head, two or more kinds of aberrations often cause problems together, so the LCAC is required to compensate for these aberrations at the same time [ 2 ] .Figure 5 shows the structure of a dual function LCAC for compensating for the coma and astigmatic aberration. E l ~ c t Br fur ~ ~astimatic ~ aberration

/

Electrode A far coma abenalion Figure 5. The structure of the dual function LCAC.

373

Figure 6 shows the experimental result curves with the data-to-clock jitter versus the disc tilt angle. In this experiment, we used the optical pick-up head that had some astigmatic aberration. The data-to-clock jitter is one of the evaluation indicators of the optical disc system and is defined as a standard deviation of a displacement between the readout data and the reference clock. In general, it is normalized by a channel clock interval. The bottom jitter value is about 11.5% and the tilt margin is about ~ 0 . 5 5 degree without any compensation. (When the tilt margin is defined as the threshold jitter value of 15%.) Both the bottom jitter value and the tilt margin are improved by an astigmatic compensating function of the LCAC. Furthermore we obtained wider tilt margin by adding a coma aberration compensating functionality 131.

Figure 6 . Compensation performance of the dual function E A C .

lti fun~tionLCAC The purpose of the multi function LCAC is to compensate for the coma, spherical and astigmatic aberration without any additional extra electrodes. The feature of the multi function LCAC’s structure is to separate the electrodes for the coma aberration compensation into two areas on each surface of two glass substrates. The electrode A is designed for the astigmatic and part of coma aberration compensation, and the electrode B is designed for the spherical and the other part of coma aberration compensation respectively (Fig. 7). As a result, three kinds of aberration that cause problems on the optical pick-up head can be

374

compensated by using only one LCAC device. This multi function LCAC has enough performance to be used for the actual production optical pick-up head, although each electrode pattern is slightly different from the optimum one for an arrangement reason.

Figure 7. The structure of the multi function LCAC.

4. The applications of the LCAC We started the implementation of the LCAC in 1997 by installing it in our first generation DVD car navigation system. This LCAC had a single function and worked to compensate for the coma aberration generated by the disc tilt only. This experience gave us lots of important knowledge for the implementation of the LCAC. In 2002, our 5th generation computer peripheral DVD drive installed the dual function LCAC in the optical pick-up head. In 2005 we applied the multi function LCAC to our 10th generation DVD drive. This LCAC technology has been adopted up to our 12th generation DVD drive that was released in 2006 (Fig. 8,9). Recently many Blu-ray Disc and High Definition-DVD (HD-DVD) drives have adopted various types of the LCAC. We hope that our LCAC technology will be used in more optical disc drives in the world.

Figure 8. Multi function LCAC.

Figure 9. The 12th generation DVD drive.

375

References 1. N. Murao, M. Iwasaki, S . Ohtaki, ISOM96 Technical Digest, 351 (1996). 2. S . Ohtaki, N. Murao, M. Ogasawara, M. Iwasaki, Jpn. J. AppZ. Phys. Vo1.38, 1744 (1999). 3. M. Ogasawara, M. Iwasaki, S. Ohtaki, 59th JSAP Meeting, 15p-V-2, (1998).

C

E ~ C I A L I ~ A T I OOF N THE ADAPTIVE SCA OPTICAL ~ I C ~ O S C O P(AS0 E

B. POTSAID AND J. T. WEN Center for Automation Technologies and Systems, Rensselaer Polytechnic Institute, Troy, New York 12180, USA S. BARRY AND A. CABLE Thorlabs, Inc., 435 Route 206, Newton, NJ 07860, USA Traditionally restricted to one-of-a-kind research or demonstration testbeds, adaptive optics technologies are now maturing to a point where they can be considered for inclusion in certain high performance commercial instrumentation. Indeed, Thorlabs, Inc. is bringing to market the Adaptive Scanning Optical Microscope (ASOM), which uses a MEMS deformable mirror as an enabling technology to achieve a greatly expanded field of view in microscopy. First, this paper explains the process of technology transfer of the ASOM technology from the university laboratory to an expert optics and instrumentation company. Next, design features of the ASOM product are described that facilitate a compact design and demonstrations of an ASOM prototype are presented.

1. ~ntroductionto the Adaptive Scanning Optical ~icroscope(A§ The optical microscope, perhaps the most used optical laboratory instrument, is continually being revitalized. The instrument has been made more flexible through the computerizationof the imaging procedures as well as the addition of accessories that support enhanced image contrast such as dark field, differential interference contrast (also known as Nomarski imaging), and fluorescence imaging. However, even with these adaptations, the traditional microscope design suffers from a small field of view at high resolution, which is a significant hindrance when using the microscope in practice. A new microscope design, called the Adaptive Scanning Optical Microscope (ASOM), uses adaptive optics in a novel optical layout to achieve high resolution imaging over a field of view approximately two orders of magnitude larger in area than a traditional microscope design. The unique wide field and high speed imaging capabilities of the instrument are obtained without requiring movement of the sample or specimen, a significant benefit to both industrial and biomedical applications. 376

377

Science camera

Figure 1 . Adaptive Scanning Optical Microscope (ASOM).

Figure 1 shows a realistic ASOM layout. Light from a source illuminates the object (specimen). The role of the scanner lens assembly is to collect light from the object and aim the light to an external pupil that is coincident with the steering mirror. The specific angle of the steering mirror defines the location of the center of the field of view on the object. By scanning over the specimen and taking a sequence of images (not point sampling as in confocal microscopy), a large mosaic image can be constructed. However, for all field positions the scanner lens introduces considerable wavefront aberrations, which blur the image. Note that intentionally allowing for large aberration reduces the lens count, complexity, and cost of the scanner lens. To manage this blurring, the light from the steering mirror enters a pupil imaging stage to be directed to the deformable mirror, which adapts its surface shape to correct for the wavefront errors introduced by the scanner lens assembly. Light exiting the deformable mirror is now well corrected and nearly aberration free. After passing through the pupil relay optics and being projected onto the camera, the light forms a sharp diffraction limited image. More detailed information about the operating principle of the ASOM can be found in a simulation based paper'. A significant pportunity exists due to the developing need for higher speed expanded field of view imaging and analysis in both research and industry; it is this need that is the primary driver for the commercializationof the ASOM. rocess of ~ o ~ e r c i a l i z a t i oand n Technology Transfer The original development and prototyping of the ASOM was conducted at the Center for Automation Technologies and Systems (CATS) at Rensselaer Polytechnic Institute. The process of technology transfer from Rensselaer to

378

Thorlabs occurred through the cooperative design and construction of an ASOM prototype to be demonstrated at an exhibition, only several months after the licensing agreement was finalized. Starting with the CATS existing prototype ASOM using a 32 actuator m M S deformable mirror and off-the-shelf optics only, shown in Figure 2, Thorlabs and CATS teams worked closely together to develop a breadboarded ASOM prototype using custom optics and a 140 actuator MEMS deformable mirror, shown in Figure 3. This jointly developed intermediate system was demonstrated live at Photonics West 2007, constituting a significant milestone in the technology transfer process. With knowledge of the essential operating principle of the ASOM and firsthand experience with the breadboarded system, Thorlabs proceeded with an internal development program to improve on the basic ASOM design for commercialization, resulting in the ASOM product shown in Figure 4.

Figure 2. Prototype ASOM built at the CATS (October 2006).

Figure 4. Thorlabs prototype commercial ASOM instrument at CLEO (May 2007) above and to the right.

Figure 3. Intermediate breadboarded ASOM jointly developed by ThorIabdCATS team for Photonics West (January 2007).

379

escription of the ASOM Product The ASOM product’ developed by Thorlabs constitutes one of the very first commercially available instruments to include adaptive optics. Whereas most adaptive optics systems are quite large (one-of-a-kind setups constructed on an optical table using long focal length lenses), the ASOM product has a small footprint and compact size that is suitable for benchtop installations. As shown in Figure 5, a fold mirror introduced into the optical path allows the imaging optics and deformable mirror to be efficiently packaged in a vertical frame. Careful use of custom optics in the pupil relayhmaging optics reduce the length of the optical path for an additional reduction in the overall instrument size. The custom designed telecentric scan lens, consisting of only 7 elements to achieve a large 40mm field size at 0.2NA, exhibits 3.4 waves of aberration for off-axis field positions. The deformable mirror, which is controlled and coordinated with the steering mirror via the integrated Pentium class computer, corrects for these aberrations to beyond the diffraction limit for all field positions. x-Y sc

Pupil Relay and Imaging Optics (custom)

Figure 5 . Thorlabs commercial ASOM product.

380

.

4. AS ASOM Product Demonstrations The deformable mirror in the ASOM must be calibrated before initial use to accommodate for manufacturing and assembly tolerances in the optics, as well as to manage variability in the residual stresses in the silicon structures of the deformable mirror itself. During imaging operations, the optimal set of actuator voltages for the deformable mirror can then be recalled and played back for high speed operation. Figure 6 shows an image of a USAF 1951 calibration target (a) before and (b) after deformable mirror shape optimization using an image sharpness metric3 and steepest descent optimization algorithm.

(a)

(b)

Figure 6 . USAF 1951 calibration target (a) before and (b) after optimization. The spacing of the closest bars represents 645 line pairs per mm in object space.

Figure 7 shows a 32 by 32 tile image mosaic of a CCD camera sensor collected by the ASOM. The total size of the composite image is 32768 by 24576 pixels, demonstrating the ability of the ASOM to rapidly image over large areas at high resolution, without any motion to the sample. Other applications that benefit from the ASOM’s unique imaging capabilities include challenging spatial-temporal biological observations and high throughout imaging for medical diagnostics and industrial manufacturing.

381

Figure 7. A 32 by 32 tile (32768 by 24576 pixel) image mosaic of a CCD camera chip.

Acknowledgments This material is based in part upon work supported by the National Science Foundation under Grant No. CMS-0301827 and by the Center for Automation Technologies and Systems (CATS) under a block grant from the New York State Office of Science, Technology, and Academic Research (NYSTAR). efere~ces

I.

B. Potsaid, Y. Bellouard, and J. T. Wen, ”Adaptive Scanning Optical Microscope (ASOM): A muI~idiscipIinaryoptical microscope design for large field of view and high resolution imaging,” Optics Express 13, pp. 6504-6518 (2005). 2. A. Cable, S. Barry, and L. Howe, “Wavefront correction finds use in bioimaging applications,” Laser Focus World, vol 43, issue 4, pp. 71-73 (2007). 3. R. A. Muller, A. BuEington, “Real-time correction of atmospherically degraded telescope images through image sharpening”, J.O.S.A., vol 6 p.p 1200-1211 (1974).

ICAL IMPLEMENTATION OF A ~ A P T TION COMPEN§~TIONIN 0 § E C T I O ~ N G~ I C ~ O S C O P ~ A. J. W I G H T , S. P. POLAND, J. VIJVERBERG AND J. M. GIRKIN Institute of Photonics, SUPA, University of Strathclyde. Wolfson Centre, 106 Rottenrow, Glasgow, UK, G4 0Nw We report on a practical method for the implementation of Adaptive Optics in optical sectioning microscopy to remove system and sample induced aberrations. Correcting for induced aberrations on a pixel-by-pixel basis would take in excess of 4 minutes and greatly increase the risk of sample damage due to photo-bleaching and photo-toxicity; this is clearly an impractical approach. We show that a single aberration correction per optical slice is adequate to significantly improve the image quality across the whole field of view. We present results illustrating the success of this method for a sample scanning and beam scanning system using confocal and multiphoton microscopy.

1. Introduction The use of adaptive optical elements to correct for sample induced aberration is an area of growing interest in optical sectioning microscopy. The significant challenge is to determine the most suitable wavefront correction in order to overcome the aberrations present and improve image resolution and contrast at depth into a biological sample. Demonstrations have been made by several groups each that take a different approach to this problem'-6. Even with the fastest method for determining a correction, the adaptive optic element can typically only be updated at 1 kHz . This means that for a 512x512 pixel image if each pixel was corrected the scan time would be in excess of 4 minutes. This is without taking into time required to deduce the aberration correction required. Clearly in a life science application where there is a great risk of sample damage and potentially photo-bleaching, pixel by pixel correction is an impractical approach. We report on the removal of sample aberrations using a single wavefront correction per optical section, an approach which greatly reduces the total scan time compared to a pixel by pixel technique.

2. Method A reflection confocal microscope built around a BioRad MRC600 scanhead which houses a confocal pin hole and the detector was used as an initial test 382

383

system. A 1OmW Helium-Neon laser was directed into the scanhead and a pair of galvanometer mirrors were used to create an x-y raster scan across the sample. The beam was focused using a 20 x microscope objective with a numerical aperture of 0.5 made by Nikon UK Ltd. The adaptive optic element was a deformable membrane mirror (DMM) made by OK0 TechElexible optical which has a maximum update rate of 1 lcHz and a stroke of 8 microns. The DMM consisted of a silicon nitride membrane mounted above 37 electrostatic actuators. A maximum of 175 V could be applied to each actuator to alter the shape of the membrane. The DMM was placed in the beam path after the scanhead and before the sample creating a double pass adaptive optic system. The samples consisted of various thicknesses of rat brain tissue sandwiched between a plain mirror and a cover slip. Figure 1 shows a schematic diagram of the experimental arrangement used.

u Wave .,..," ~

Plate

-t--l-

I

BioRAD MRC-600 Scan Head

Polarising Beam Splitter

\I

I

a

II

He-Ne

Coverslip Plain mirror

Piezo 2 Drive Sample

Figurel: Schematic of the experimental set up.

384

We employed an optimisation algorithm technique to determine the shape required by the DMM in order to overcome the sample induced aberrations. A genetic algorithm was used that rapidly changed the DMM shape in order to optimise a property of the image, in this case the intensity of the reflection from a point on the plain mirror. We optimised for a point in the centre of the image and then determined the impact this correction had on the image quality across the whole field of view. In order to quantify the level of image improvement made we recorded the axial point spread function by moving the sample and plain mirror relative to the microscope objective and monitoring the reflected intensity from the plain mirror. The axial resolution of the system could then be calculated directly from the full-width half-ma~imum(FWHM) of the point spread function. With the initial test completed the system was converted to a multiphoton fluorescent microscope. The Helium-Neon laser was replaced by a 2.5 W, pulsed, Titanium Sapphire laser operating at a wavelength of 800 nm (Mai Tai, Spectra Physics) and the detector was moved to immediately after the sample with a dichoric mirror added. We imaged a 76x56 pm fluorescent crystalline structure that emitted in the green. The aberration correction was determined by optimising on the intensity of a feature in the centre of the image and this single correction was then applied across the whole optical section.

3. Results Figure 2 shows the corrected and uncorrected axial FWHM taken at various lateral positions across the sample for a sample of 100 pm thick brain slice for

4,5! 4.0

... g 350

.

5 30*

Figure 2: FWHM recorded a various lateral position across a sample consisting of 100 microns of rat brain tissue. The plot shows a comparison between the FWHM when a single correction is applied to the DMM and when no correction is applied. lo (a) a sample scanning system was used and in (b) a laser beam scanning system was used.

385

0

10

20

30

50

40

70

60

80

X position (micrometer)

-._2 5 .L7

zoo

? i

150 100

50 O

i 0

.

, 10

. ,

20

,

30

.

1

40

.

, . ,

50

60

.

. ... 80,

70

X position (micrometers)

Corrected

0

10

20

30

40

50

60

70

80

X position (micrometer)

Figure 3: On the left hand side are two multiphon fluorescent images taken of a cryatalline structure, the top image was recorded when no aberration correction was applied to the DMM and the bottom image when a single aberration correction was applied to the DMM. Image dimensions are 76x56 pn. These images were taken using the galvanometer mirrors to scan the laser beam across the sample. The line profiles on the right hand side of the figure illustrate the level of image improvement made in the corrected as opposed to the uncorrected image.

reflection confocal. For all these measurements the correction applied to the DMM had been determined at a point in the centre of the image. Figure 2a was taken using a stage scanning approach when the position of the sample was moved not the laser beam in order to build up a two dimensional image. This has the benefit that the direction of beam propagation is always perpendicular to the back aperture of the microscope objective, but the disadvantage is that it is not always practical to move the sample and this can introduce additional image

386

perturbations. Figure 2b was taken using laser beam scanning system where the galvanometers were used create a two dimensional raster scan across the In both situations by correcting for the aberrations at a single point in the of the image we were able to improve the overall quality of the image across the whole field of view. For the beam scanning situation the average improvement factor for the axial FWHh4, and hence the axial resolution, was 1.5 and for the sample scanning case the average improvement factor was 6. Figure 3 compares two multiphoton images of the fluorescent structure taken before and after the aberration correction has been case of the corrected image a single aberration correction was appli whole field of view. The level of image improvement achieved adaptive optics is highlighted in the line profiles on the right-han figure taken at three different lateral positions across the sample.

. Conclusion and Discussion We have investigated the viability of using a single aberration the whole field of view in an adaptive optic confocal, a systems. The aberration correction required was initial1 point of the image and then this single shape was appli whole image was recorded. In the sample scanning confocal sys same level of image improvement at the centre of the sample was optimized, and for a lateral distance 250 pm away from the centre of the sample. This was also true for lateral distance of up to 30 pm in the laser beam scanning case. For the laser beam scanning situation there was greater variation in the level of improvement achieved due to the angle of the laser beam changing at the back aperture of the microscope objective. The power of this technique can also be seen in the multiphoton fluorescent images which show a significant image improvement across the whole 76x56 pm image when using a single adaptive optic correction. Many features in the sample were brightness enhanced by at least a factor of 2 and frequently features that were not originally visible could be seen when using a single adaptive optic correction. We believe that this form of aberration correction makes adaptive optics a real practical application for in-depth microscopy as it significantly decreases scanning times and therefore reduces the risk of photo-bleaching and phototoxicity compared to pixel-by-pixel optimisation.

387

Ackno~iedgmen~ We gratefully acknowledge the assistance of Dr. S. Cobb at The University of Glasgow in the preparation of the biological tissue.

eferences 1. A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, J. M. Girkin, ‘Exploration of the optimization algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy’, Microscopy Research and Technique, vol. 67,2005. 2. M. J. Booth, M. A. A. Neil, R. JuSkaitis, T. Wilson, ‘Adaptive aberration correction in a confocal microscope’, PNAS, vol. 99 no. 9,2002. 3. P. N. Marsh, D. Burns, J. M. Girkin, ‘Practical implementation of adaptive optics in multiphoton microscopy’, Optics Express, vol. 11,2003. 4. M. J. Booth, ‘Wave front sensor-less adaptive optics: a modal-based approach using sphere packings’, Optics Express, vol. 14 no. 4,2006. 5. 0. Albert, L. Sherman, G. Mourou, T. B. Norris, ‘Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy’, Optics Letters, 2552-54,2000. 6. M. Rueckel, J. A. Mack-Bucher, W. Denk, ‘Active wavefront correction in two-photo microscopy using coherence-gated wavefront correction’, PNAS, no. 103, no. 46,2006.

S P POLAND, A J WRIGHT, J M GIRKIN Imtitute of Photonics, SUPA, University of Strathclyde, Glasgow, G4 ONW A significant challenge for in vivo imaging is to remove movement artifacts. These movements, (typically due to either respiration, cardiac related movement or surface chemical response) are normally limited to the axial direction and hence features move in and out of the focal plane. This presents a real problem for optically sectioned imaging techniques such as confocal and multiphoton microscopy. To overcome this we have developed an actively locked focus tracking system based around a deformable membrane mirror (DMM). This has significant advantages over more conventional systems as the active optical element is not in direct, or indirect, contact with the sample. In order to examine the operational limits and to demonstrate possible applications for this form of focus-locking sample oscillation and movement was simulated.

1. Introduction Conventional focus-locking systems used in optical sectioning microscopy are composed of an element (usually a piezo mounted objective lens) coupled to the particular focus related aspect (intensity of the image) within a feedback loop. The piezo mounted objective is dithered into out of focus to provide the error signal to maintain focus [ 11. Although efficient at maintaining a focus lock when imaging in air, dithering of the objective causes significant problems when the sample is immersed within a liquid or in contact with the sample. At the high speed required for effective locking the lens movement causes considerable rippling effects in the water, which results in a high degree of image distortion (see figures 1 and 2).

Sample immersed in water

Figure 1: The origin of distortion due to objective dithering in a water immersed sample.

Figure 2: Showing a metallic surface immersed in water dithered with the (a) DMM and (b) with the piezo objective mount.

388

389

We report on a novel method utilising the ability of adaptive optics to be moved rapidly to provide the dithering defocus component and thus remove the cause of the distortion altogether.

ntal Arrangement The experimental layout shown in Figure 3 was based around a laser scanning confocal microscope, operating in reflection mode. A HeNe laser (633 nm, 10 mW maximum output power) was directed into a BioRad MlRC 600 scan head. An infinity corrected Nikon air-objective (coverslip compensating) with a numerical aperture of 0.5 and 20x magnification was used to focus the laser beam onto the sample. The detection photomultiplier tube (PMT) and confocal aperture were housed in the scan head. The DMM [Okotech] is placed into the system with appropriate relay optics to ensure that it is conjugate to both the scanning galvanometer mirrors and the back-aperture of the objective [2]. The objective was mounted on a piezoelectric translational device (PZT) (E662 LVPZT Physik Instumente, Germany) to control the position of the beam focus along the optical axis. was mounted on a piezoelectric translational device [E662 LVPZT Physik Instumente] (which has a range of 400pm) to control the position of the beam focus along the optical axis. The DMM operating with bias provides the defocus dither (figures 3 and 4). By applying a sinusoidal voltage signal onto all of the actuators, a defocus dither is applied to the system. The PMT signal is fed into the lock-in amplifier and the resultant error signal from the lock-in amplifier [Femto LIA-MV 1501 controls via a PZT, the position of the objective, or sample, thus maintaining focus.

Figure 3: The focus-locking set-up incorporating the deformable membrane mirror.

Figure 4: The focus response of the DMM using x20 0.5N.A. Nikon air objective.

390

otential applications In order to examine the operational limits and to illustrate some possible uses for this form of focus-locking, a piezo mounted mirror sample was imaged using the confocal system. A signal generator was used to control the piezo translational device [PI-Hera stage] to simulate some forms of in vivo sample oscillation (see figure 5).

Figure 5 : Showing the piezo mounted objective and piezo mounted sample stage.

3.1. Vascular movement correction When imaging in vivo within a biological specimen, movement in vascular tissue due to cardiac blood flow results in a periodic axial displacement. When imaging confocally, this represents a serious problem causing features to move in and out of the focal plane. By applying our system, a focus-lock can be maintained and any oscillatory movement due to cardiac blood flow thus compensated for. In order to show the effectiveness of the focus-locking system, the in vivo oscillation of a small rat arteriole was simulated using a sinusoidal signal to control the piezo mounted sample stage. The sample was oscillated at a number of frequencies for a range of amplitudes to test the system at maintaining focuslock. Figure 6 (a) and (b) show the system with and without focus lock.

391

1

10

0.9

0.8 0.7 0.6

0.5

p

8

5

*

t 5

* 5

0.5

Y

0.1

p

0.8 0.7 0.6

5

5

Y

0.4 2 0.3 0.2

0.9

0.4 f

d

0.3 0.2

E II 2

0.1

d

;

2

0

30

32

34

36

38

Tirne(s?c)

40

30

~

+

32

_ srn.oscillelion

34

_

36

40

38

Tirne(sec)

_____ Intensit

Lock-in EOIIBCIIO~

Figure 6: Simulated axial oscillation of a small Figure 7: Simulated axial oscillation of a rat arteriole without focus-lock. small rat arteriole with focus-lock.

It was found that the present incarnation of the system was able to compensate for an axial oscillation of up to +/- 1Opm at an equivalent heart rate of -200 beats per minute, comparable to the rat heart beat. Further system optimisation should improve both the rate and amplitude at which the amplitude oscillation could go.

3.2. ~eal-timedenial etching Another possible application for this focus locking system would be to confocally monitor the dental enamel surface during an acid etching process in real-time. Dental Enamel is composed of hydroxyapatite crystals embedded within a protein matrix structure. Human dentinal enamel is composed of hydroxyapatite crystals (87% vol.), water (11% vol.) and organic material (2% vol.) [3 and 41. It is the hardest biologically formed material present in nature and has both a rigid structure as well as a high modulus of elasticity. Enamel acts as the outer protective surface of the tooth. Acids in our diets, such as carbonic and phosphoric acid (soft drinks) as well as citric and ascorbic acid (present in fruits and fruit juices), have the effect of etching away the enamel tooth surface. Due to the complex structure of enamel as well as acid buffering agents in saliva, these acid etching and remineralisation interactions are not fully understood and currently require a technique which has the ability to monitor in real-time.

392

Figure 8: Structure of the tooth and surrounding tissues.

Figure 9: Confocal image of an etched enamel surface (141 x 94 pm).

Previous results taken using the confocal system have shown a -1pm thick loss enamel per 10 second period using acid etching solution with a pH of 2.0. Using our focus locking system, we tested to see if we would be able to monitor this axial displacement. Using a mirror mounted on a piezo stage, the axial displacement associated with etching was simulated. Using a mirror mounted on a piezo stage (which was computer controlled to move at constant velocities), the etching process was simulated to investigate the focus-lock capabilities of the system for this process (see figure 10 and 11).

Figure 1 0 Showing the focus locking ability of the system at a rate of 0.6 pml sec.

Figure 11: Showing the focus locking ability of the system at a rate of 21.3 pml sec.

393

It was shown from simulations that the present version of the system was capable of monitoring etching rates -2Opdsec. It can be deduced from these simulations that the focus-locking system will be effective at monitoring dental etching in real-time.

. Conclusions We have demonstrated the use of the focus-locking system, incorporating the DMM to counteract axial displacements for a number of simulated scenarios. The limitations of the system are the speed and degree of displacement at which the DMM can be dithered. Adaptive optic elements which allow more stroke could in future be used to provide both the dither and axial correction. eferences 1. A. R. Carter, G. M. King, T. A. Ulrich, W. Halsey, D. Alchenberger, and T. T. Perkins, Appl. Opt. 46,421-427, (2007) 2. A. J. Wright, B. A. Patterson, S. P. Poland, J. M. Girkin, G. M. Gibson, and M. J. Padgett, Opt. Express 14,222-228, (2006). 3. G. N. Jenkins Blackwell Scientific, Oxford, 54-112, (1978). 4. J. J Ten Bosch and D. Spitzer, Calcgcated Tissue Research 17, 129-137, (1974).

§ FOUR-~IMENSIO~AL PARTICLE T

NG FO

BIOLOGICAL APPLICATION§* H. I. CAMPBELL', P. A. DALGARNO', A. PUTOUD', c.c. DIE^, A. BAIRD', S. G. AITKEN', D. P. TOWERS', C. E. TOWRS', R. J. WARBURTON' AND A. H. GREENAWAY' 'EPS, Heriot- Watt University, Riccarton, Edinburgh, Midlothian E M 4 4AS, U.K. School of Mechanical Engineering University of Leeds, Leeds LS2 SJT, U.K. Observing biological processes in real-time and in single live cells is a vital step towards understanding cell hehaviour and the way cells interact with the world around them, However, this requires real time three dimensional (4D) tracking of nanoparticles which is challenging and traditionally relies on sequential capture of 2D images to construct a 3D picture. We discuss a new approach to 4D nanoparticle tracking that utilises a specially designed diffraction grating which behaves as a lens with a different focal length in each diffraction order thereby producing pseudo 3D imaging over the imaged field. The current experimental system has the ability to track a single particle in a 5Ox50x6pn volume, with an accuracy of better than 50 nm in each dimension.

1. Introduction The ability to observe biological processes in single cells and in real-time, is a key step to understanding cell behaviour. In recent years technological advances in high resolution microscopy, camera technology and biological tagging have led to significant developments in the study of biological processes as a function of time, for example in tracking the infection pathways of single viruses within a single living cell [ 11. However, real-time three-dimensional (4D) tracking of nanoparticles remains experimentally challenging. Many techniques, such as confocal and multi-photon microscopy, rely on sequentially capturing twodimensional (2D) images to build a t~ee-dimensional(3D) picture. The capture speed of these 2D images is a limiting factor in the accuracy of the 4D map and therefore in determining the chemical and biological processes that can be observed. We present a technique designed to capture information from several object planes simultaneously and demonstrate how this can allow for accurate 3D particle tracking in real time.

* This work is supported by awards from EPSRC and STFC Research Councils

394

395

1.1. Three-Dimensional Imaging using a Distorted Diffraction Grating Our technique is based on a quadratically distorted diffractive grating (QDDG) which has the ability to simultaneously image several object planes onto a single image plane [2,3]. This is shown schematically in figure 1:

Figure 1. Multi-plane imaging with a QDDG [3].

The QDDG method is an extension of a technique which has previously been applied to phase diversity wavefront sensing and laser beam quality measurements [2, 41. The QDDG acts as a lens with a different focal length in each diffraction order, producing pseudo 3D imaging over the imaged field. The design parameters of the QDDG determine the separation of the imaged planes and therefore the volume within which the particle can be tracked [2, 3, 51. Therefore the potential exists to match the dynamic range of the process we wish to observe with the focal volume sampled by the QDDG. The etch depth of the QDDG determines the number of diffraction orders present and the intensity diffracted into each. With careful positioning of the QDDG relative to the lens (fL in figure 1) the magnification in each image can be equalized. This is known as the telecentric imaging condition and is achieved when the QDDG and lens are either co-planar (as pictured in figure 1) or separated by a distance of fL[5]. While it is convenient to use the QDDG to obtain the data it could also be done using a programmable liquid crystal spatial light modulator. Such an approach would be more costly but would provide the opportunity to easily alter the plane separation and thus the focal volume to suit different applications. Alternatively, mounting several different QDDGs into a filter wheel would achieve the same result if preferred plane separations were known in advance.

396

2. Experimental Details ensional Im~gingin ~ i c r o s c o p y A high magnification microscope was constructed using a high numerical aperture (NA=1.3) infinity-corrected lOOx oil-immersion objective in combination with a 200mm focal length tube lens. This delivers a magnified image of the sample 200mm behind the tube lens, with an experimentally measured magnification (M) of 105. A relay lens pair (fRELAy = 215mm) is placed in a 2f-2f configuration to relay the magnified image onto the CCD camera. The QDDG is then placed in the telecentric position, fmLAY behind the lens pair. The etch depth of the QDDG used was chosen to distribute the light evenly between the first 3 diffraction orders. The QQDG was designed to give a plane separation of 0.115mm about the magnified image plane (see [3, 5]), therefore plane separation at the sample is a factor of M2 smaller (1.1pm). Nano-holes (diameter=205nm) in an Aluminium mask were illuminated from below to simulate point sources such as fluorescently tagged bio-particles. Piezo positioners were used to move the sample with lnm resolution in the 2 axis. Full-width-half-maximum (FVVHM) measurements of single nano-hole microscope images, with and without the QDDG (and in all three diffraction orders), showed that diffraction-limitedimaging was achieved with this set-up. A number of techniques can be used to obtain 3D ‘depth imaging’ of biological samples; perhaps the most well known are confocal and multi-photon microscopy [6]. Depth imaging is achieved by obtaining a sequence of optical sections collected at different levels perpendicular to the optic axis (2). This sequence of images is commonly referred to as a ‘Z-series’, figure 2 demonstrates this using a single nano-hole (images captured 0.56pm apart).

Figure 2. A through-focal (2-Series) series for a single uano-hole - images captured 0.56ymapart.

397

Figure 3 shows a single snapshot image captured when the 0" order was infocus (i.e. the nano-hole was located in the object plane imaged by the QDDG in this order). Figure 3 shows that for a given sample position the three images correspond to different points within the individual Z-series (figure 2). Simultaneously gathering image information from three (or more) planes means the Z-Series is captured quickly and with fewer movements of the sample/objective. The particle is also less likely to be 'lost' as it moves between object planes since it is visible in more than one diffraction order at a time.

Figure 3. Example data image captured when the nano-hole was located in the 0' order focal plane.

3. Three-Dimensional Position MEasurement using the Z-Series

We created an algorithm to extract 3D (X,Y,Z) co-ordinates for a moving particle using image sharpness. This technique can be applied to our QDDG system to provide an unambiguous determination of the particle's Z position over a range of several microns. The X and Y axis co-ordinates were obtained by a simple centre of mass calculation [7].

age S h a ~ n e s and s its Applicatio~to Depth ~easurement Historically image sharpness, as described by Muller and Buffington [8], was adopted by Astronomers as an image quality metric used to focus telescopes. Sharpness is maximized at focus where the brightest, most compact image is produced. It is calculated by either integrating the square of the intensity of the whole image, or by calculating the area under its Modulation Transfer Function (MTF). As wavefront aberration increases the MTF curve collapses, the area under it is reduced and consequently the image sharpness is reduced.

3.2. ~ x p e ~ m e n t~ael s u l t s The image sharpness curve for a single Z-Series (as in figure 2) can be seen by considering only the O& order sharpness plot in figure 4. From this we see that a single sharpness value could correspond to two different depths. Adding the grating removes this ambiguity since for each depth there are now three separate images, and therefore three measures of sharpness to be compared. The widths, heights, and shapes of the sharpness curves depend on the aberrations present in the images. If the only aberration were defocus each of

398

these curves would be symmetric and identical. Using this algorithm we have achieved particle tracking of a single nano-hole through a 5Ox5Ox6pm volume with a repeatability accuracy of better than 50nm in each direction. This compares favorably with other currently used systems whose accuracy is typically in the tens of nanometers range [7]. Image Sharpness vs. Particle Displacement

120

',

100

+

t +I

4 .

p

xc

80

. *

t

+

+

+

0th

RIX

8E 60

r

%c X

K X

Ql

.

r

.+ +

m

-E

m 20

4

-4

-3

-2 -1 0 1 2 Particle Displacement (pm)

3

4

Figure 4. Image sharpness vs. particle displacement for a nano-hole imaged on 3 planes (1.1pm apart).

-

4. AppIications Live Cell Imaging and Beyond The QDDG based system has also been mounted on an Olympus IX71 inverted microscope. It is a simple matter to build the 3D imaging QDDG setup as an add-on to a microscope CCD exit port. The QDDG can be designed for use with bright-field, dark-field, phase-contrast, differential interference contrast, and fluorescence microscopy. While diffraction gratings are intrinsically narrowband devices this system can also work with broadband illumination if a pair of blazed gratings are included [9]. Therefore, this multi-plane imaging technique allows fast capture of 2;-Series and should be of use when studying dynamic processes in vivo. The QDDG method can also be applied to Particle Imaging Velocimetry (PIV) to track multiple targets within the imaged volume. One benefit of this is in the study of fuel mixing in combustion engines where a potential 30% fuel saving could be made if the mixing process is optimized through better understanding of its dynamics. Initial experiments mapping the trajectory of a single fluorescent bead have provided 3D resolution from a single view-point that matches state-of-the-artaccuracy [ 101.

399

5. Conclusions and Future Work A future aim of this research is to track Brownian motion of fluorescent particles for applications to virus tracking and cell dynamics. We are also investigating 3D phase contrast imaging and initial tests gave positive results. As a transmitted light technique no potentially harmful contrast agentsldyes are required and imaging on multiple planes simultaneously should allow observation and tracking of rapid changes in cell shape (for example during mitosis). Finally we would like to perform wave-front sensing on the acquired data, which only requires further processing not added equipment. This would allow us to study both system and specimen-induced aberrations. Some static system aberrations (i.e. spherical aberration) could potentially be precompensated in the QDDG design, whereas others could be corrected using adaptive optics. Also, since the image sharpness technique depends heavily on defocus, characterization and subsequent rejection of non-defocus modes in the images could further improve the accuracy of the Z-depth measurement. In conclusion, QDDG 3D imaging is easy to incorporate into existing microscope technology, is inexpensive, unobtrusive and uses only well established imaging techniques. Initial experiments focusing on biological application have yielded promising results but there remains the potential for application of this technique to many other state-of-the-art microscope systems.

eferences

1. G. Seisenberger, M.U. Ried, T. Endress, H. Buning et al., Science. 294 1929 (2001)* 2. P.M. Blanchard, D.J. Fisher, S.C. Woods & A.H. Greenaway, Appl. Opt. 39(35) 6649 (2000). 3. P.M. Blanchard & A.H. Greenaway, Appl. Opt. 38(32) 6692 (1999). 4. R.W. Lambert, R. Cortes-Martinez, A.J. Waddie, J.D. Shephard, et al., Appl. Opt. 43(26) 5037 (2004). 5 . S . Djidel, J.K. Gansel, H.I. Campbell & A.H. Greenaway, Opt. Exp. 14(18) 8269 (2006). 6. D.J. Stephens & V.J. Allan, Science. 300 82 (2003). 7. M. Speidel, A. Jonas & E.-L. Florin, Opt. Lett.. 28(2) 69 (2003). 8. R.A. Muller and A. Buffington, J.0pt.Soc.Am.A. 64(9) 1200 (1974). 9. P.M. Blanchard & A.H. Greenaway, Opt. Comms. 183(1-4) 29 (2000). 10. C.E. Towers, D.P. Towers, H.I. Campbell, S . Zhang et al., Opt. Lett. 31(9) 1220 (2006).

A

IVE O P ~ I C SFOR ~ I C R O S C O

X. LEVECQ Imagine Optic, 18 rue Charles de Gaulle, Orsay, France. Following are the first experiments with an close loop adaptive optics system in microscopy field. Equally presented is an example of the gain obtained using the device in a closed-loop configuration.

1. ~ r e s e n ~ t i oofnthe issues Optical microscopy is an inescapable technique in the life sciences, in particular for studying the intracellular organisation of biochemical events. However, there is an increasing need in a variety of fields (neurophysiology, developmental biology, biopsy, ...) to image cells in their native environment, i,e. intact tissue. The task is difficult because tissues are heterogeneous media that strongly affect light propagation, causing large amounts of scattering and wavefiont aberration at large depths. These effects reduce the signal and contrast in usual optical techniques (such as confocal microscopy), and prevent them to provide images deep within intact tissue. Dealing with scattering: multiphoton excitation, OCT : Since the 90s, two effective approaches have been demonstrated for coping with scattering and providing subcellular resolution images at a few 100 pm depths inside tissue: nonlinear (or multiphoton) microscopy, and optical coherence tomography (OCT). Multiphoton microscopy selects ballistic (unscattered) excitation light by using a nonlinear contrast mechanism such as two-photon-excited fluorescence (2PEF), second-harmonic generation (SHG), third-harmonic generation (THG), or coherent anti-Stokes Raman scattering (CARS). OCT selects ballistic backscattered light by coherence-gated interferometry. These techniques are being increasingly used in a variety of applications. Dealing with wavefront aberrations: adaptive optics (AO).: However, a number of studies -including our experiments (figure 2) made in collaboration with Dr E. Beaurepaire LOB, Palaiseau- are now pointing out the fact that wavefront aberration by tissue limits signal and contrast in deep-tissue 400

401

multiphoton microscopy and OCT (figure 1). As the focused excitation beam propagates through successive layers of biological material with different geometries and optical properties, aberrations distort the focal spot (Fig. lb) : in the presence of aberrations the intensity distribution of the spot probing the sample does deviate from the ideal, diffraction-limited case, and resolution and signal intensity are reduced. This phenomenon significantly affects imaging quality, particularly in multiphoton techniques where the signal scales with the square (2PEF, SHG) or the cube (THG) of the focal spot intensity. These effects limit the resolution and achievable imaging depth, but they could be eliminated by introducing an active optical element such as a deformable mirror in the optical path, that can compensate for the sample-induced aberrations (Fig lc).

Figure 1 . Principle of aberration correction in deep-tissue microscopy. (a) Undistorted focused beam. (b) Focused beam distorted by sample-induced aberrations. (c) Aberration correction using an active element.

Figure 2. Deep imaging of complex samples, where aberrations degrade image quality (unpublished data). (a) Third-harmonic generation (THG) images of a gastrulating Drosophila embryo recorded 50 and 100 pm below the surface (collaboration between Dr E. Beaurepaire, LOB, Palaiseau and Dr E Farge, Institut Curie, Paris). Because of its ovoid, layered structure (see bottom panel yellow arrow), signal and contrast are largely degraded in the central part. (b) Two-photon-excited fluorescence (2PEF) imaging of villosities inside fresh mouse colon tissue. Contrast is rapidly degraded with depth because of the heterogeneous structure of the tissue (collaboration between Dr E. Beaurepaire, LOB, Palaiseau and Dr E Farge, Institut Curie, Paris).

402

2. E x p e ~ m e nsetup ~l We have developed a close loop adaptive optics based on an auto-fluorescent microscope. The optical setup is shown figure 3 including a HAS03 Shack Hartmann (principle shown figure 4) wavefront sensor (from Imagine Optic) and a mirao (main characteristics figure 5 ) electromagnetic deformable mirror (from Imagine Optic).

Figure 3. Experimentalsetup.

Basic c h ~ r ~ c ~ ~ ~ i s t i c s : * 52 actuators * Effective diameter 15 mm * Overall size: 66 mm * Voltage range: -1.Oto +I .O V *Measured linearitv > 98% Measured c. 1%

-

range :

Figure 4.Shack Hartmann principle.

Figure 5. Mirao : main characteristics.

403

3. Results First results have been done with 200nm beads in water/glycerol mixture with a 1.4 NA oil immersion objective. You can notice in figures 6 and 7 the improvement in depth (z axis) resolution when the correction is on : all the aberrations (mainly spherical aberration) are corrected and the depth of field is diffracted limited. X

2

. i uncorrected image

/

Corrected image

Figure 6. 200 nm beads in water/glycerol mixture at depth 67pm below coverslip were imaged with a I .4 NA oil immersion objective (cut X-2).

Figure 7 . Log scale cut of the z axis intensity repartition with and without correction for test of figure 6.

4. Conclusion

First experiments of adaptive optics integrated in a microscope configuration are successful. We have shown a significant improvement in depth resolution. These results are very promising for future.

This page intentionally left blank

This page intentionally left blank

QUALITY OF A HIGH POWER Y LASER*

D. 6. HARRIS, F. D. PATEL, C. E. TURNER, JR,and M. M. JOHNSON The Boeing Co., 8531 Fallbrook Ave West Hills, CA 91304, U.S.A. A method to improve the beam quality of a high power diode pumped solid state rod laser is described. The beam quality of the described laser is limited by aberrations present in the medium, which may be due to mode-medium effects in the Yb:YAG laser rod. A diffractive optics propagation model was developed to predict the phase distortions present on the laser wavefront. Resonator mirrors were then fabricated with the proper correction applied to correct the distorted wavefront. The beam quality improved from MZ= 2.0 to M2 =1.3.

1. Introduction Diode Pumped Solid State Lasers (DPSSLs) are compact efficient high power sources of laser radiation, but have been linlited to power levels of a few hundred watts with good (M2 < 2) beam quality. To date in order retain good beam quality at high powers has required nonlinear optical techniques such as SBS (Stimulated Brillouin Scattering) or STS (Stimulated Thermal Scattering) phase conjugation. An approach that will provide good beam quality with an uncomplicated design is very appealing. The dual rod Yb:YAG laser offers promising possibilities as a compact robust device of a simple design. 1.1. h s e r Arch~ecture We have investigated the scaling limitations of a kilowatt class Yb:YAG rod laser. It is worthwhile to understand the issues and approaches which will allow this architecture scale to high powers while retaining good beam quality. We also want to keep the resonator design simple, and without reliance upon nonlinear phenomena SBS or STS phase conjugation which frequently adds complex optical elements to the architecture. Yb:YAG was chosen because of its low quantum defect (7%) translating to higher quantum efficiency and less * This work is supported by the Joint Technology Ofice and Boeing Internal Funding.

407

408

heat deposited into the host material as compared to Nd:YAG (27%). The quasithree level nature of Yb does, however, require high pump rates to achieve transparency. The laser is a Yb3+:YAGlaser that has been described previously'. An endpumped dual rod architecture has been chosen, as shown in Figure 1. The thermally induced birefringence compensation is achieved with dual rods configured in a stable resonator cavity which has a quartz optical rotator located between the rods'. The rotator has the effect of changing the polarization and making the resonator appear symmetrical with regard to the two indices of refraction (n, and nphi). The rods are end pumped by diode arrays. The diode pumping radiation is transferred to the rods by hollow lensducts; at the entrance to the lensduct is a focusing lens which focuses most of the radiation into the laser rod. The lensduct captures that pumping radiation escaping from the optical system and redirects it into the rod. Once the pumping rays enter the 2mm diameter Yb:YAG rod, they rapidly and uniformly fill the laser rod by total internal reflection.

Figure 1. Schematic diagram of the end pumped dual rod laser.

1.2. Laser Performance While the device reliably and reproducibly operated at 530 W with M' of 2, we have noted, during laser operation, that the lasing mode size in the rod is smaller than is desired for efficient optical extraction of the lasing power3. Efforts to enlarge the mode, to more completely fill the laser rod, and increase the extraction efficiency, have not been successful. This limitation is attributed to the thermal induced aberrations in the rod not allowing a larger mode to lase.

409

2. Laser Scaling Limitations have noted that spherical aberration caused by thermo-optic distortions in the gain medium can be an impediment to scaling solid state lasers to high powers. If the pump distribution is uniform in the laser rod, then spherical aberration can be attributed to at least two different effects: temperature dependence of the thermal conductivity and lasing induced heating (or cooling) of the gain medium. The former effect has been observed in Nd3+:YAG2.In Yb3+:YAG however, it appears that the observed lasing induced aberration is the domina~teffect in our experiments3. Unlike the diode pump distribution, the lasing mode intensity distribution can be non-uniform, especially in stable resonators with near diffraction limited beam quality. Consequently, if the lasing mode can be made to fill the laser rod, and extract the gain uniformly, the thermal aberrations will be minimized. A static diffractive element may be useful in controlling the laser mode as well as for compensating for the aberrations in the wavefront. Rather than use a transmissive element, we have chosen to alter the laser resonator mirrors themselves, by adding an appropriate figure. The technique is effective because the thermally induced aberrations in the laser rod are reproducible at the nominal operating point.

2.1. ResonatorMirror Design Applroach The designs for the mirror profiles were developed using a diffractive propagation computer code. The approach is to use static phase conjugating elements which are reflective rather than transmissive, to define the preferred mode (one with the lowest loss), in a resonator. Briefly, a super-Gaussian beam was propagated from the center of the cavity, through the medium to a resonator mirror, where the conjugate phase was then calculated and placed on the resonator mirror. From here the mode was propagated back to the center of the cavity and using a Fox-Li analysis it was verified to be a low order eigenmode of the resonator. Inputs to the propagation model consist of optical schematic element parameters, distances, focal lengths, indices of refraction (Q, and n2focusing), initial mode (intensity, phase, wavelength and polarization) and flags for controlling the number of round trip iterations, parametric sensitivities, and plots. The code outputs include graphs of the fields at designated locations, the radial phase profile of the phase conjugating elements and iteration histories (power loss, fill factors and phase Strehl).

410

2.2. Fabrication Several approaches to fabrication of the profile were considered: chemical etching, ion machining, photolithographic techniques, laser ablation, and magneto-rheological finishing (MIW). The first attempt at constructing a DOE utilized the photolithographic approach of building up layers from the mirror substrate. Initially, a single layer was attempted to investigate the feasibility of such an approach. The results were inconclusive. The step in the coating did not provide sufficient cavity loss to the higher order modes and allowed too many transverse modes to oscillate. More sophisticated modeling indicated that 8 steps would be required to produce the digital binary step optic with the necessary fidelity to emulate the calculated profile. Each step in the process requires a photolithographic mask to be fabricated and aligned to the previously built step. This approach was not pursued because there are many process steps required in the fabrication. The technique of laser ablation was also investigated as a possible method to produce the optic. The technique, while relatively new, is able to controllably remove small amounts of material, from the fused silica substrates. However, the surface roughness of the produced optic is too high. The resulting surface may be smoothed by a chemical polish. While the technique seems to hold promise, given that all of these processes (ablation & chemical etch) would have to be developed and calibrated, it was deemed too immature for this project. The technique of magneto-rheological finishing (MRF) has demonstrated excellent results previously for polishing large optical elements. QED Technologies of Rochester, NY is the premier company in this area. Until recently, the machines in use were not able to effectively polish the small areas (approximately 2 mm diameter) required for this project. Fortunately, a new process and machine have recently become available to fabricate surfaces on small parts. The diffractive optics code was used to develop three designs of mirrors to provide Super-Gaussian modes. The diffractive propagation model uses symmetry to calculate the modes in the left and right half of the resonator. There are n2, and n2phiindices of refraction. The code calculated each index based on the laser’s operating point, which is anchored to laboratory experiments. Figure 2 shows the experimentally measured profile of two substrates compared to the desired mirror profile. Additionally, a third mirror design was calculated for the average of the indices of refraction (n2, and n2phi).

411

E

Figure 2. Design (solid line) and fabricated (cirlces & squares) profiles of corrected resonator mirrors.

2.3. Results The n2aYg mirrors, which were designed by anchoring our model to an average of the n2, and n2,G values of the two rods, performed the best of the three designs we tried. With this profile mirror in place (J3R and 20% reflectivity OC) the best results obtained were an output power of 550 W at an M2 of 1.3 at the design point of incident pump power of 2980W. This result corresponds to a factor of 2 improvement in brightness of the laser. The amplitude jitter in the power measurement (mode stability) was very low, indeed, the same as for spherical mirrors.

3. Co~clusion The onset of aberrations has limited the beam quality of the rod Yb:YAG laser archtecture. Using a diffractive optical element for mode control and mode discrimination at high powers the performance was improved from 530 W and M2 = 2.0 to 555 W with M2 = 1.3. The improvement was achieved by using a diffractive optics model of propagation to design the required resonator mirror profile. MRF technology was able to easily fabricate the require mirror profile.

412

The success of this approach is promising for scaling DPSSLs to high powers with improved beam quality.

eferences 1. R.J. Beach, E.C. Honea, S.B. Sutton, C.M. Bibeau, J.A. Skidmore, M.A. Emanuel, S.A. Payne, P.V. Avizonis, R.S. Monroe, and D.G. Harris, “HighAverage-Power Diode-Pumped Yb:YAG Lasers,” in Proc. SPJE, Vol. 3$$9, p 246-261, (1999). 2. W.C. Scott, M. dewit, “Birefringence Compensation and TEMw Mode Enhancement in a Nd:YAG Laser,” Appl. Phys. Lett. 18,3-5, (1971). 3. L.F. Rubin, K.C. Widen and D.G. Harris, “InterferometricMeasurements on a High Power Yb3+:YAGLaser,” OSA Trends in Optics and Photonics VoE. 83, Advanced Solid State Lasers, John J. Zayhowski, ed. (Optical Society of America, Washington, D.C.) 348 (2003). 4. N. Hodgson and H. Weber,”Influence of Spherical Aberration of the Active Medium on the Performance of Nd:YAG lasers”, IEEE Jnl. of Quant. Elec., 29, pp2497-2507, (1993). 5. Jkr8me Bourderionnet, Arnaud Brignon, Jean-Pierre Huignard and Robert Frey, “Influence of aberrations on fundamental mode of high power rod solid-state lasers”, Optics Communications,204, pp 299-3 10, (2002). 6. C. Kennedy, “Improved Brightness Laser Oscillator with Spherical Aberration,” OSA Trends in Optics and Photonics Vol. 68, Advanced Solid State Lasers, M.E. Fermann and L.A. Marshal, eds. (Optical Society of America, Washington, D.C.) 458, (2002).

TI

P. WELP, H.-M. HEUCK, AND U. WITlROCK Photonics Laboratory, Miinster University of Applied Sciences, Stegerwaldstr. 39 48565 Steinfirt, Germany Thermally induced optical distortions in the gain medium are one of the main issues that have to be overcome when realizing lasers with high efficiency in the fundamental mode. One novel approach to deal with these distortions is the use of an intra-cavity adaptive mirror for compensation. In this paper we demonstrate an Nd:YV04-hser with a closedloop adaptive resonator, achieving a beam quality enhancement from M2 = 5 to M2 = 1.7 with a power drop of 5.6 W to 5.3 W at 26 W of pump power.

1. Introduction A major problem for the realization of high-brightness operation in solid-state lasers is heat generation in the gain medium. Temperature gradients lead to a thermal lens afflicted with aberrations. While a suitable laser resonator design can compensate the low-order aberrations of the thermal lens, higher-order aberrations can not be compensated with standard optical components. According to numerical simulations, these aberrations then lead to a degradation of beam quality [ 11. A common method for achieving fundamental mode laser operation is the incorporation of hard apertures into the laser resonator [2, 31. This is a very convenient way of achieving fundamental mode operation, but it decreases the efficiency of the laser. Compensation of the thermo-optical aberrations - on the other hand - should lead to fundamental mode operation without severely decreasing the laser efficiency.

2. Experiments 2.1. Constraints of the resonator ~ y o u t When setting up a laser resonator, in which an adaptive mirror shall be used intracavity to compensate for thermo-optical aberrations, several restrictions have to be taken into account. As a matter of course, it has to be ensured that the resonator itself is designed so that the fundamental mode size matches the 413

414

diameter of the gain at the given pump power. If this is not the case and the fundamental mode does not completely fill the gain medium, higher-order modes start lasing, regardless of the aberrations of the thermal lens. Of course, an adaptive mirror could be used to adjust the size of the fundamental mode to the size of the gain, but this is pure alignment and can be done cheaper and easier with a proper resonator design. However, when the size of the fundamental mode matches the size of the gain and the resonator is still not able to achieve fundamental mode operation, aberrations of the thermal lens of the gain medium are likely to be the reason. Compensation of these aberrations then should lead to an enhancement of beam quality. Another design restriction is the suitability of the adaptive mirror for the resonator. First of all it has to be able to compensate the aberrations of the particular thermal lens. The stroke and the spatial characteristics of the mirror thus have to match the thermo-optical aberrations. In addition the adaptive mirror has to be able to stand - without damage or thermal deformation - the high intensities commonly found inside a laser resonator. Depending on the control scheme of the adaptive mirror, even further constraints may apply to the resonator layout in order to get a suitable control signal.

2.2. Resonator layout The studied resonator consists of an end-pumped Nd:YV04-crystal, placed between a 19-actuator 10 mm diameter micromachined deformable membrane mirror (MMDM) from FZexibEe Optical [4] and an output coupler (Fig. 1). As there is no hard aperture in the system, the gain medium itself acts as the limiting aperture of the resonator. Imaging the Nd:YV04-crystal onto the flat output coupler consequently ensures a constant beam diameter there.

t*iesCOp* Pump CCD

Figure 1. Set-up of the closed-loop adaptive resonator.

415

This makes it possible to use the beam divergence as sole criterion for beam quality in the feedback loop [S]. An evolutionary algorithm is employed to optimize the deformation of the MMDM and thus optimize the resonator. In addition to beam divergence, the resonator can also be optimized for output power or a combination of both. A CCD camera or a photodiode are used to record the feedback signal. The deformation of the MMDM is monitored through an interferometer or a Shack-Hartmann sensor, alternatively.

esonator experiments 3.1. ~ x p e ~ m e nwithout ts a d d ~ o n aarhficiul l aberrations Before starting to optimize the laser resonator by means of the adaptive mirror, the thermo-optical aberrations of the Nd:YV04 crystal have been measured under lasing and non-lasing conditions. With a thin-film polarizer, a 1050 nm probe beam was injected into the resonator. After propagating through the Nd:YV04 crystal, a second thin-film polarizer reflected the probe beam out of the resonator and onto a Shack-Hartmann sensor. A relay telescope was used to image the crystal onto the sensor. At the same time, a fraction of the 1064 nm laser beam was used to image the Nd:YV04 crystal onto a CCD-camera in order to measure the exact diameter and position of the laser beam inside the crystal. The aberrations were analyzed over 7d2 times the 1/e2-diameterof the laser beam at the crystal. This diameter is equivalent to a power inclusion of 99% and a common choice for hard apertures in fundamental mode laser resonators. With all higher-order Zernike coefficients below 0.1 pm at a pump power of 33 W, the aberrations of the thermal lens were found to be rather low (Fig. 2).

Figure 2. Aberrations of the thermal lens at 33 W of pump power expanded into Zernike coefficients. The diameter of the Zernike unit circle was chosen to be 7rJ2 times the l/e2-diameter of the laser beam.

416

0

1000 Individuals

2000

Figure 3. Progression of the normalized control signal during optimization. The start generation consisted of 100 individuals, every following generation of 30 individuals.

The aberrations did not vary significantly when changing from lasing to nonlasing conditions. To find out if these rather small aberrations of the thermal lens affect the laser beam quality at all, the resonator design was first tested with a conventional high-reflecting concave glass mirror instead of the MMDM. Maximum output power of 7 W with an M2 of 5.2 was reached at 32 W of pump power. When replacing the conventional HR mirror with the MMDM set to 225 V bias voltage - equivalent to the radius of curvature of the conventional glass mirror - we measured a maximum output power of 5.6 W at 26.6 W of pump power. The M2 amounted to 5.0. The drop in output power can be explained by the additional losses the DM introduced into the cavity, At this point, the evolutionary algorithm was initialized. At the beginning the laser is not lasing at all. But after typically about 30 iteration steps, each with 30 different voltage patterns, usually 90% of the optimum feedback signal is reached after an optimisation time of 25 s. A typical development of the feedback signal over time during the optimization process is shown in Fig.3. The optimized resonator exhibited 5.2 W of output power with an M2 of 1.7. At first sight his enhancement of beam quality from M2= 5.0 to M2 = 1.7 without signi~cantdrop of output power seems to support the assumption that compensation of aberrations leads to an improved beam quality. To analyze whether this is true or if the evolutionary algorithm did not optimize the resonator in terms of aberrations but just provided an optimum alignment, which as well could have been achieved without the algorithm, the deformation of the MMDM, manually adjusted for tip/ tilt and defocus, and the deformation of the MMDM, optimized by the evolutionary algorithm, have been compared. In

417

Seidel aberrations, the difference of the two membrane deformations over the beam footprint (l/e2 diameter of 5 mm) amounted to 0.08 pm of tilt, -0.08 pm of defocus, 0.24 pm of astigmatism, 0.22 pm of coma and -0.08 pm of spherical aberration. It seems that the MMDM slightly aligned the resonator, but mainly compensated for aberrations. In principle, the measured astigmatism and coma terms could also be artefacts of the MMDM. With a l/e2 diameter of 5 mm on the adaptive mirror and an actuator pitch of the MMDM of 4.3 mm, the beam should be mainly influenced by just 7 actuators of the mirror. The deformation, the mirror can provide over the beam diameter, is thus limited in stroke and spatial diversity. Therefore it is possible - especially with regard to the fact, that the measured aberrations of the thermal lens were rather low - that the evolutionary algorithm and the MMDM mainly aligned the resonator and that the optimized tip/ tilt and defocus deformation of the mirror membrane just could not be reached without the measured astigmatism and coma terms. To confirm that this is not the case, but that the improvement of beam quality is really due to compensation of aberrations and not due to pure alignment, additional artificial aberrations were introduced into the resonator.

3.2. Expe~mentswith a d d ~ o n aarlipciul l aberrations Additional artificial aberrations were introduced into the laser resonator with a second MMDM. Again a MMDM from Flexible Optical with 15 mm diameter was chosen. Two thin-film polarisers deflected the beam first by 24" onto the MMDM and then back into the former resonator path. An additional lens compensated for the bias curvature of the MMDM. The deformation of the MMDM over the l/e2 diameter of the beam was monitored with an interferometer or alternatively with a Shack-Hartmann sensor. First of all, the additional MMDM was set to have pure defocus deformation. The resonator was manually aligned and then the deformation of the first MMDM was optimized with the evolutionary algorithm. Power and beam quality have been measured. Then the chosen additional deformation was added to the defocus of the additional MMDM. Before now measuring power and beam quality again, the two end mirrors of the resonator were manually aligned for tip/ tilt. As the last step, the evolutionary algorithm (EA) was again used to optimize the deformation of the first MMDM. Results of these experiments are shown in Tab. 1. The optimization with the first MMDM leads to an enhancement of beam quality and laser output power (PL). This has to be due to a - at least partial - compensation of the additional

418

aberrations. In reverse, this leads to the conclusion that the beam quality enhancement described in the previous paragraph also was due to compensation of aberrations and not due to the alignment of the laser. Table 1. Compensation of additional aberrations. No additional aberrations EA optimized resonator Additional aberration Manually adjusted tip/ tilt Optimization via EA

+

+ +

PL = 2.15 W M2 = 3.5

PL = 3 W M2 = 3.5

0.3 pm astigmatism 0.3 pm coma PL = 2.76 W M2 = 3.8 PL = 3 W M2 = 3.8

PL = 2.4 W M2 = 3.8 PL = 3 W M2 = 3.4

PL = 2.75 W M2 = 3.5 0.18 pm spherical aberration PL = 1.45 W M2 = 4.5 PL = 2.45 W MZ=4

. ~onclu§ionand outlook We have described a closed-loop adaptive optics laser resonator, achieving a beam quality enhancement from M2 = 5 to M2= 1.7 with a power drop of 5.6 W to 5.3 W at 26 W of pump power. A lot of care has been taken to make sure that this beam quality enhancement was really due to compensation of thermo-optical aberrations and not merely due to alignment of the resonator by means of the adaptive mirror. Additional artificial aberrations could be compensated as well. After these proof-of-principle experiments with the rather low-power Nd:YV04 laser, we now plan to set up a closed-loop resonator containing two arc lamp pumped Nd:YAG rods with a maximum electrical pump power of 36 kW. As our MMDMs suffer from thermally induced deformations due to the incident laser beams, a piezo-electrical deformable mirror will replace the MMDM.

References 1. I. Buske and U. Wittrock, Proc. of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, World Scientific (1999) 2. A. E. Siegman, Lasers, University Science Books, California (1986) 3. W. Koechner, Solid-state Laser Engineering, Springer-Verlag (1999) 4. Flexible Optical BV, Rlintgenweg 1,2624 BD Delft, Netherlands 5. U. Wittrock, I. Buske, and H.-M. Heuck, Proc. CLEO (Baltimore 2003)

SULTS IN HIGH POWER LASER BEA CO~ECTION ALEXIS KUDRYASHOV, ALEX ALEXANDROV, VADIM SAMARKIN, VALENTINA ZAVALOVA, ALEXEY RUKOSUEV Moscow State Open University, Sudostroitel’nayal8, bld. 5, I IS407 Moscow,Russia Some peculiarities of the use of adaptive optical elements and the whole system to correct for the aberrations of high power lasers are discussed in this paper. The examples of the use of adaptive system to correct for the aberrations of some lasers are presented. As a corrector we used bimorph multi electrode deformable mirror while as a sensor Shack-Hartmann wavefront sensor or M2-meter.

1. Introdu~tion It is very well known that the wavefront of the radiation of most of high power lasers is highly aberrated. This does not allow to obtain a good focus and high concentration of the energy of laser beam. The reason for the wavefront distortions are first of all thermally induced aberrations in active elements and also some residual aberrations of various optical elements. In general the initial quality of each optical element is high enough (P-V about UlO) but the whole optical setup consists of tens of such elements that altogether introduce sufficiently large aberration. One of the most modern ways to compensate for such aberrations is to use adaptive optics’. Originally, adaptive optical systems were invented to control for wavefront distortions in astronomy - the aberrations of the light from the stars that passed through atmospheric turbulence. Such systems had to compensate rapidly changing high order aberrations to improve the vision of the objects, in fact, not always the astronomical ones’. They were rather expensive (up to 2-3 million USD), large, and of course could not be used for commercial application in lasers and laser complexes. But the development of contemporary adaptive optics technique allowed nowadays to believe that such systems could be used in various apparatus, including lasers. In our Company Night N (opt) Ltd. together with Laboratory of Shatura branch of Moscow State Open University we managed to design commercially available adaptive optical system for laser beam control. Such system consists of wavefront corrector - in our case, bimorph deformable mirror, wavefront sensor - Shack-Hartmanntype of sensor or M2-meter, control unit and software. 419

420

defor~ablemirror The standard bimorph mirror consists of a substrate made of glass, copper, silicon with thickness about 3 mm and two thin (about 0.3mm) piezoceramic discs firmly glued to the substrate (Fig. 1). The first disk has two round electrodes and serves for general curvature control. The second disk also has two electrodes, but the outer electrode of the disk is divided into a number of sectors as it shown on Fig. 2. This disc serves to reproduce low-order aberrations such as coma, astigmatism, spherical. 1 substrate

GND el. #1 (defocus)

/

piezoceramic discs

el. ##2-17 Fig. 1 . Mirror design

Fig. 2. Scheme of electrodes

Applying the voltage on some electrode produces expansion or compression of the sector and, as the piezoceramic disk is glued to the substrate, the mirror surface changes. Response functions of some electrodes are presented on Fig. 3.

Fig. 3. Response functions of electrodes # # 3,6, 10, 13

421

2 - ~ e t e to r analyse the beam In our work as a sensor we used M2-Meter that was designed in our group earlier 131 (Fig. 4). Such sensor consists of the focusing lens, CCD and the software that allows not only to obtain the intensity distribution of the beam but also to calculate the beam diameter, M2, divergence angle, ellipticity of the beam, etc. All the measurements of these parameters correspond to the International Standard IS0 11146 [4].

Fig. 4.Photography of the M2 meter

a r t ~ n wavefront n sensor The wavefront measurements by Shack-Hartmann wavefront sensor (SHS) are based on the measurements of a local slopes of a distorted wave front a@&. So, the whole wavefront is divided in several subapertures by some phase plate or lenslet array and the deviation of the focal spot from some reference position in each subaperture is measured. The experimental setup of SHS for laser beam diagnostics is shown on Figure 5. To synchronise the beam size of the incoming beam with the size of the CCD (1/2”) we suggest to use a simple lens. Of course in this case we would be able to determine the phase front up to defocus but this does not harm the correct measurements of the rest aberrations of the beam.

Fig. 5. Scheme of experimental sample

422

The experimental sample of the SHS was able to analyse wavefront aberrations with the frequency of 25 Hz.The maximal P-V aberrations determinations are in the range of +/- 8 1.1. Sensitivity of the proposed SHS depends on the number of lenses on the aperture of the CCD window and for lenslet array 25x19 is about w10.

4. Some interesting new results To control for the mirror we usually propose to use phase conjugate system based on the Shack-Hartmann wavefront sensor. But to get the good focused laser beam it is not useful to use Shack-Hartmann wavefront sensor. We tried to obtain a perfect focal spot in JAERI in 40-TW TiS femto-second laser. Here we used our standard phase conjugate adaptive optical system, the aberrations of the beam were compensated and a focal spot obtained with 5 m focusing lens was also improved Fig. 6.

Fig. 6 . Focal spot before and after correction

But when we introduced parabolic mirror to focus the beam on the target in vacuum chamber we did not obtain as good focal spot as we expected (Fig. 7). There are several reasons for this: the aberrations of the optical elements placed after Shack-Hartmann wavefront sensor, aberrations of parabolic mirror, poor adjustment of this mirror etc. That is why we suggest a scheme where instead of Shack-Hartmann wavefront sensor we use M2 meter. We just analyse the focal spot that is measured by M2 meter and calculate voltages to be applied to the mirror electrodes according to the measurements.

423

Fig. 7. Focal spot after parabolic mirror

In our experiments in JAERI we placed a CCD camera at the focal plane of parabolic mirror and tried to obtain good focal spot. The result of correction based on analysis of focal spot is presented on Fig. 8. The wavefront measured by Shack-Wartmann wavefront sensor before the parabolic mirror was distorted, but the focal spot was almost diffraction limited and had 75% of input power in first diffraction maximum.

Fig. 8. Focal spot after parabolic mirror, before and after correction

In INRS (Varennes), in Canada, we made a very interesting recent experiment by placing Shack-Hartmann wavefront sensor before focusing chamber and also after it, as shown on Fig. 9.

424 uulse

Fig. 9. INRS experimental setup

The results of correction using wavefront sensor placed after focusing chamber are given on Fig. 10. We can clearly see the improvement of the focal spot. But the main problem here is how to use such a setup in the real experimental conditions when the in the focal place the target is going to be situated.

Fig. 10. Focal spot before and after correction

5. Con~l~sions

The proposed adaptive optical system allows:

- to correct for static or slow changing aberrations; -

to form high quality beam; the system is simple in realization and very reasonable.

425

eferences 1.

J.E.Pearson, Atmospheric turbulence compensation using coherent optical adaptive techniques, Appl. Opt., 15, N3, p. 611 (1976). 2, Laser Resonators: novel design and development. Alexis Kudryashov, Horst Weber, editors, SPZE Press, 301 p. (1999). 3. J.V.Sheldakova, T.Yu.Cherezova, A.Kudryashov, "Low-cost M2-sensor for the adaptive optical system", Proc. SPIE 4493, pp. 285-293 (2002). 4. Test method for laser beam parameters: Beam width, divergence angle and beam propagation factor, Document ISODIS 11146, IntemationaI Organization for Standardization, 1996.

TIVE OPTICAL SYSTEMS FOR THE SHENGUANG-I11 ~ROTOTYPEFACILITY ZEPING YANG*, CHUNLIN GUAN, ENDE LI, MUWEN FAN, NINGPING SHI, M I N G W AO, YUDONG ZHANG, WENHAN JIANG Institute of Optics & Electronics, Chinese Academy of Sciences, P. 0.Box 350, Shuangliu, Chengdu,610209, China Shenguang-Ill (SGIII) prototype facility is an 8-heam laser currently under construction in China and will be used as driver of an inertial confinement fusion (ICF) system. It requires that 95% of the laser energy is focused into region of 10 times diffraction limit. To meet its beam quality specification, eight adaptive optical systems were built and tested, in which each system consists of a 45-channel deformable mirror and a 22 x 22 Hartmann wave-front sensor. This paper describes the latest progress of adaptive optics on the SGIII prototype facility. Online experiments shows that after the static and thermal induced aberration was compensated, typically the rms aberration of the residual wavefront was less than O.2h, and 95% of the laser energy can be focused into a 7 times diffraction limit(DL) region.

1. Introduction The SGIII facility is a new generation inertial confinement fusion laser system under construction in China. In 1999, a principle prototype for this laser system was built and used as a physical experiments platform to verify the laser amplifier technologies and demonstrate the performance of the future ICF laser system'. Then a single channel prototype was built to carry out the experiment study. Now an eight-beam laser was built as an engineering prototype of the future SGIII facility. The primary wavefront requirement for this system is that it should have the ability to focus 95% of the total energy of the laser pulse into a region of about 10 times diffraction limit. In inertial confinement fusion (ICF) system, a high power laser pulse is generated, amplified, frequency converted and focused on a target to initiate nuclear fusion reaction. The laser was used as driver of the ICF system is because it can produce high energy short laser pulse with low divergence angle. But in such large scale solid laser system, there are many aberration sources that will degrade the laser beam quality; the static errors mainly come from optical manufacturing errors of optical components, inhomogeneity of optical materials, and optical components assembling; the dynamic errors come from the thermal 426

427

distortion induced by pumping light and the non-linear phenomena of the high power laser, and the turbulence in the optical path. The wavefront aberrations existing in the laser beam will decrease the frequency conversion efficiency, increase the focal spot size and decrease the power density at the target. To improve the laser beam quality to meet the wavefront requirements, adaptive optical system was designed to correct the wavefront aberration in the laser beam before entering the 3w frequency conversion system.

2. ~ a v e f r o ncharacteristic t of the Shenguang-111 prototype s y s t e ~ Figure 1 is the schematic of a single channel of the laser system. It consists of the front-end and preamplifier, the four-pass master amplifier (Amp. 1). the singlepass booster amplifier (Amp.2). The front-end and pre-amplifying unit generates the spatially and temporally shaped pulse. This laser pulse was then injected into the amplifier chain.

Figure 1 . Schematic of a single channel laser system. It consists of the laser amplifier chain and AOS.

Before the adaptive optical system was built, we conducted a series of experiment to investigate the wavefront characteristic of the SGIII prototype facility. Both static and dynamic wavefront were studied. In figure 1, there are two Shack-Hartmann wavefront sensors, one is placed at the injection stage, and another one is placed at the output stage of the whole laser amplifier chain. The first sensor was used to monitor the wavefront of the injection laser, and the second one was used to measure the wavefront aberration of the whole system.

428

Figure 2(a) shows that the main aberration of the injection laser is astigmatism and the variance of the Zernike coefficients are very small. So in the final adaptive optical system, the first wavefront sensor was removed. , ,,

. .,

........... ,#

.......

2..

,....... ..j .. ~

(a)

(b)

Figure 2. (a) %mike representation of average injection seed laser wavefront and the rms of Zemike coefficientsof the wavefront series; (b) The output wavefront of the whole laser system.

Figure 2(b) is the static output wavefront of the whole laser system. We can see that the main aberration of the static wavefront consists of the first 16 order Zernike modes; the largest component is also astigmatism. According to this research, when designing the prototype laser system, a special rotation cavity was used to minimize the aberration. Because the astigmatism has the form of x2-y2,it could be self-corrected by a 90" rotation. Further experiment study shows that astigmatism was greatly reduced using this new architecture.

...........

*

Figure 3. Wave-fronts of four channel lasers.

429

Figure 3 shows the static wavefront from four channel of the laser system. We can see that the spatial characteristic and range of wavefront aberration are quite different between beams. The static rms aberration is about 0.5h to 1.6h, it’s much smaller that in Figure 2(b). Also the pump induced dynamic wavefront aberration for each laser channel was measured. Figure 4 shows the dynamic pump-induced aberration is about 0.5h (nns). The main wavefront aberration type is defocus, coma and astigmatism. Previous study shows that without the rotation cavity design, the basic type of the dynamic wavefront aberration would be a cylinder (can be expressed as x’), now the largest component is defocus, that is because with cavity rotation, the x2 item in the wavefront was transformed into x’+y’. These pump-induced wavefront aberration will be pre-corrected before laser shot. 1

J

-

. .. S2.PV2.8 R M S 0 . W

E

S4,PV:Z.S RMSOdW

‘

”

”

”

-

_

w

N1.PV:Z.K RMS0.614

..

m

m

m

i

o

m

m

N2,PY:24 RMS:0.519 ..

._. ...

. ,. .

m

M.PV3.S RMS0.672

Figure 4. Pump induced wavefiont aberration of each channel of the laser system.

430

The study indicates that the main wavefront aberration in this laser system can be expressed with the first 16 order Zernike modes; they must be minimized by the adaptive optical technology to meet the requirements of the laser system.

3. Adaptive optical system design and its performance There are several functions that the adaptive optical system should perform. It includes the control of the output wavefront of each beam in the time preceding a laser system shot and applying a pre-compensation for previously-measured pump induced wavefront distortion. According to the previous study of the wavefront characteristic of the laser system, the adaptive optical system was optimized to minimize the first 10 order Zernike aberrations; and also the system should have the ability to correct the higher modes up to 16 order Zernike aberrations. The architecture of the A 0 system was shown in figure 1. It contains a 22x22 Shack-Hartmann wavefront sensor, a 45 channel PZT type deformable mirror and corresponding control electronics for each beam.

&"*a

(a)

Mads l n d n

(b)

Figure 5 . (a) The configuration of deformable mirror and Hartmann sensor. (b) The relative residual wavefront error for the first 16 order Zernike modes.

Configuration of the deformable mirror actuators and the Shack-Hartmann sensor are shown in Figure 5 (a). Figure 5 (b) shows the correcting ability of this A 0 system for the first 16-order Zernike aberrations. The relative residual error for both PV and RMS error is less than 7%. For our laser system, the typical peak-to-valley wavefront aberration is about 6A, the PV error will be less than 0.6h, it is sufficient to meet the system wavefront requirements. All eight A 0 systems are calibrated and tested offline. The offline experiments indicate that the simulated results are highly consistent with the

43 1

close loop correction results. In the experiments six phase plates were used to test the system performance. The PV error of these phase plates vary from 2h to 9% and the main component of aberration include defocus, astigmatism and coma. After close loop operation, the absolute PV error between the simulated and measured one is less than h/15, and the rms error is less than MlOO. So we can now accurately predict the performance of the A 0 systems. Figure 7 shows the comparison of the simulated and measured residual wavefront. Online experiments show that after the static and thermal induced aberration was compensated, the rms aberration of the residual wave-front was less than 0.2h, and 95% of the Figure 7 Comparison of predicted and measured residual wavefront aberration in laser energy can be focused into a close-loop operation for six phase plates. region of about 8DL. Figure 8 indicates a correction results. Before A 0 correction, the system is about 12 (DL) and 95% of the energy is in 15DL, the Strehl ratio is only 0.02. After A 0 correction, it’s 3DL and 95% energy in about 7DL, the Strehl ratio is 0.46.

Figure 8. The far-field energy distribution before and after correction.

432

4. Summary We have successfully constructed eight adaptive optical systems for the SGIII prototype facility. These robust A 0 systems are now in operation online. They are used to correct the static and pump-induced thermal wavefront aberration to improve the beam quality so the system specification can be achieved.

efere~ce 1. W.H. Jiang, Y.D. Zhang, etc, Proceeding of the second international workshop on AOLM, 1999, Durham, England

O ~ T CONT ~ ~ SOL OF $ O L I ~ - $ T A T ~ W. LUBEIGT AND D. BURNS institute of Photonics, Universityof Strathclyde 106 Rottenrow, Glasgow G4 O W , UK

M. GRIF'FITH AND L. LAYCOCK BAE Systems Advanced Technology Centre West Hanningfield Road, Great Baddow, Chelmsford, CM2 8HN, UK Adaptive optics techniques were implemented inside a laser cavity in order to enhance its capabilities. Firstly, a closed-loop system using a deformable membrane mirror, a fitness sensor and a control algorithm was developed. This was successfully used to enhance the brightness of a grazing-incidenceNdGdV04 laser operating at steady-stateby a factor of 10. Secondly, the transient time of a side-pumped NdYLF laser (i.e. the time taken by the laser to reach its full brightness) was reduced by at least an order of magnitude based on the automatic translation of one of the intra-cavity mirror. Finally, investigations are currently under way based on the use of a new type of large-stroke bimorph mirror.

1. ~ntroduction Thermally-induced aberrations impose a fundamental limit in scaling the output power and brightness of solid-state lasers [I]. Within the gain medium, the thermal loading introduced by the pump deposition is directly responsible for producing a lens inside the material. Although, the first order of this lens can be accounted for by adequate cavity design, there is no simple and effective way to compensate against high-order aberration. Intra-cavity adaptive optics techniques have the potential to compensate for the thermal lens and therefore enhance the brightness of the output laser beam. A method to automatically enhance the brightness of a Nd:GdV04 laser operating at steady-state has been previously reported [2,3,4] using a deformable membrane mirror (DMM) from Flexible Optical B.V. [ 5 ] . Intra-cavity adaptive optics techniques also have the potential to compensate for the build-up of the thermal lens during the turn-on phase of the laser. The reduction of the time to full brightness is considered very important in some applications, particularly for military laser systems. We reported the successful use of a translating output coupler leading to the reduction of the turn-on time of a Nd:YLF laser [ 6 ] . 433

434

This paper describes the work undertaken towards the implementation of both the steady-state and transient optimisation techniques based on a single corrective element: a large stroke deformable mirror. The following section first describes the A 0 steady-state optimisation technique and its results on a grazingincidence Nd:GdVO4 laser. Then, section 3 presents the transient optimisation technique and its results on a side-pumped Nd:YL,F laser. Finally the steps towards the implementation of both techniques are introduced in section 4. 2. Steady-state brightness optimisation A DMM f?om OK0 technology [5] was used as a cavity end-mirror in a 15W grazing-incidence Nd:GdV04 laser. A computer-controlled, self-optimisation, feedback scheme was developed using the intra-cavity DMM, a beam quality assessor to determine a ‘fitness value’ and a control program featuring different optimisation algorithms to drive the DMM so that the fitness value reaches its global maximum. The resulting iterative feedback loop is shown in figure 1. PC + optimisation algorithm +mirror driver

Figure 1 . Schematic of the intracavity laser adaptive optics control loop

The beam quality sensor was based on second harmonic generation and consisted of a lens focusing the laser output beam onto the KTP crystal as shown in figure 2. The green light was then filtered out and recorded by a photodiode providing the fitness value. The control program was based on a set of search algorithms such as a modified hill-climbing, the genetic, the simulated annealing, the random search and the adaptive random search algorithms. All these algorithms were described and their results were reported in [4]. Using this apparatus an enhancement in the laser brightness by approximately an order of magnitude was demonstrated [2,3]. The system can

435

also be used to automatically compensate for operational changes such as alignment and temperature variations. Since this system requires an iterative control scheme to search for the optimum shape of the DMM, the optimisation time could be substantial (on the order of tens of seconds).

Figure 2. Experimental set-up of the SHG-based laser brightness sensor

3. Transient opti~sation The enhancement of output beam brightness during the turn-on phase of the laser - the time to full brightness - is considered very important in some applications, particularly for military laser systems. During this transient phase, the change in the temperature distribution in the gain medium can be dramatic as the high pump powers induce a large heat build-up in the initially cold gain medium rapidly establishing a new (hot) thermal equilibrium. The duration of this transient phase, of course, depends on several parameters such as the pumping, cooling and resonator configurations, the nature of the gain medium, and the degree of pumping; however, for a typical system, it is of the order of a few seconds. Not only does this timescale preclude the use of the DMM control system, discussed above, designed for steady-state optimisation, but the DMM stroke is also insufficient. Therefore, an alternative system was designed to allow the fast application of large, albeit first-order, aberration correction. This system was based on the direct translation of one of the resonator mirrors - the system was realised and assessed using a simple Nd:YLF laser [6] as shown schematically in figure 3. Initially, a study of the thermal lens build-up was undertaken and optimal positions as a function of time were found for the translating output coupler such that the size of the fundamental mode in the gain medium remained constant during the thermal build-up phase. This system worked well as shown in figure 4; however, its use is limited as moving the mirror a few centimetres at high speed was considered impractical for real application. Furthermore, the inertia of the mirror and its mount also limit the necessary speed, and so, the flexibility of this technique.

436

Plane 20% output coupler

Radius of curvature 0.Sm

Translation Figure 3. Transient thermal lens optimisation scheme - as the laser rod heats, the end mirror is translated such that the fundamental spot sizes in the laser rod remain constant

Figure 4. Transverse intensity distribution at the turn-on time without and with output coupler translation

. ~mplementationof both technique using a single element The DMM maximum stroke was deemed insufficient for transient optimisation technique. It was also shown in section 3 that the translation of one of the cavity element albeit successful is impractical to implement inside ‘real’ laser cavities. Therefore, the translation of the DMM to both compensate for steady-state and transient optimisations cannot be developed. Instead, the use of a large stroke deformable mirror is possible with the development of a new bimorph mirror from BAE ATC [7]. The next sub-section describes the deformable mirror. Subsection 4.2 deals with the control program featuring the hysterisis compensation technique.

.I. The b i m o ~ h mirror Bimorph mirrors have been used successfully inside laser cavities and can handle high level of intra-cavity power [8]. The bimorph mirror is made of 31 actuators over an 18mm diameter aperture as shown in figure 5a and 5b. Its frequency response is 6MIz and the maximum correction is about -1.2D and 0.4D for all actuators at the maximum and ~ n i m u m voltages respectively. Each actuator could be driven with voltages ranging from -5OVto 250V with 12-bit coding.

437

a

b

Figure 5. a. view of the bimorph mirror, h. the actuator pattern

. ~ o n ~ofo the l mirror The software control program was written using CVI-Labwindows and features the functions to address the voltage to the actuators. It also contains the fitness meas~ementfunction based on either a photodiode or a webcam and the transient optimisation function. Finally, one inherent problem when working with bimorph mirror is the hysterisis. To reduce its effects, a pinging function should be written delivering the voltage into different steps oscillating between the maximum and minimum value before reaching its final value. However, since the voltage applied to each actuator cannot go below -5OV, the actual pinging function written has a voltage oscillating between -5OV and 250V. Both ideal and actual pinging functions are shown in figure 7a. The effects of the real hysterisis function are shown in figure 7b. Using the modified pinging function effectively reduces the hysterisis from 10%to 2.5%.

a

b

Figure 7. a. The ideal and real pinging functions interface of the control program; b. effect of the hysterisis funcQon

438

5. C Q n c l ~ i Q n

We have demonstrated automatic brightness enhancement of a grazing-incidence Nd:GdV04 laser using a closed loop system featuring an intra-cavity deforrnable membrane mirror, a brightness sensor and a search algorithm. Active optics technique based on the automatic translation of the output coupler was also used to significantly reduce the turn-on time of a Nd:YLF laser. Finally, investigations based on a new type of large-stroke bimorph mirror are currently under way to enable us to, at the same time and with the same correcting device, reduce the transient time and increase the brightness of a Nd:YLF laser.

Ac~Q~led~rnen~ This work was funded under the UK government DTI technology program.

eferences 1. W. Koechner, Solid-state Laser Engineering 6’ Edition, chp.7, Springer Series in Optical Science, New York, 2006. 2. W. Lubeigt, G. Valentine, J. Girkin, E. Bente and D. Burns, “Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror,” Opt. Express 10, pp. 550-555 (2002). 3. W. Lubeigt, G . Valentine and D. Burns, “Intracavity adaptive optics optimisation of a grazing incidence Nd:GdV04 laser, paper CThJJ5 presented at the Conference on Lasers and Electro-Optics, (2004). 4. W. Lubeigt, G. Valentine and D. Bums, “Intracavity adaptive optic control of 1pm solid-state lasers,” paper 3-26, 5” International Workshop on Adaptive Optics for Industry and Medicine, Beijing (2005). 5. Flexible Optical B.V., Rontgenweg 1,2624 BD, Delft, The Netherlands. 6. W. Lubeigt and D. Burns, “Adaptive Optics Control of Solid-state Lasers,” Proc. SPIE Vol. 6452,64520B, (2007). 7. BAE Systems Advanced Technology Centre, West Hanningfield road, Great Baddow, Chelmsford, CM2 8HN, UK 8. I.V. Ilyina, T.Y. Cherezova and A.V. Kudryashov, “Far-Field Laser Intensity Distribution by Means of Intracavity Adaptive Optics,” Proc. SPIE Vol. 6452,6452OC, (2007).

GE

ERG-§AXTON A L G O R I T FOR ~ ~ ~ULTI- ODE BEA RE§HAPING

INNA V. ILYINA, TATYANA YU. CHEREZOVA Physical Department, Moscow State Lomanosov University, Vorobyovy Gory,1 ,Moscow, 11 9899, Russia

In this paper we present the results of the given intensity distribution formation in far-field by means of liquid crystal modulator (LCM) and semipassive bimorph deformable mirror (SBDM) both placed in near-field. Phase delay of LCM or SBDM is calculated by means of Gerchberg-Saxtou algorithm. It is known that Gerchherg-Saxton algorithm fails in the case of multimode beam transformation. In this paper we suggest the modification of such algorithm that allows making not only single-mode beam transformation, but also multimode one. The phase delay of LCM or SBDM is calculated as the sum of each mode phase multiplied by its relative intensity. We discuss some practical examples of several given intensity distributions formation from different combination of laser transversal modes.

1

Intr~uction

Given intensity distribution formation, so called beam shaping problem, is important for many industrial and scientific applications. Various techniques have been developed to solve this problem. One of the simplest techniques is beam aperturing', which affects intensity distribution of input beam to form the desired intensity distribution in the output plane. However, this technique introduces high power losses. That is why most of beam shapers affecting only the beam phase have been designed. Reflective, refractive, or diffractive optics are used in such beam transformers'. The desired phase ~ n c t i o nof the beam transformer can be calculated by various methods. For example, the beam shaping problem can be obtained by applying the method of stationary phase' or the method of geometrical transformations3. Both of these methods allow obtaining closed form solutions. However, in some cases there is no way to solve the problem analytically. In that case iterative4 and optimization algorithms5 can be used. Unfortunately, most of techniques listed work well only for single-mode beams. In this work we present the method that is suitable for calculation of phase function for both single-mode and multimode beams. This method is based on Gerchberg-Saxton algorithm6. The main steps of the classical Gerchberg-Saxton algorithm for the problem of single-mode beam reshaping are discussed in section 2. Here the results of the given intensity distribution formation obtained with Gerchberg-Saxton algorithm are presented. Liquid-crystal modulator is used in this case as the phase element. Section 3 describes the modification of classical Gerchberg-Saxton algorithms so as to perform multimode beam transformation. Bimorph deformable mirror is used to reconstruct the phase profile calculated with modified Gerchberg-Saxton algorithm. Results of multimode beam reshaping are presented here. 439

440 2

Gerchber~Saxtonalgorithm for single-mode beam reshaping

Gerchberg-Saxton algorithm is an iterative procedure that allows the phase information reconstruction from two intensity measurements. Schematic diagram of the algorithm is shown in Figure 1. The algorithm is started by assuming the initial phase of the beam. This phase function is then multiplied by the respective amplitude function measured in the input plane. The complex function is then Fourier transformed, and the resulting magnitude is replaced by the amplitude function prescribed in the output plane. This amplitude function is combined with the phase resulting from transformation and then the Inverse Fourier Transformation is performed. Thus, one can obtain new phase estimation in the input plane. The iteration is repeated unless the necessary accuracy is reached. When the algorithm converges, resulting phase function tpn is reconstructed with phase element.

A(r,O) = / m / e x p ( & , , ( t . , O ) )

i t ( r ' . ~ '= ) l~'(r',~')~e~p~\i/,,(r',~'))

Figure 1. Schematic diagram of Gerchberg-Saxton algorithm

In our experiment we use Liquid-crystal modulator (Holoeye LC-2002) to reproduce the phase function, calculated with Gerchberg-Saxton algorithm. The main parameters of the LCM are listed in Table 1. Table 1. Main characteristics of LCM Holoeye LC-2002.

The experimental set-up for single-mode beam transformation is shown in Figure 2. Beam of a He-Ne laser (h=633nm) passes through the beam expander and LC modulator. LCM reconstructs the phase function calculated with classical Gerchberg-Saxton

441

Transforming

lens

Figure 2. Experimental set-up for single-mode beam reshaping

algorithm and directs beam into the transforming lens. The far-field intensity distribution is recorded in the focal plane of the lens by a CCD camera consisting of 0.4 Mpixels each having size 8.6(h)x8.3(v) pm. Since the LC modulator has high spatial resolution, it is especially useful for producing complicated patterns, such as logos, photographs, and art. Figure 3 demonstrates some results of single-mode beam reshaping. Desired intensity patterns are depicted in the first column, phase functions of LCM are shown in the second column, and intensity patterns measured in far-filed zone are demonstrated in the third column.

Figure 3. Single-mode beam reshaping with the help of liquid-crystal modulator

442

3 Modified Gerchberg-Saxton algorithm for multi-mode beam reshaping

~ i ~ ( p ~=, A:o(u',e')exp(iyr~o(r',e')) e ~ )

A ~ ) " ( ~ ,=O J) m e x p ( i c p n ( r , e ) )

A,,(r,e)=& w e x p ( r e ) e x p ( i c p n

(r,eq-'

2, (yi,e

xo,(r,e) = ;1,,to)ex~(itp"l:)

&,(O) = k,tY,e,exPGcp;;i)

~;,(~i,e')= ~ ; , ( r f , e ' ) e x p 4 t p;,(rr,er))

'w-

f, Jm& (yi,e '1) =

exp(iyi

A(JuF,8#)= ~ ~ e ~ ~ ~ ~ ~ i ( r f

443

5. The new phase function in the input plane is calculated and combined with the given amplitude functions. The main difference of the suggested modification of Gerchberg-Saxton algorithm from the classical Gerchberg-Saxton algorithm is that each mode's intensity distribution as well as the mode's phase distribution is taken N

into account in the phase function calculation:

pn+'(Y, 6) = i=l

where ai = I i ( r , $ f

i = l . ..N, N - is the number of modes, ll{r,8)-is i=l

the intensity distribution of the i-th mode,

( r ,8) - is the phase of the i-th mode

in the n-th iteration. Steps 2-5) are repeated unless the necessary accuracy is reached. At each stage we consider ideal corrector to reconstruct phase function @(r). When the algorithm converges, the resulting estimate p(r) is approximated with real corrector. Bimorph deformable mirror7 placed in the input plane instead of LCM (Fig.2) is employed as a real corrector in case of multi-mode beam reshaping. The complex amplitude is then transformed according to Fresnel-Kirchhoff equation and the resulting intensity distribution in the output plane is calculated. For the case of 3rdorder supergaussian beam formation from the combination of two modes the best result was obtained for the following parameters: wavelength /t=IO.6pm, Lt=5m, Lz=f=O.45m, W'=0.35mm,@=65m, where w is the waist of the input beam, f is the focal length of the lens. The mean square error (MSE) of formation with ideal corrector was 4.9%, the MSE of formation with deformable mirror was 5.3%. Accuracy of the desired phase function reconstruction with deformable mirror (MSE) was 0.46%. We also applied this algorithm for 6th order supergaussian beam formation from combination of four modes: lin(r,@=O. 1STEM2~+0. 351TEMo112+0.I STEM210+0.351TEMo2I2..

The best result of formation was obtained for the following parameters: /t=10.6pm, Ll=Sm, Lz=f=O.45m, w'=0.35mm, @=9.6inm.The accuracy of formation with the help of ideal corrector and deformable mirror was 1.47% and 1.6% respectively. The MSE of the phase-function reconstruction by real bimorph mirror was 1.5%. The results of formation for the last case are shown in Fig.6. 4

Conclusions

In this paper we applied Gerchberg-Saxton algorithm to the problem of single-mode beam reshaping. To reconstruct the phase function we used liquid-crystal modulator. Experimental results of single-mode beam transformation into intensity profiles with complex structure are presented. We have also proposed modification of GerchbergSaxton algorithm in order to perform the multi-mode beam shaping. In this modification

444

phase function is calculated as the sum of each modes phase multiplied by its relative intensity. We demonstrate the 31d order supergaussian irradiance formation from the combination of two modes and from combination of four lower transversal modes. Bimorph deformable mirror was used to reconstruct calculated phase profile. The accuracy of formation was equal to 5.3% and 1.6%,respectively.

1

1

Figure 6. 3d order supergaussian beam formation form combination of 4 modes : (a) - initial intensity distribution in the input plane, (b) - surface profile of bimorpb deformable mirror, (c) - desired intensity distribution, (d)-formed intensity distribution

eferences 1. F. M. Dickey, S. C. Holswade, D. L. Shealy, Laser beam shaping applications, CRC Press (2006). 2. 3 . 3 . Stamnes, Waves in focal regions, IOP Publishing, England (1986). 3 . 0. Bryngdahl, J. Opt. SOC.Am, 64 (8), 1092 (1974). 4. J. R. Fienup, Appl. Opt., 21(15), 2758 (1982). 5 . N. C. Evans, D. L. Shealy, AppLOpt., 37(22), 5216 (1998). 6. R. W. Gerchberg, W. 0. Saxton, Optic(Stuttgart), 35,237 (1972). 7. A V. Kudryashov, V. I. Shmalhausen, Opt.Eng., 35,3064 (1996).

ew ~lgorithmof Combining for Spatial C o h e ~ n t Ruofu Yang

The Institute of Optics And Electronics, The Chinese Academy of Sciences, ShuangLiu, ChengDu, 610209, China Graduate University of Chinese Academy of Sciences, BeiJing, 100049, China Xiaojun Zhang

Feng Shen Wenhan Jiang

The Institute of Optics And Electronics, The Chinese Academy of Sciences, ShuangLiu, ChengDu, 610209, China Abstract: A Peak-Rate (PR) algorithm of combining for spatial coherent beams is presented which is based on the abstraction of image's character captured by CCD. The algorithm is simulated and applied in experiment and two collimated beams with piston aberration are coherently combined. Piston aberration is introduced into two coherent beams and Active Segmented Mirrors (ASMs) are

used to correct it by PR algorithm. The experiment results indicate that far-field interferometric pattern is stable and beams are coherently combined accurately.

Keywords: coherent combining; piston aberration; Peak-Rate algorithm; Active Segmented Mirror

1. Introduction To achieve the high brightness's requirement for many laser applications it is necessary to phase-lock multi-element optical arrays. Recently, many companies and research institutes developed various coherent combining systems to combine lower power laser arrays to higher power and kept the quality of beams at the same time. There are some combining schemes such as Self-organized coherence in fiber laser arrays"], Phased Array of Phased Arrays(PAF'A)[2', Adaptive Optics'31, MOPA[41,etc. The combining efficiency of Self-organized theme is prominent when fiber laser arrays are fewer, but with the increase of arrays and power of every fiber laser the combining efficiency decreases. In PAPA method, the power of laser beam is limited and the polarization is demanded; wave-front of every beam is corrected by Liquid Space Modulator (LSM). At present, MOPA method is popular because of its 445

446

simple and high real-time process. However, in MOPA method the phase modulators can not stand higher power. Adaptive optics can be used to correct wave-front aberrations of beams. Wave-fronts of beams are detected by modified Hartmann-Shack detector and corrected by ASMs. This method overcomes the effect of high power and can correct the tilt and piston aberrations of every beam. The far-field combining pattern’s character of 7 coherent beams which only have piston aberration is analyzed firstly. Based on the character, PR is presented to judge the quality of coherent combining. Then, in experiment piston aberration is introduced between beams and is corrected to desired situation which PR is in the round of ideal PR value.

athematic Piston Module Analysis The far-field diffraction of arbitrary wave-front is Fraunhofer diffraction which is two-dimensional Fourier transform. The diffraction pattern distribution can be got by two-dimensional FFT

In the Eq.l,R,

and f represent the wavelength, area of two coherent

1

beams and focus length of lens, respectively. c =: - ;k Zil

and

?!,(

=I:

2lr -; El (xl, y, ) il

x, y ) represent incident and far-field complex amplitude, respectively.

Far-field diffraction distribution of energy is

From Eq.(l), the complex amplitude distribution in diffraction plane is two-dimensional Fourier transform of incident wave except for phase factor ahead of integrator. As to multiple incident beams, the far-field diffraction pattern can be acquired by expressing multiple incident beams with complex amplitude distribution. Usually in coherent combining the piston and tilt aberrations are considered only. In 7 beam’s configuration, the complex amplitude wave-front is

447

(3) i=l

In Eq.(3),

wi(x, y)

presents aberration of ind beam and ( c i , q i )

represents the center coordination of ind sub-aperture. Fig.1 (a) and Fig.1 (b) present the far-field combining pattern with zero aberration and random piston aberration, respectively. Beams are perfectly combining in Fig. 1 (a), the center lobe is more concentrated and peak value is higher than Fig. 1 (b).

Figure 1. Seven monochromatic beams far-field diffraction patterns (f=O.lm), (a) presents piston between beams is in-phase; (b) presents piston is random.

For piston phase extraction of 2 coherent collimated beams, piston subtract method such as Hartmann-Shack sensor[51 with ASM is referred in large segmented telescope. For wave-front piston extraction, Chanan, etc introduced PR algorithm in large-aperture segmented mirrors for astronomical telescope. To a specific piston of two coherent beams a specific two-dimensional energy distribution pattern is produced, to decrease influence of background and CCD noise, a one-dimensional array is obtained through adding every row of two-dimensional energy distribution. A specific PR value is acquired from the one-dimensional array. First, the one-dimensional array is searched to find the maximum, and then two sub-maximums are gotten through searching two sides of maximum. If left-maximum is higher than right-maximum, PR is maximum divided by left-maximum, or, PR is right-maximum divided by maximum.

448 3. Close-Loop CalibrationExperiments For performing efficient coherent combining for two beams, adequate pixels combining pattern takes are necessary. In this experiment, a lens and stop, which are put vertically center of the two beams, is adopted, Fig2 is schematic block graph.

i i

Collimated beam

ASMs

C

3 Indushial

computer

High-voltage Amplifier

Figure 2. Schematic block graph of coherent combining; the radius of stop is 4.5mm; the radius of circular ASM is 16.5mm and distance of them is 0.5mm; the focus distance of convergent lens is 900mm; the wavelength of light source is 632.8nm.

Every ASM, which has 3 degrees of freedom, can be used to correct the tilt and piston aberrations; a MINTRON CCD which has 25Hz f p s , 8um*8um Pixel Size, 8-bit Data Format, 100% Fill Factor is adopted. In this configuration, the, useful pixel area is about 32*32.Before close-loop, a test needs to be done to measure the relation between PR value and feedback voltage. A step voltage is added to 3 piezoelectric ceramics simultaneously, Present CCD pattern is captured after a new voltage is updated. Noise Gate and Median Filtering are performed to decrease the effect of noise and smooth the image, then, a one-dimensional array is acquired and PR is calculated by said methods. In the close-loop experiment, a signal generator is introduced to generate piston aberration between two beams; the signal is magnified by high voltage amplifier and sent to 3 electrodes of 1'' ASM. The Znd ASM is used to calibrate this piston aberration. Before close-loop, 1'' ASM is disconnected and a step-voltage is added to ZndASMto find the PR value in in-phase situation. In

449

close-loop, after a new image in CCD is captured and present PR is acquired, update voltage is calculated by the difference between the present PR and PR of in-phase.

esults of ~ ~ e r i ~and e nAnalysis t Because of the lower fps of CCD,for improving the speed of capture, only 64 row pixels are captured for one frame. Different frequency and amplitude of signal generator are introduced to generate the periodic piston aberration. Fig.3 is long-exposure pattern at open-loop and close-loop. Every sub-image is obtained by averaging 100 images. When amplitude of signal is larger, even in low frequency, the velocity of variational pattern is faster than lower amplitude. So, when the feedback voltage is applied to 2"d ASM, because of hysteresis of close-loop, the combining effect is not perfect. When employing high-speed CCD, in limited amplitude and high frequency, the piston aberration will be real-time controlled.

Figure 3. Close-loop(al,bl,acl,dl) and open-loop (a2,b2,c2,d2) far-field long exposure combining patterns, frequency of al,bl,cl and d l is equal to a2,b2,c2 and d2, respectively. Al: 0.7Hz, small amplitude; bl:l.OHz, small amplitude; cl: 0.3Hz, large amplitude; dl:O.SHz,large amplitude.

In the every sub-figure of Fig.4, the top curve presents signal voltage and the lower feedback voltage. The both voltage waveforms are similar, but, with the augment of frequency and amplitude of signal, the hysteresis that effects the combined effect slightly happens between the signal and feedback voltage wave in sub-figure (b) and (d). Because the f p s of CCD is lower, the hysteresis is primarily introduced by the low-speed CCD,and the time consumption which is about 2-4ms by processing the data is much less than capturing image.

450

(C)

(d)

Figure 4. Contrast graphs between signal and feedback voltage waveform.

5. Conclusion The detecting and correcting for piston aberration are analyzed in detail using PR algorithm which is derived from large segmented mirrors for astronomical telescope. From the close-loop experiment, a desirable result is acquired by the scheme. In next work, a high speed CCD will be adopted for improving the close-loop bandwidth, and three beams coherent combining experiment will be carried on later.

eferences 1. Bruesselbach, H. Minden, etc, 200W self-organized coherent fiber arrays. CLEO, 3(CMDD4):532-- 534 (2005). 2. Steven. Serati, Hugh Masterson and Anna Linnenberger. Beam combining using a Phased Array of Phased Arrays (PAPA). 0-7803-8155 IEEE (2004). 3. D.R.Neal, S.D.Tucker, etc. Multi-Segment coherent beam combining. SPIE, 2534-10, July (1995). 4. T.M.shay, etc. Narrow Line-width Coherent Beam Combining of Optical Fiber Amplifier Arrays. SPIE ~01.6451(2007). 5. G. Chanan, M. Troy, C. Ohara. Phasing the Primary Mirror Segments of the Keck Telescopes: A comparison of Different Techniques. SPIE 4003, 188-201 (2000).

traca~tymode control of a solid-state laser using a 19-elementdeforma~lemirror Ping Yang'*2,Wei Yang'22,Yuan Liu'*2,Mingwu Ao'", Shijie Hu', Bing Xu', Wenhan Jiang' Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209 Graduate School of the Chinese Academy of Sciences, Beijing 100039 "EMw laser beam are most useful in practice, however, in order to obtain the fundamental transverse mode oscillation from the industrial solid-state lasers, the problem of thermally induced phase aberrations must be solved. In this paper, a way of using intracavity adaptive optics technology to control the mode structure of laser beam is presented. An adaptive optical system has been developed for mode control of a solid-state laser. In this system, a 19-elementpiezoelectricity deformable mirror which is used as an intracavity rear mirror of the resonator is applied to adaptively control and optimize the mode of a flash lamp-pumped continuous-wave solid-state laser. A global genetic algorithm is adopted to search the optimum voltages which are used to control the deformable mirror. The experimental results showed that it is efftcient to use the 19-element piezoelectricity deformable mirror to change "EMl1, TEMto and TEMzo mode into fundamental TEMw mode. After phase aberrations in laser resonators are corrected by deformable mirror, the output laser powers are also optimized automatically.

1. ~ntro~uction In past a few years, improving the output power of solid-state lasers is maybe the major goal of laser experts and laser users ,thus, the necessary of raising the laser beam quality sometimes is neglected. However, nowadays, as solid-state lasers are widely used in many fields, more and more application fields not only need them to generate high power output, but also need they to generate relatively high quality laser beam. However, since the thermal effects in solid-state laser resonators are the main obstacles for generating high quality output beam thus, for obtaining high quality output, the thermal effects must be compensated. There are many ways to compensate thermal effects in solid-state lasers for generating high quality TEMoo output beam. One of the most convenient ways is to insert a pinhole in the laser resonators. However, this way will reduce output power greatly and can cause pinhole to be damaged when the power density in resonators is beyond the threshold of pinhole. In another way, although excellent laser crystals can be used to obtain high quality TEMoomode with a relatively high power, whereas it is difficult to produce those crystals and

',

Email: pingyang25 16@ 163.com

451

452

the prices may be too expensive to afford. In general, thermal lens and thermally induced birefringence are the main aberrations in thermal induced distortions. Luckily, through carefully selecting a natural birefringent crystal, thermally induced birefringence can be eliminated successfully; the spherical component of the thermal lens can also be compensated by designing the resonator cavity well However, the non-spherical aberrations can not be corrected in the same way. In the past, adaptive optics technique are mostly used to correct the phase aberrations in astronomical systems As a key component of adaptive optical systems(AOS), deformable mirror(DM) can also be used to compensate the phase aberrations in no-ideal optical systems. In our laboratory, a 19-element piezoelectricity DM was adopted as one rear intracavity mirror to compensate the phase aberrations in a solid-state lasers resonator. The DM is controlled by a real encoding genetic algorithm (GA)4-5, In this paper , the performance of this adaptive optics system under different conditions will be discussed in detail.

’.

’,

2. E x ~ e r i ~ eSetup n~i Figure 1 is the schematic of experimental setup. As can be seen in this schematic, the DM is taken as the rear intracavity mirror of the YAG laser, a expand telescope which consists of L1, L2 is used to make the beam sizetabout 6mm) in the cavity to match the effect work aperture of the 19-element DM(32mm). The laser is a flash lamp-pumped YAG solid-state laser. The DM which is fabricated in our laboratory is coated high reflectivity(R>99.5%) at the wavelength of 1064nm. The output coupler (OC) is a 10% transmission plate mirror with a diameter of 25.4 mm. A narrow band filter (1064 nm 210 nm) behind the OC forbids other wavelength beam pass through it. After the beam , the output beam is divided into two parts by a beam splitter(BSj.one beam passes through the BS and detected by a power meter, another output beam which is reflected by (BS) is focused onto an infrared CCD camera. To make sure that the laser intensity will not exceed the saturation threshold of the CCD camera an attenuator which has a variable transmission rate is used. The intensity information on the CCD is acquired by a frame grabber with a rate of 25Hz. The intensity information is regarded as the object function to maximize, the GA which is programmed in the industrial computer is used to calculate the voltages that needed to compensate the phase aberrations in resonators so as to obtain TEMoo laser mode. When light intensity reach its maximum value, the

453

voltages at the moment are saved and amplified by a high voltage amplifier (HVA) before applied on the 19 actuators of the DM.

L1

12

Figure 1. The schematic of experimental setup.

3. ~ x ~ e r i m e n aResults tl and Analysis Figure 2 is the transverse mode distributions before and after optimization at the pump current of 1%. Before the phase aberrations in the resonator were corrected, the transverse mode distribution was an obvious TEMlo mode, however, after optimization the laser mode was changed into TEMm. The phenomenon can be shown as follows: at the c voltages on the actuators of the DM are changed, as the DM are also changed, at last, resulting in a ch the resonator, thus establishes the sufficient TEMmmode and restricts the generation of high minutes to finish the whole course based on 400MB CPU and 256MB RAM. Through watching the power meter, we also found that, after optimization, the average output power was brought down to 2.9W from 3.4W. The reduction can be explained as follows: After optimization, the overlap of the TEMmmode with the pumped volume within the crystal is not as large as that of multi-modes. When higher order modes are suppressed by DM, the mode volume in the resonators will become smaller, therefore, the crystal may not used efficiently, as a result, the average output power will be reduced.

454 Open Loop

Close Loco

Figure 2. Transverse mode distributionbefore (left) and after (right) optimization at 15A.

During the experimental course, we found that, the output transverse laser mode became more and more complex as the pump current increased, and it was not very effectively to change multi-modes into TEMm mode just depending on the DM. Thus, in order to control the mode efficiently in a relatively high power status, a variable size pinhole was inserted near the OC to coarsely select the laser mode; Figure 3 is the transverse mode distribution before and after optimization at the pump current of 16.7A with a 2 mm pinhole in the resonator. It took about 4 minutes to change the TEMzo mode into TEMw mode. The output power was reduced to 2.1W from 2.5W when mode optimization was finished.

Ooen LOOO

Close Lo00

Figure 3. Transverse mode distribution before(1eft) and after(right) optimization at 16.7A.

Similarly, Figure 4 is the transverse mode distribution before and after optimization at the pump current of 19A with a 2 mm pinhole in the resonator. After optimization, the beam mode was changed from TEMll to TEMmmode, and the output power was changed slightly from 4.4W to 4.3W. The whole course lasted about 5 minutes.

455 Open Loop

Close LOOP

Figure 4. Transverse mode distribution before(1eft) and after(right) optimization at 19A.

Besides automation mode optimization, The misalignment of the laser resonators could also be solved by automation adjusting the DM. Changing the surface shape of the DM could improve the output beam power and quality. Figure 5 is the transverse mode distributions before and after automation aligning the laser resonator at the pump current of 20A. We can see that after automation alignment was accomplished. The beam intensity distributions became more symmetrical and brighter. The output power was increased from 5.5W to 11.4W.

Figure 5. Beam profile before and after automation alignment the laser resonator at 20A.

.

~oncl~ions

In summary, a set of intracavity solid-state laser mode control system has been set up in our laboratory and some promising results have been obtained. These results show that, it is efficient to use our 19-element deformable mirror as the rear mirror of the laser resonator to compensate phase aberrations and select laser modes.

456

efe~enees [I] Walter Lubeigt et al, 0pt.Express. 10 (2002), 550-555. [2] D.Bms. et al, SPZE proc.4629( 2002),4629-18. [ 3 ] J.W.Hardy,Adaptive Optics for Astronomical telescope, Oxford University Press, 1998. [4] P Yang. et al, Journal of Physics: Conference series. 48(2006), 1017-1024. [5] Goldberg D E. Genetic algorithms in search, optimization and machine learning.(Reading M A, USA: Addison-Wesley Publishing Company, Inc) 1989.

NESS SENSOR FOR LASE C O ~ ~ ~ C A ~ I O N S KRISTINN. WALKER*, ROBERTK. TYSON Department of Physics and Optical Science, University of North Carolina at Charlotte Charlotte, NC 28223, USA Conventional adaptive optics systems use direct wavefront sensing, such as the ShackHartmann sensor, requiring the measurement and reconstruction of the incoming wavefront at the pupil plane. Indirect wavefront sensing, such as image sharpening, is based upon information in the image itself. Image sharpening with adaptive optics can he applied where the object is known, as in a laser communication link. We are developing an image sharpness sensor based on the information found in the Fourier spectrum of the image. High spatial frequencies contain information ahout the edges and fine detail of the image. Our premise is that maximizing the high spatial frequencies will sharpen the image. In our method the Fourier transform of the image is generated optically (and essentially instantaneously) and then the low spatial frequencies are filtered out with an opaque mask. The remaining high spatial frequencies of the Fourier spectrum are integrated optically and a sharpness signal is measured with a single photodetector. The collected sharpness value i s used in a closed-loop to control the deformable mirror until the sharpness is maximized. We have constructed a simulation to study the sensor and its performance in an adaptive optics system. We will discuss the sensitivity of this method based on the results of our investigation and mention some of the limitations of the system.

1. IntrQdu~tiQn Throughout the development in the field of adaptive optics several forms of wavefront sensors have been used[l]. Most adaptive optics systems today use direct wavefront sensing techniques such as the Shack-Hartmann sensor through measurement and reconstruction of the incoming wavefront at the pupil plane. Muller and Buffington[2] first introduced a method of image plane (indirect) wavefront sensing known as image sharpening. Image sharpening uses information from the image plane to measure and maximize the sharpness value of the image. Various sharpness metrics have been expIored[2] including sharpness value S = I ( x ~, ) ~ d . d. yWe are developing an image sharpness

s

sensor using a metric based on the Fourier spectrum of the image. * [email protected].

459

460

2. Theory One common area of Fourier optics is the analysis of the frequency domain of an optical imaging system. Abbe and Porter[3] first presented results showing how placing a spatial filter in the frequency domain will alter the image spectrum and therefore the image itself. Figure 1 shows an object and the resulting images after passing through a low pass and high pass frequency filter. Low frequencies contain information about the basic size and gross shape of the object while high spatial frequencies contain information about the edges and fine detail of the object.

Figure 1. (a) Object (b) Low pass frequency filtered image. (c) High pass frequency filtered image.

Optical linear systems theory shows the image spectrum, in the frequency domain, is the product of the object spectrum and the optical transfer function (OTF). The OTF represents how spatial frequencies are transferred through an optical system. In the incoherent case the OTF is the normalized autocorrelation of the pupil function[3,4].

(a)

(b)

(c)

Figure 2. Incoherent O W cross-section of a system with a circular pupil and (a) no aberrations present. (b) defocus present. (c) coma present.

46 1

Figure 2a shows the OTF cross-section of a diffraction-limitedsystem with a circular pupil. Aberration effects on the OTF can be seen in Figure 2b and 2c. High spatial frequencies are greatest in the diffraction limited case and the presence of aberrations decreases the high spatial frequencies. Given that high spatial frequencies carry the edges of an object and are greatest in the absence of aberrations our premise is that maximizing the high spatial frequencies will sharpen the image. o ~ r i e rImage § ~ a r ~ n eSensor §§ Figure 3 shows the schematic diagram of an optical system incorporating an imaging telescope, a deformable mirror correction device, and the Fourier image sharpness. The Fourier transform of the image plane is performed optically (and essentially instantaneously) using a single lens. At the Fourier plane the low spatial frequencies are filtered out of the image spectrum with an opaque mask. The remaining image spectrum is integrated optically and recorded with a single photodetector. The sharpness value collected from the photodetector is used in a closed-loop to control the deformable mirror until the sharpness is maximized. Using this configuration we plan to assess different types of objects and experiment with masks of various sizes.

Fourier transform recording

€iec~roffjc or opthi feedback Figure 3. Fourier image sharpness sensor experimental. setup.

462

4. Modeling We have developed an imaging system simulation to study the Fourier based image sharpness sensor and its performance in an adaptive optics system. The simulation was used to analyze the sensitivity of the high spatial frequency metric to various deterministic and random aberrations. The high special frequency metric was calculated with various aberration strengths and mask sizes. Using the model the image of a given object was generated after propagating through an aberrated system. The Fourier transform of the generated image was numerically calculated by performing a direct fast Fourier transform (DFET). After the DFET was calculated the low frequencies were blocked with a “mask” centered on the spectrum. The remaining high spatial frequencies were integrated into a single number (figure-of-merit) that was recorded with respect to the changing aberration strengths and mask sizes. Figure 4 shows the figure-of-merit values for a point source with increasing Zernike defocus strengths for various masks, hence the multiple curves. Ideally one desires curves with high slope with the figure-of-merit decreasing continually as the aberration strength increases. It can be seen in figure 4 that even for a point source object there are limitations to the high-frequency metric. Under most conditions small masks show greater sensitivity than large masks. This leads us to not only experiment with circular masks that act as high-pass filters, but also with masks that filter out various frequency bands.

Figure 4. High spatial frequency metric value vs. Zemike defocus strength for a point source object with various mask sizes.

463

Figure 5 was obtained using the same model described before with a cross object and a small mask. As the wavefront error changed, by adding various strengths of up to 22 Zernike aberration modes, the high spatial frequency sharpness metric was measured and the final image was obtained. Putting these values together in figure 5 shows that the sharpness increases as the wavefront error decreases. 12,

I

Figure 5. Sharpness metric for various aberration strengths. The vertical scale represents RMS wavefront error in radians or a sharpness metric in arbitrary units.

5. Discussion Simulation results show that the Fourier-based image sharpness sensor is feasible with some limitations. Figure 4 shows there are limitations in using the highfrequency metric even for the point source object; the sensitivity changes slope if the aberration strength becomes too large. Another limitation is the sensor’s inability to detect image motion or phase tilt from the Fourier transform intensity. Since the sensor uses the Fourier spectrum, object motion in the spatial domain causes a phase shift in the frequency domain which is not detected by the magnitude of the Fourier transform. To correctly separate atmospheric tilt from actual image motion, we anticipate using the division of temporal frequencies to isolate the faster atmospheric tilt.

464

One possible application of the Fourier image sharpening sensor is for laser communications. One advantage of this sensor over conventional wavefront sensors is that a point source isn't necessary, thereby a passive and secure system is possible. This passive system is described by figure 6 . Light from the passive scene reaches the detector where a sharpness value is recorded. The deformable mirror changes and another sharpness value is recorded. Once the sharpness value is maximized the laser is turned on and the wavefront is corrected as it passes through the atmosphere toward the receiver. For a system where there is a point source at the receiver the point source image can be optimized by maximizing the entire OTF. In other cases where the object is known the image can be optimized by matching its Fourier transform with the expected transform. Passive D

Parrive

D

Faunwlmage

Sharpness Ssnsw

Laser

Laser

Figure 6. Use of the Fourier image sharpness sensor in laser communications with a passive source.

Acknowledgment The authors wish to acknowledge support from L3Com - Brashear (Pittsburgh, PA, USA), AgilOptics (Albuquerque, NM, USA), and Block MEMS LLC (Marlborough, MA, USA)

eferences 1. R. K. Tyson, Principles ofAdaptive Optics, 2ndEdition., Academic, Boston

(1998). 2. R. A. Muller and A. Buffington, J. Opt. SOC.Am. 6 3. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill., New York, (1968). 4. J. I).Gaskill, Linear Systems, Fourier Transforms, and Optics, John Wiley & Sons, New York (1978).

OP A~APTIVEOPTICS SYSTE

IVO BUSKE, WOLFGANG RIEDE G e m n Aerospace Center, Institute of Technical Physics, Pfa~enwa~dring 38-40 D-70569Stuttgart, Germany We present an adaptive optics approach to improve the image quality of telescopes observing targets through atmospheric turbulences. Intended as an enhancement for offthe-shelf imaging systems an f/10 achromatic lens telescope is expanded by relay telescopes and dichroitic beam splitters to satisfy the adaptive optics requirements. A high speed Shack-Hartmann wavefront sensor and an adaptive membrane mirror are located in conjugated planes. A non-deterministic PC system provides a fast closed-loop frequency of 500 Hz. The system characteristicsare investigated and first results in terms of wavefront diagrams and resolution charts are presented.

. Introduction Images recorded with long-range high resolution surveillance systems are often blurred due to the propagation of light through turbulent layers [l]. Typical scenarios are the identification of fast moving objects observed in horizontal direction from ground stations or flying platforms. In these applications, the imaging telescope is usually stabilized on a mechanical platform and equipped with a high accuracy laser beam tracking system. Besides ground-based applications, we foresee the use of this method in conjunction with laser sensors operated in aircrafts. Here, the beam has to propagate through an airplane window, where a subsequent turbulent boundary layer. This boundary layer is omnipresent outside the aircraft body, and will strongly distort the laser beam, unless being precompensated.

2. Optical Setup A resolution chart is used as the target object. The fiber output of a laser beam at h = 780 nm is implemented as a point source in the target plane to provide a spherical reference wave required by the adaptive optics system. After a free propagation length of 4 m, we created a turbulence layer by means of intermixing the air flows from a heating coil located on the optical table and a flow box mounted above the optical table. We did not attempt to identify the 465

466

characteristics of this turbulence layer (especially its correlation with Kolomogorov statistics). The 3 inches diameter achromatic objective lens of the telescope has a focal length of 750 mm. The adaptive optics (AO) system is intended as an add-on unit for imaging telescopes and hence had to fulfill several conditions: First, it had to be configured such that it allows toggling between the A 0 and non-A0 path; Second, the A 0 setup should be designed as simple as possible with a minimum number of additional optical elements; Third and being self-evident, a degradation of the imaging quality should be prevented. The optical setup can be inferred from Fig. 1. . (

10 mm

USAF test groups 11 single mode fiber Laser: 780 nm,cw

Figure 1. Optical setup of the adaptive optics laboratory testbed. The conjugated planes of the turbulent layer are marked by circled lines. Adaptive membrane mirror and Shack-Hartmann wavefront sensor are supplied by Imagine Optic [ 2 ] .

With the current setup, the tipkilt correction is also performed by the A 0 mirror, but should favorably be done with a separate tiphilt mirror (see Fig. 1) in conjunction with a position sensing device (quadrant diode) [3]. The fiber port is suitable to check and characterize the adaptive optics path. The adaptive mirror with an aperture of 15 mm is located in a plane conjugated to the turbulent layer. The electromagnetically operated deformable membrane mirror is driven by

467

52 coils, which are located behind a membrane. Small permanent magnets are fixed on the membrane to ensure full pushlpull operation of k 6 pm per actuator. The mirror type is known for its high linearity and low hysteresis in combination with a limited cut-off frequency of about 300 Hz [4]. Another conjugated plane on the Shack-Hartmann wavefront sensor is provided by a relay telescope. The wavefront sensor can acquire full frames of 256 x 256 pixels with a rate of around 1 kHz with a microlens array of 16 x 16 microlenses being used to reconstruct the wavefront. The wavefront sensor has high wavefront accuracy (U100) and large dynamic range (50h).Dichroitic beam splitter and edge filters are used to spectrally decouple the reference wave acquisition with the target imaging process in the VIS range. 3. System characteri5tic5 The actuators were designed to compensate the spatial frequencies under typical turbulence conditions. These spatial characteristics of the mirror are investigated by presetting the closed-loop control to generate only pure Zernike polynomials. The results of the Zernike coefficients and the corresponding deviations after convergence of the mirror membrane (cross-hatch bars) are shown in Fig. 2. As expected the amplitudes of high order polynomials are reduced - but additionally it seems, that it is easier for the adaptive optics system to generate azimuthally varying polynomials than radially varying polynomials.

30

35

Brel PVerror ES re1 RMS error

30

_I

P 20

25

.E

e

20

25 =j

.-

2 15 10

15 10

5

5

0

0

Figure 2. Adaptive mirror shapes of pure Zemike polynomials. The peak-to-valley (PV) and the correspondingdeviations compared to the Zemike polynomial shapes are displayed.

468

The wavefront sensor is running at 1 kHz, the wavefront reconstruction reduces the frequency down to 680 Hz, and the adaptation can be done under closed-loop configuration with a bandwidth of 500 Hz. Our closed-loop system applies the singular value decomposition (SVD) formalism for zonal wavefront reconstruction and correction. The first calculated singular modes are printed as contour plots in Fig. 3. We investigate the closedloop system to determine how many of these system-inherent modes are necessary for the optimization and stable operation depending on the closed-loop gain. As can be inferred from Fig. 3 there is an upper stability limit at 51 modes. If the number of used singular modes is decreased, the calculation can be done faster but the residual wavefront distortion will increase. An optimum of 46 modes was found for a closed-loop gain of 0.2. 0.6

c1

r: 0.3

cia?, 5

g

0.2

0.0 0

5

10

15

20

25

30

35

40

45

50

55

singular modes for control matrix

Figure 3. Influence of the control matrix singular modes (SVD) on the closed-loop performance. A minimal residual wavefront distortion could be obtained with 46 singular modes for a gain = 0.2.

To characterize the performance of a feedback control we determined the system error rejection function. Therefore, only one actuator was excited with a voltage signal defined by fixed amplitude and a frequency sweep form 0 Hz to 1000 Hz. Simultaneously the closed-loop adaptive optics calculate the corresponding control signal to minimized the excited stroke. Depending on the closed-loop gain and the actuator, one can calculate the error rejection curve showed in Fig. 4. The adaptive mirror limited the bandwidth of the A 0 system to 30 - 40 Hz.

469

The temporal closed-loop performance is additionally limited by different system properties like the delay of camera exposure duration, processing time and adaptive mirror response. Furthermore, the non-realtime windows operating system introduces a timing jitter of the closed-loop. 5 0

R.5

;EL,

.-cm

r:

-10

0

f3 .% -15 2

-20 -25 0

10

20

30

40

50

60

70

80

90

100

~equency[Hz] Figure 4. System error rejection curve as the response of the marked actuator. A maximum rejection gain of 20 dB for low frequency disturbances and a 0 dB bandwidth at 30 Hz could be determined.

4. Imaging results In a first step, the system was run with the A 0 system under fast closed-loop operation, but without artificially introduced turbulence. All static aberrations of the optical setup were corrected and the adaptive mirror was flattened. In a second step, the adaptive optics closed-loop was disrupted and the mirror voltages of the last correction loop were fixed as they are. This ensures that we measure only the influence of the dynamic turbulences. A direct comparison of the improvement in imaging quality due to the adaptive optics is now possible. Typical wavefront distortions of the artificial turbulence layer are on the order of peak-to-valley (PV) 1.5 pm and RMS 0.2 pm. Therefore, strong scintillation is currently not object of the investigations. After we have turned on again the closed-loop the RMS was improved to 12 nm and the PV value could be optimized at 73 pm. In Fig. 5 are shown the corresponding wavefront diagrams (Please note the different scaling in Fig. 5). Fig. 6 visualizes the image quality improvement.

470

Figure 5. Typical wavefront distortion causes by t h e ~ a l l yinduced turbulence

Figure 6. Resolution chart blurred by turbulence

Measured wavefront during the closed-loop run of the adaptive optics system

Corrected resolution chart

5. S u ~ a r and y Outlook

Promising applications will be imaging and beam propagation through a single turbulence layer located in a well-known distance in front of a high quality imaging telescope. Small residual blurring and moving image parts could be observed in closed-loop operation, being due to bandwidth limitation of the adaptive mirror. An update of the fast closed-loop software including the ability to use the features of multi-core processors is under progress. A replacement of the adaptive mirror will improve the system bandwidth of the A 0 system. eferences

1. 2. 3. 4.

M.C. Roggemann and B. Welsh, Imaging through turbulence, (1996). Imagine Optics, 18 rue Charles de Gaulle, Orsay France I. Buske and W. Riede, Proc. SPIE 6397,63970J(2006). E. J. Fernandez, L. Vabre, et al., Opt. Express 14, 8900 (2006).

SIS R.J. EASTWOOD, A.M. JOHNSON, C. KOLPER, A.H. GREENAWAY. Waves and Fields Group, EPS-Physics, David Brewster Building, Heriot- Watt University, Edinburgh, EH14 4AS, UK Aperture synthesis instruments clearly demonstrate the fundamental role of redundancy in adaptive optics wavefront calibration. This controlled redundancy facilitates the formulation of wavefront sensing or active instrument calibration in terms of a system of equations with the same structure, and we give a synopsis of these methods here. Dilute apertures are also being investigated for use in line-of-sight optical communications, where atmospheric perturbations cause signal fadddrop out. We report preliminary work on experimental and theoretical modeling of scintillation statistics resulting from atmospheric propagation, eventually to be used, to inform array design so as to maximize the probability of signal detection.

1. Intro~uction 1.1. I ~ a g i n gwith dilute apertures Dilute apertures sample the spatial frequency content of a scene over a finite number of discrete regions. Typically the sub-apertures can be distributed over an area much greater than it is feasible to construct a monolithic aperture, giving a corresponding increase in angular resolution. When imaging through turbulent atmosphere, the phase at each aperture is likely to be variable and uncorrelated from aperture to aperture, introducing distortion into the image. Here we briefly give an overview of our work on a method for active calibration of piston only aperture phase. We then turn to the main focus of this paper - illustrating the effects of non-calibration of the array under turbulent atmosphere for free space optical communications.

1.2. Free Space ~ p t i c aCom~unication~ l Optical communications by fibre optics have significant advantages over traditional free space radio and electronic methods: data bandwidth limitations are significantly higher, eavesdropping is more difficult (a feature shared with electronic transmission) and spectral licensing is not needed (again shared with 471

472

electronic communications). Of course, these advantages can only be realized in point-to-point transmission along a predetermined path. Free space optical communications (FSOC) aims to enable high bandwidth data links between distant, and most importantly, moving platforms (e.g. airborne), especially where secure transmission is a requirement. Such platforms also need to be low in mass, therefore be low power, and of as low a cost as possible. In general this is implemented, in either half or full duplex, by laser propagation from the source onto a detector at the target, typically using simple binary encoding. Unfortunately, propagation of a laser beam through the turbulent atmosphere leads to the break-up of the amplitude field into caustics and eventually speckles as the distance increases. This is essentially coherent imaging of a distant point through a highly distorting medium. Detection of the raw signal then becomes a random process as regions of scintillation and darkness traverse the detector, driven by the motion of the turbulence. Here we report our work on examining the properties of wavefront intensity functions at various propagation distances, and their relationship with the aberrations causing them. Our aim is then to understand how best to design aperture arrays so as to maximise the probability of at least one collector detecting the aberrated signal, mitigating signal dropout.

edundant Spacings Calibration In a dilute aperture array possessing a limited number of repeated spacings, redundant spacings calibration allows active piston phase correction (for imaging) or explicit calculation of object and instrument phases to be made so that a reconstruction of the object is possible [ 11. Both of these cases are related by their use of the same matrix in dealing with the instrument phases, indicating that the methods share a number of properties. Significant among these is the uniqueness of the solution [2]. 2.1. Active correction

As compared to the unaberrated case, the Parseval’s theorem tells us that the quality of imaging is maximised if the phase component of the pupil-wavefront auto-correlation consists of a tilt plane. In the case of a dilute aperture, this means the phases corresponding to the spatial frequency sampling patches should lie on this plane. Generally, in order to achieve this, some correction on the aperture phases is needed. This requirement can be represented as a system of linear equations that, for each aperture pair, describe the relationship between the correcting phases, auto-correlation tilt values, and wavefront phases. If and

473

only if the array configuration possesses sufficient redundancy can the tilt values in N - 3 of the equations cancel [l]; then image sharpness be used as an evaluation function to match the aperture phases to the tilt plane.

2.2. Phase Retrieval According to the van Cittert-Zernike imaging theorem, taking the inverse Fourier transform of the image allows information about the combined object and instrument phases to be found in terms of the corresponding measured phase. The matrix used is identical to that for active correction, indicating the common basis and shared properties of both methods. Once the object phases have been calculated, this information can be used along with the corresponding magnitude components to reconstruct the object brightness distribution. The instrument information alone could be used to inform an active correction, or as a wavefront sensor, sampling the phase at each aperture location so that the whole wavefront can be reconstructed.

3. Free Space Optical Communication Addressing the signal detection problem in terms of an array of sparsely located small apertures allows the weight and cost requirements mentioned earlier to be satisfied, while increasing the subtended angle of collection. However, in doing so, we introduce the possibility of i l l u ~ n at i o nbeing focused between the apertures and signal dropout resulting. We are interested in the probabilistic properties of the intensity functions at the array plane, and especially their relationship to those of the atmospheric conditions and propagation distance from which they result. Our approach has been to validate experimental, simulated and theoretical findings as the basis for elucidating the theoretical relationships in the future.

3.1. Theoretical model We made use of the random walk phenomenological model 131 wherein intensity statistics are calculated based on a description of the source field as a finite number of scattering points; each point in the target field then results from a finite complex summation. Subject to assumptions that each of scattering centres is emitting with the same amplitude, their phases are subject to a uniform distribution, and they are spatially distributed according to the negative binomial distribution, the scintillation index

474

calculated at near-to-mid field propagation is then found in closed form to match the K-distribution [3].

3.2. ~ b # r a t Experiments #~ and ~ i m u ~ ~ n s As we are unable to perform genuine experimental investigation of the laser propagation over several kilometres, we devised a simple thin phase screen experiment to represent this in the laboratory. However, as the random walk model is essentially also a thin screen method, this experiment provides only a verification under this hypothesis. Once the theoretical model is shown to be reasonable, however, we can justifiably generalise it to more complex and realistic situations. Furthermore, to validate our laboratory approach, we used computer simulation of the situation being modelled by the experiment.

3.3. ~ x p e ~ m e n t s The experimental setup is shown in Figure 1. A collimated 633m laser beam was propagated through a distorted diffraction grating (DDG) creating correlated random phase functions in its orders by the detour phase effect, one of which is selected by an iris and acts as the thin screen atmospheric approximation. A programmable grating approach has previously been used [4]. The beam is imaged by lens L2 before being re-imaged by L3 and the scintillation pattern captured by the detector. By translating L3 we were able to image the plane a distance behind the grating, the complex amplitude at which is such that when propagated to the grating plane would result in the thin screen phase function.

Figure 1, A simple laboratory demonstration, propagating a laser beam a range of distances through a thin screen model atmosphere generated by a distorted diffraction grating.

475

Scintillation statistics for a variety of simulated atmospheric conditions were calculated from the images of each propagation distance. Under the assumption of ergodicity across a reasonable area of the captured patterns, frequency distributions and scintillation index versus propagation distance were found within this area and compared with the theoretical and simulated predictions.

3.4. Simu~tion~ The propagation simulations were performed by the angular spectrum of plane waves method [51, using the DDG phase function with uniform amplitude as the source field. The results were found to be in good agreement with experiment, as shown in Figure 2, where examples of the experimental and simulated intensity functions are shown for the same applied conditions, and Figure 3, where the frequency distribution of scintillation index under near and far field propagation are compared including with fit to the theoretically predicted density functions.

(a)

@)

Figure 2. Two sets of caustic patterns, corresponding to phase screens With a long (a) and a short (b) correlation length, generated in the laboratory (upper) and computationally(lower).

J

re

Figure 3. Scintillation index frequency distiibutions for near and far field propagation, calculated from experimental and simulated intensity patters, and compared to the probability density functions predicted by theory.

476

3.5. Second Phase Screen A programmable spatial light modulator is currently being used to improve the experimental model by introducing a second thin phase screen to account for aerial amplitude effects and anisoplanatism, wavefront curvature and timevarying effects.

Ae~owledgemen~ Effort sponsored by the Air Force Offke of Scientific Research, Air Force Material Command, USAI?, under grant number FA8655-05-1-3050. The U.S. government is authorised to reproduce and distribute reprints for government purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.

References 1. A.H. Greenaway, Terrestrial Optical Aperture Synthesis Technique (Toast), Optics Communications, 58(3), p. 149-154, 1986. 2. A.H. Greenaway, Self-calibrating dilute-aperture optics, SPlE Proceedings 1351, p. 86-96, 1990. 3. E. Jakeman, K-distributed noise, J. Opt. A: Pure Appl. Opt., 1, p. 784-789, 1999. 4. C. Dainty, Low cost adaptive optics, Opt. Pura. Apl., 40(1), p. 13-15,2007. 5. J. W. Goodman, Introduction to Fourier Optics (2ndEd), p. 55-61, McGraw Hill Higher Education, 1996.

Adaptive optics system for a small telescope GLEB VDOVIN, MIKHAIL LOKTEV and OLEG SOLOVIEV Flexible Optical B. V., Rontgenweg 1 , 2624 BD, Delft, the Netherlands *E-mail: glebQokotech.com We describe a compact integrated module implementing a low-cost portable adaptive optics (AO) system. This module is targeted t o a small amateur telescope with the primary mirror diameter in the range of 25 cm to 1 m. The first tests with a 25 cm telescope have demonstrated a stable closedloop operation and correction of aberrations using natural guide star with a magnitude of 2.2. To our knowledge this is the smallest adaptive optical telescope ever operated with the A 0 loop closed on a natural star. Apart from astronomy, the system is applicable as a general-purpose A 0 system for correction of static and dynamic aberrations in laser systems and in some vision applications. Keywords: Amateur astronomy, adaptive optics deformable mirror, wavefront corrector.

1. Concept of a low-cost A 0 system

Low-cost adaptive optics is the bet of technology-pushers. It is widely believed that as soon as adaptive optics is inexpensive, many useful and profitable applications will pop up. One of these potential applications is in astronomy. The modern high-end astronomy is already strongly dependent on the adaptive optics, however the low-end astronomy with small telescopes and low budgets is believed to stay free of adaptive optics simply because the amateurs can not pay for using the AO. Moreover, it is more difficult technically to build an A 0 system for a light-starved small telescope. On the other hand, for many amateurs, a low-cost A 0 system would be quite beneficial even in statical case, as many of them do not have a good permanent location for astronomic observations and use portable systems exposed to static aberrati0ns.l Dynamically, the A 0 system could provide a certain improvement in the performance compared to existing commercial 477

478

systems for amateur telescopes that only partly correct for t i ~ - t i l t . The ~l~ real A 0 should allow for stable imaging of bright objects such as stars, double stars, and planets. Another advantage of using such a system is that it can correct for aberrations of the telescope itself, improving the quality of optics, for instance making the cooling period of the mirror of a portable telescope also available for observations. In some cases, the correction of the static aberration can be done on a bright star only once, and then the system can be used in static correction mode. Preliminary technical requirements for this system (based on a very useful discussion in sci.astro.amateur newsgroup) are as follows: To be mounted in 1.25 inch ocular socket. To be used with telescopes with diameter in the range of 25 cm to 1 m. To be implemented as an afocal mirror system, transparent in the visible and near IR and fully operational even with A 0 switched off. To achieve this, we’ll use a system with a field of a couple of mm (in the primary focus) for a focal ratio of 1/10. The field and F/# are compromised to reduce the complexity of the optics, but the field will be limited anyway by the anisoplanatism of the A 0 and the F/# must be small for a high-resolution imaging. To have a1 least 19 degrees of freedom (depending on the seeing can be good to correct up to 13 Zernike terms to about 10% of the uncorrected value). To operate on a natural star with magnitude of at least 4 (with a 25 cm telescope), using 50% of light for running the A 0 and 50% for registration. To be easy in setting up and running. To use two cables connecting the system with the deformable mirror controller and ShackHartmann wavefront sensor, both operated by a dedicated laptop N

PC. The total weight of the optical correction unit mounted to the telescope is about 2 kg. The mirror controller should weight about 1kg including power supply, with some extra for cables and laptop. In case of serial production, the target price should be less than 5 thousand euros for the complete setup without computer. The idea of a low-end A 0 for an amateur is complementary to the future giant A 0 projects. Such a system will certainly have at least some

479

market, bringing the low-cost A 0 to students and amateur astronomers and making the A 0 foundations in the professional astronomy even more solid. When used in non-astronomical fields, the newly developed portable A 0 module will facilitate integration of the A 0 into existing systems, saving the development time and money. 2. Optical system

The optical correction unit is built using afocal Ofher configuration with spherical mirrors. It has two functions:

It images the input pupil onto the deformable mirror and it translates the position of the primary focus without changing the geometrical beam parameters (but correcting the aberrations).

Fig. 1. CAD drawing of the portable compact A 0 module.

The correction of aberrations is performed by a specially designed micromachined membrane deformable m i r r ~ r . ~ The wavefront sensing part consists of a low-cost CCD camera with a USB interface. The camera is fed by a 50% of the available light through a beamsplitter. The Hartmann-Shack sensor operates with 49 subapertures. The system is controlled by the Frontsurfer software package debveloped by O K 0 Technologies. The CAD drawing of the first prototype of the optical system is shown in Fig. 1.

480

3. Optical test results The first prototype of the system with total dimensions of 188x291~145mm was assembled and tested at O K 0 Technologies. The optical correction unit mounted on 25 cm a telescope is shown in Figure 2.

Fig. 2.

Compact A 0 module mounted on a 25 cm telescope.

The first tests of the A 0 system was performed with a laser source. A clean aberration-free collimated light beam was focused into the primary focus. Exactly as it was predicted by the model, the system has shown some amount of astigmatism caused by the off-axis operation in the Offner setup. This astigmatism - see Fig. 3 is almost completely compensated by the closed-loop operation of the system. A dynamic correction test was done with the dynamic aberration introduced by a rotating disk aberrator. The system demonstrated satisfactory correction with frame frequency of the order of 45 Hz. This frequency can be significantly increased by using a more powerful laptop. In another test, the system was mounted on a 25 cm Newtonian telescope with 1.2 m focus. We used a 2x Barlow lens to adapt the focal number of the telescope to the range acceptable for the A 0 system. We corrected the image of a LED placed at a distance of about 50 m away - which also served as a guide star for running the adaptive optics. On 12 Aug., 2007, M. Loktev tested the system on real sky objects:

481

Fig. 3. Interferogram of the intial aberration of the assembled AOS, model far field, measured far field (top row left to right); interferogram of the corrected aberration of the assembled AOS, model far field, measured far field (bottom row, left to right)

Altair (apparent magnitude of 0.75) and Sadr (magnitude of 2.21). In both cases the object also served as a guide star for running the adaptive optics. The wavefront sensor was operated with software-generated reference, that allowed for fast dynamic correction combined with manual control of major low-order Zernike terms. With the A 0 correction off, the image was strongly aberrated, mainly due to the astigmatism of the A 0 system; static aberrations of the telescope and the dynamic aberrations due to the atmospheric turbulence were found less significant in these tests. With the A 0 correction on, the static aberrations were compensated which resulted in the subjective image quality similar or better than those without the A 0 correction. Frontsurfer controls were used for fine adjustment of the defocus and low-order aberrations. We found that the A 0 allows for a very fine focus contol, much finer than with the mechanical adjustments of the telescope. Since the ErontSurfer software allows for precise control of low-order Zernike terms, we found it to be a very efficient tool for subjective corrections of the static aberrations of the telescope and even of the observer’s eye - in a way similar to the described in.5

482 4. Applications and future work

Although the first tests of the system with a natural star were surprisingly successful, more effort and testing is needed to define the field of application in which the amateur astronomer would benefit from such a system. Unfortunately the summer of 2007 in the Western Europe was extremely rainy, so we didn’t have too many clear nights for extended testing of the system on a wide range of objects and in different atmospheric conditions. We plan to extensively test the system using amateur telescopes in the range 25 cm to 1 m, before the end of 2007. Outside of the astronomic field, the low price and compactness of the system, make it very attractive in applications that require low-cost dynamic correction of low-order aberrations, such as laboratory laser setups and vision systems. 5. Conclusions We have designed and implemented a compact portable low-cost A 0 system targeted to a small telescope with a diameter in the range of 25 cm to 1 m. Laboratory tests have demonstrated satisfactory correction of the statical aberration of the system itself and good correction of the dynamic aberrations introduced by a rotating disk aberrator. The first test on natural sky objects conducted by M. Loktev on 12 Aug., 2007 with a 25-cm telescope, demonstrated stable operation of the A 0 feedback loop and efficient correction of static aberrations with a natural star of magnitude -2.21. To our knowledge this is the smallest adaptive optical telescope ever operated with the A 0 loop closed on a natural star.

References 1. Discussion in sca.astro.arnateur newsgroup: http://groups .google. com/group/sci. astro .amateur/ b r o w s e - ~ / t h r ~ d / a ~ ecfb7e ~ g f77~668,’ 2. Santa Barbara Instrument Group, Inc., AO-8 and AO-L Adaptive Optics systems, http://www.sbag. com/sbwhtmls/ao8.htm

3. Stellar Products, AO-5 Adaptive Optics system, http://www.stella~roducts.com/adaptive/A051at. htm 4. G. Vdovin and P. M. Sarro, ”Flexiblemirror micromachinedin silicon,’’Appl. Opt. 34, 2968- (1995) 5. G. Vdovin, M. Loktev, A. Simonov, V. Kijko, S. Volkov, ”Adaptivecorrection of human-eye aberrations in a subjective feedback loop”, Optics Letters 30, 795-797 (2005)

FAST CORRECTION OF ATMOSPHERIC TURBULENCE USING A MEMBRANE DEFORMABLE MIRROR IVAN CAPRARO* , STEFAN0 BONORA and PAOLO VILLORESI

Department of Information Engineering, via Gradenigo 6/b 35131 Padova, Italy. CNR-INFM LUXOR Laboratoty for X ray and U V Optical Research, via Gradenigo 6/b 35131 Padova, Italy *E-mail: ivan.capraroQdei.zmipd.it In this paper we present a first working test setup for an adaptive optics system that we are developing. The aim of the research is t o compensate for atmospheric tilt in a Free Space Quantum Key Distribution (QKD) link. We use a home made membrane deformable mirror as active element and a novel fast PWM (Pulse Width Modulation) driven amplifier with a DSP (Digital Signal Processor) developed in our labs. The system implementation choices and setup are presented as well as the lab calibration of the system and a outdoor trial over 100 m in urban environment.

Keywords: Quantum Cryptography, Deformable Mirror, Free Space Link, Atmosphere, Tilt.

1. I~troduction

Atmospheric turbulence is one of the most relevant limitations for free space optical communication. These are rapidly becoming very important either for classical last mile traffic distribution and for guarantee secure communication through quantum key distribution protocols (QKD) or chaotic steganography.192Other attempts to solve this problem run at sub hertz loop frequency correcting only for slow drift due to daily temperature gradient.3 In urban environment the frequency of turbulence induced fluctuation is much higher and its correction requires different approaches such as fast adaptive optics devices. Electrostatic membrane mirrors are a relative inexpensive and better solution to this problem compared to MEMS or piezoelectric devices that present problems of low reflectivity, heat and costs.

*

483

484 2. Hardware and Software Description

The mirror, completely developed in our laboratory, is a thin nitrocellulose membrane aluminum coated deformable by 37 hexagonally shaped electrodes. It is deformed by electrostatic force created by applying a high voltage drop between the electrodes. The membrane is 5 mm thick; its initial flatness is less than 60 nm rms. Pulling all the electrodes at the maximum voltage of 230 V, the distance from the central point of the deflected surface to the plan0 is about 10 pm as depicted in the interferogram. This deformation is a paraboloid that corresponds to a focal length of about 2 m. Fig. 1 shows the interferograms, taken by a Zygo interferometer, of the flat surface and of the mirror pulled by the half of maximum voltage: 115V.

Fig. 1. Interferogram of the flat surface and of the mirror pulled by half of maximum voltage. Flat Peak t o Valley 295 nm, RMS flatness 52 nm.

In order to detect the tilt displacement at the focal plane of our receiver we use a PSD (Position Sensing Detector). This is a 9 x 9 mm Dumaa sensor with a resolution of O.lpm, an analog bandwidth of 30KHz and a minimum input power of 1pW. Our mirror driver uses the PWM (Pulse Width Modulation) modulation to produce the high voltage driving signals for the mirror electrodes. The kernel of whole system is a DSP processor card that performs three main tasks. It acquires the x,y analog signals corning from the PSD using a 12-bit AD converter and a multiplexer, runs the algorithm and produces the 37 PWM signals. The mirror, the electronics and the PSD sensor are depicted in Fig. 2 (left). The C++ software running in the DSP has been designed to facilitate calibration and usage in different operating conditions and to optimize the closed loop performances in terms of DSP memory usage and algorithm speed. The software also take into account non perfect radial symmetry of

485

Fig. 2. Left: the home made deformable mirror and electronic unit and the DUMA Position Sensing Detector. Right: the optical setup: a) Tx telescope b) Rx telescope c) Signal laser d) Alignment laser e) filters f) Deformable mirror g) Focusing lens h) PSD detector i) Electronics.

the mirror itself compensating it in order to correct the maximum possible deviation. 3. Optical Setup

The optical setup for the characterization of the system is composed by the following elements. At the transmitter a 10mW, 850 nm laser diode and a red laser diode, used for initial alignment, are magnified by a keplerian telescope (M=12). At the receiver, 100 m away from the transmitter, a Galilean telescope (M=0.13 ; D=8cm) collects the light that is subsequently directed toward the membrane mirror. After that the beam is focused with an f=150 mm lens and deviated towards a ND filter and an interferential filter before it reaches the PSD detector. A block scheme of the system is depicted in Fig. 2 (right). 4. Calibrations and Results

The overall tilt bandwidth of the system in closed loop configuration is found to be 400Nz with a max tilt of 400rad. The bandwidth is depicted in Fig. 3. In Fig. 4 you can see 60 seconds of sampling of the turbulence effect on the spot position and its relative correction. On the y-axis is represented the distance of the spot centroind from the target position. The rms displacement goes from 7.2pm (48prad of tilt) to 1.4pm (9.3prad of tilt) demonstrating an improvement of 5 times in the radius. A better picture of the situation can be deduced from Fig. 5 , which corresponds to the trace of the centroid positions on the PSD detector screen after 60 second of integration, for the corrected and not corrected beam respectively. Notice that this image gives also a first rough measure of the correla-

486

0 0 01

Fig. 4. Uncorrected (bottom) and corrected (top) beam centroid displacement from a target zero point over 60 seconds.

tion between the two axis that result almost uncorrelated. The corrected spot is comparable with the noise of the system measured during calibration in the lab. that is a limit for the displacement of the corrected beam. This corresponds of a rms tilt of Sprad (rms displacement of 1.35pm). The maximum displacement caused by the turbulence (40pm) instead is not the maximum that we can correct i.e. the maximum tilt projected on the PSD plane (60pm for 400prad). A frequency analysis has been carried out and the power spectral density is depicted in Fig. 6 .

487

14

Fig. 5.

Spot centroids trace on the PSD plane after an integration of 60 seconds.

Fig. 6.

Power Spectral Density of the tilt induced displacement.

The correction system reduces unwanted tilt with a maximum frequency of 400 Hz. Although being present over the whole correcting bandwidth the effects of tilt correction at least in this setup and conditions is appreciable for frequencies up to 60Hz. Those result where used to calculate some useful parameter of the beam propagation: we have a standard deviation of 7.2pm on the position on the PSD due to atmospheric effects. Retracing the beam through the f = 15mm focusing lens and the M = 0.13 receiving telescope we calculate the tilt angle at the entrance of the receiver from the spot displacement on the PSD

488

detector: we obtain a: = 4.49 x lO-l'rad of tilt angle variance. Inverting the formulas for the tilt angle variance and the Fried coherence length for a horizontal path5 we obtain:

-5/3

A2

-

4Ln2 Plugging our results into these formulas we get a Fried coherence length of ro = 7.6 cm and a index of refraction structure constant of C: = 3.16 x m-2/3. If we compare these values with a standard model such as SLC daytime Model6 we obtain: C: = 1.7 x m-2/3and ro = 11 crn demonstrating a good agreement with the experimental data. 5. Conclusions

The system presented is capable of correcting fast tilt jitter caused by atmospheric turbulence. It has been tested in an urban environment over a loom optical path. All the devices and the electronics have been developed in our labs and are low cost and performing devices. The control software guarantees an easy set up and good correction capabilities with a reduction of the displacement variance up to five times. Further developments will be t o test the system in increasing distances up t o some kilometers, and integrate the system in a Quantum Key Distribution system in order t o verify the increase in key rate due t o the better spatial filtering.

eferences 1. M. Gabay and S. Arnor, Optical Engineering 44 (2005). 2. S. Donati and C. Mirasso, IEEE Journal of Quantum Electronics 38 (2002). 3. H. Weier, T. Schmitt-Manderbach, N. Regner, C. Kurtsiefer and H. Weinfurter, Fortschr. Phys. 54, 840 (2006). 4. S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino and P. Villoresi, REVIEW OF SCIENTIFIC IN STRUM EN^^ 77 (2006). 5. R. K. Tyson, Principle of Adaptive Optics (Academic Press, 525 B Street, Suite 1900, San Diego, California, Usa, 1997). 6. Atmospheric propagation of Radiation (SPIE Optical Engineering Press, 1996).

ERIC TURBULENCE A 3KM ~ O ~ I Z O N T A ARTMANN ~ A ~ E F ~ OSENS N T R.Mackey*, K.Murphy and C.Dainty

Applied Optics Group, National University of Ireland, Galway, Galway, Ireland *E-mail: ~th.mackey~nuigalway.ie http://opt~cs.nuigalway.ie R.Mackey A 3km optical link operating at 635 nm has been set up across Galway city to measure the effect of atmospheric turbulence on beam propagation and to demonstrate the effect of phase compensation with an adaptive optics system. In this paper we use a Shack-Hartmann wavefront sensor to measure the strength of the atmospheric turbulence along the propagation path in terms of the angle-of-arrival fluctuations and try to detect the presence of branch points from the wavefront sensor slope data using the branch point potential method proposed by Wild and Le Bigot.'

Keywords: Atmospheric turbulence; Scintillation; Branch point detection.

1. Introduction

In recent years there has been increasing interest in applying adaptive optics (AO) in strong turbulence conditions along horizontal paths and at large zenith angles for application to line-of-sight free-space optical (FSO) communication. Atmospheric turbulence effects of scintillation and beam wander severely degrade the performance of FSO communication systems introducing signal fades and surges, increasing the bit-error-rate (BER). These errors are particularly limiting in low-light level applications such as quantum key distribution.2 Phase compensation of an outgoing laser beam has the potential to reduce the BER, however, in strong scintillation conditions conventional adaptive optics techniques of wavefront sensing and phase conjugation break down due to the presence of phase singularities in regions of zero i n t e n ~ i t y These . ~ ~ ~ effects make wavefront sensing difficult 489

490

and necessitate the use of branch point sensitive wavefront

reconstructor^.^

2. 3km Propagation Path.

A 3km optical link has been set up across Galway city to measure the effect of atmospheric turbulence on beam propagation and to demonstrate the effect of phase compensation with an adaptive optics system. The beacon laser used for wavefront sensing is a 5mW 635nm diode laser. It is launched through a 90mm diameter Meade ETX telescope from the roof of the seven-storey Eircom building on the edge of Galway City towards the optical receiver at the Applied Optics group at NU1 Galway. The beam height is approximately 10-20 m above the ground and crosses varying landscape; including roads, commercial buildings, a river and open grass1and.The beam is made to diverge slightly so that the diameter at the receiver is approximately 3 m. For all analysis it is approximated as a plane wave.

3. Optical Receiver The receiver is a 125 mm diameter Maksutov-Cassegrain with an adaptive optics system comprising of a Tip-Tilt mirror, an O K 0 37 actuator membrane deformable mirror and a Shack-Hartmann wavefront sensor (SHWFS) with high speed CMOS camera capable of framerates greater than 1000 fps over a region of interest of 320 x 320 pixels (figure 1). The wavefront sensor consists of a square lenslet array with pitch of 100 pm and focal length of 2.7 mm. An optical relay is used between the lenslet array and the detector with a magnification of 1.5. There are 21 lenslets across the pupil diameter with a total of 196 useable subapertures within the pupil. The lenslet diameter in the telescope pupil plane is 5.7 mm. 4. Wavefront Sensor Analysis Each measurement set contained 3000 frames of data measured at 1023Hz. After flat-fielding and dark frame removal, the frames were combined to create an average image. A centroiding algorithm was used with intensity thresholding to find the reference centroid positions. These positions where then used to define search regions in each frame of data. The sum of pixel values in each search region was compared with a minimum threshold intensity and a saturation intensity. Search regions with the sum of pixel values falling outside this range were discounted from the analysis.

491

I

OK0 37-actuator membrane mirror

,To PSF

e

Photon Focus CMOS camera Framerate > lOOOHz

Fig. 1. Schematic of the adaptive optics receiver with Shack-Hartmann wavefront sensor

Fig. 2. Average image of 3000 frames of data taken over 3 seconds (left). A typical frame of scintillated Shack-Hartman subimages (right)

5. Angle-of-arrival Fluctuations The variance of differential angle-of-arrival was used as a measure of the turbulence strength. Following Sarazin and Roddie@ the longitudinal and transverse variance of angle-of-arrival for subapertures separated by a distance, d, for a plane wave are given by

( ~ z , L ( d0), = 2B,(0,0)

"&(O,d)

[-

1 0.56 -

= 2Ba(0,0) 1 - 0.83

(~)-""1 -

492

where the the variance of the angle-of-arrival of a single subaperture, B,(0,0), is found by using the structure function of the phase for a plane wave to define the phase variance between two points separated by the diameter of the subaperture, D.

where r g is the F'ried parameter and

X is the wavelength.

Fig. 3. Differential image motion with Shack-Hartmann lenslet separation of 5 subapertures. Figure (a) is an example of turbulence strength in the middle of the day with an estimated TO of 1.4 cm. Figure (b) is an example of turbulence strength 1.5 hours after sunset, with an estimated TO of 4.4 cm.

In figure 3, examples of measured probability distributions of differential angle-of-arrival over a 3 second period are plotted for strong and weak refractive index fluctuations. 6. Branch Point Detection

The wavefront sensor slope data can also be used to detect the presence of branch points. When branch points are present in the phase the slopes contain a curl component that is not reconstructed by the usual least squares gradient reconstructor. The phase that is not reconstructed is the so-called hidden phase, +hid, which can be expressed as the curl of a vector potential, h.

493

where A is the geometry matrix of 1's and -1's representing the discrete gradient operator of the lenslet geometry used and W is the discrete curl operator. We use a method proposed by Wild and Le Bigot1 that uses the least squares inverse of the discrete curl operator to reconstruct the vector potential function from the non-zero curl component of the slope data. W can be expressed in terms of the geometry matrix A as,

where A, and A, are the discrete gradients in the x- and y-directions. The vector potential, h is found by applying the least squares inverse of W to the slopes. This can be recast in terms of the least squares inverse of the geometry matrix, A+, after a rotation of the slopes by 90".

where R,p is a matrix that rotates the slopes by 90". The weighting of in the least squares inverse is determined by the lenslet geometry matrix. In practice there are often many missing Shack-Hartmann subimages due to scintillation. To avoid biasing of the reconstruction, subapertures obscured by scintillation are removed from the geometry matrix before calculating the least squares inverse. In figure 4 a time sequence of the evolution of branch points over 3 frames is shown. The slope discrepancy after the least-squares component of the phase has been removed and the least squares reconstruction of vector potential are shown for comparison. 7. Acknowledgements This work was funded by Science Foundation Ireland under grant no. SFI/Ol/PL2/BO39C and by the Embark Initiative from the Irish Research Council for Science Engineering and Technology.

References 1. W. J. Wild and E. 0. Le Bigot, Opt. Lett. 24, 19O(Feb 1999). 2. T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger and H. Weinfurter, Phgs. Rev. Lett. 98, 1 (2007).

494 12 hj

8 0

0 0 0 0

I

"

Fig. 4. Evolution of branch points in a 3 frame time series. Slope discrepancy (top), and the least squares reconstruction of the vector potential plotted t o the power of 5 (centre and bottom).

3. D. L. Fried and J. L. Vaughn, Appl. Opt. 31,2865 (1992). 4. D. L. Fried, J. Opt. SOC.Am. A 15,2759 (1998). 5 . C. A. Primmenman, T. R. Rice, R. A. Humphreys, B. G. Zollars, H. T. Barclay and J. Herrmann, Appl. Opt. 34,2081 (1995). 6. M, Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

FIELD-ORIE~ED~ A V E F R O N TSENSOR FO LASER GUIDE STARS L. A. Bolbasova,* A. V. Goncharov,**and V. P. Lukin*

* Institute of Atmospheric Optics SB RAS, I Akademicheskii Avenue Tomsk, Russia, E-mail: [email protected] **Applied Optics Group, Department of Experimental Physics, National University of Ireland, Galway, Ireland We propose a modified approach [I, 21 to f m a laser guide star (LGS) with a collimated laser beam launched through the full aperture of a telescope. Using a special form of field stop (diaphragm) uniquely positioned for each subapertures, the wavefront sensor "sees" only a small part of the source corresponding to the area on the sky, which is cut out by the field stop. Each of these spherical waves subtends the area of a separate subaperture at the telescope pupil. Thus, the LGS is formed of a set of spherical waves. Since the Linear size of the subaperture is approximately equal to the coherence radius, the measured wavefront can be restored as a smooth phase function. The use of this scheme is investigated.

1. Introdu~tion It is well known that adaptive optical systems (AO) operating on astronomical telescopes with an LGS have limitations due to the effect of the focal anisoplanatism, since the spherical wavefront that comes from the LGS does not pass through the same portion of atmospheric turbulence as a plane wavefront arriving from an infinitely distant natural guide star (NGS). This effect becomes more sever as the diameter of the telescope aperture increases. Several different approaches have been proposed to overcome the focal anisoplanatism. In the method suggested by Buscher et al [l]. sensing of the turbulence-induced wavefront distortions is performed on the outgoing path of a collimated laser beam by forming an extended intensity pattern in the atmosphere and analyzing its distortion from ground. In a recent work 121, the prospect of using a collimated laser beam launched through the main telescope has been revisited and a special wavefront sensing scheme has been proposed. In the present paper we show a possible implementation for this scheme 131 and give an analytical analysis of the A 0 performance. 495

496

e ~ r i n c i ~of l ethe ~eld-orientedwavef~ontsensor The wavefront sensor (WFS) works with an extended area of the Sodium layer i~~uminated by a collimated laser beam. Using a special form of field stop positioned at the telescope focal plane makes possible to image only a small patch of the layer in each subaperture. This scheme helps to avoid image overlap in the adjacent subapertures and allows the WFS to operate only with narrow cones of back-scattered light traveling along a pre-defined direction. Because of this field-selecting function of the WFS, we refer to it as field-oriented WFS. Figure 1 shows how the field stop cuts the back-scattered light and reduces the original cone of light to a smaller cone that fills only one subaperture. Due to the reciprocity of travel of light, the central part of the image formed by each subaperture is motionless, while the peripheral part will show intensity variations owing to image distortion. These variations are used to recover the local wavefront tilt at each border of adjacent subapertures.

Wavefront from

Collmted beam

Telescope focal

\

Field-onented wavefront sensor

Figure 1. Schematic layout of the telescope, collimated laser beam, and the wavefront sensor

ciency of wavefront sensing with reduced cones of light In order to estimate the efficiency of the proposed scheme utilizing a collimated beam for illumination of the Sodium layer and reduced cones of the backscattered light, we compare it with the traditional scheme based on a full aperture cone. For simplicity we consider one spherical wave propagating along the telescope optical axis and N x N array of spherical waves filling the pupil. Assuming that phase fluctuations are Gaussian with a zero mean, the focal plane irradiance of an NGS after A 0 correction with a single LGS on axis is

497

For the last term in angular brackets in Eq. (1) we have:

where D!'(lzi, -p2),D,"(fi, - h )are structure function for a plane and spherical waves. In order to calculate Exp. (2), we describe phases for the case of a plane and spherical waves in the geometrical optics approximation [4]: X

= k SdrSfd'n(P,x-r)exp(~a+ ik@),

S,,(O,@)

0 X

S , (0,d ) = k Jdc I f d 'nn(Z, x -

5)exp[i@{l x + ia0 (1 - { I x)].

0

To facilitate the analytical calculation of Exp. (2),we introduce

where

p j ,j

= I,,,, N

are coordinates of sources of spherical waves. Then we have

Here we shall use the isotropic model of power spectral density for refractiveindex fluctuations defined by

where K,,, = 5.92 11, .

498

For a condition K , Ifil - fizl>> 1, the first two terms in Eq.(4) are found

In order to simplify the notation in the following analysis we write the square brackets term as a sum [. ..] = ZI+ 12 + Z3 + Z4 ,where

I, = - 2 n J Q [ K ( 1 - r / n ) l h -jjj1], I , = - 2 r J 0 [ K ( 1 - {/ x ) l f i ~- Pjl] 1, = 2 n J 0 [K l f i j (1 - 5 / X) - Pz+

9

file/ XI]

,

1, = 2 n J Q [ K l $ j ( l - r / X ) - f i l + h { / x 1 ] .

Now we can calculate the integral in Eq. (6). Assuming that on the propagation

-~JI

2

path (’-”’)’

liiji 4

2

>> 1 and using the following approximation

Km

the integral reduces to

I(

m

...)dK =

0

I-( -5 / 6) (1-~/X)s’3(fil-jjjj1513. 28’31?(11/6)

Combining the above results we find that Exp. (4) is given by X

A j ( j j I , f i z )= -8n20.033k2 j d { C : ( x - c ) 0

r(-5 / 6 ) 28‘3r ( l l / 6)

- fi21513 +

499

The mean irradiance of the field in the focal plane is expressed by

cc Nz Nz


,PI >=

ffdzpld2p2exp(-~~-pj)212d2)exp(-~2-~)21~2)

1=1 j=1

(8)

xGo(O,PI -f ,PIG,*(0,P , ;- f P )exp(-ikp’ f 2f + ikpi I2f) x < expIi[Spt( P I )- spt(P2>1- i[s, . I

The traditional launching scheme with a focused laser beam provides a single LGS on the telescope axis. In this case fit = jj = 0 and the integration is carried out over the full telescope aperture. For the illumination with a collimated laser beam and limiting filed stop, the integration is done within the area of each subaperture with a diameterd = 2RI N . Thus, for a focused LGS, when ij[ = p = 0 ,dispersion of phases fluctuations < S 2 > is given by Eq.(7)

Integration is carried out over the relevant area, which is defined by operation conditions. For a telescope operating in a vacuum, it is given by p 5 R ,where R is the pupil radius. For a telescope operating in turbulent atmosphere, it is given by p < ro, where ro is the coherent radius of a plane wave. For the case of a single LGS, the area is given by p IR , but it will be limited by the size of the coherent area, which is increased as result of the A 0 correction, also within the ~ e a l pI l R the reduction will take place always. For the case of a collimated LGS, the integration is within the subaperture, that is p c R / N . Assuming a quadratic approximation for the case rii, = 3, = 0 , we find X

A(fil,Pl) =2.82kz ~ d { C ~ ( x - ~ ) [ l-PIr” Pl + 0 + ( t 1 ~ ) 5 / 3 p ~

-I-ij1

+ ( 1 - t 1 ~ ) 5 / 3 p , r ~ +~ ( 1 - t / X ) 5 ’ 3 i p l r i 3

+~~iiz(t/x>r’~

-

+ ~ l ( t / ~ ~ ~ ’-P$ 3~l=(t/~~

As a result, we can calculate the irradiance from Eq. (1) in vacuum < Z , ( - f , f i ) > =4nR4 ~ e x p ( - k 2 p 2 R 2f12 )

f

500

in a turbulence medium

The Strehl ratio after A 0 correction is defined by

It leads to

SR =

1+

1 4R2

'

(9)

N (6q2

where

It is worth noting that the A 0 correction is equivalent to increasing the size of the coherent length in the telescope aperture [ 5 ] , which is defined by Eq. (10). According to our calculations, this increase ranges from 15 to 25 times for 100 km height and various models of turbulence profile. For example, we calculated numerically the coherence radius of a plane wave for a modified Hufnagel-Valley (HV) turbulence profile [ 6 ] ,ro = 0.18 m. The traditional A 0 correction (using a single LGS) increases the size of the coherent length in the telescope aperture to approximately 3-5 m. As a result, wavefront sensing with a single LGS increases the efficiency of the telescope, one can calculate Strehl ratio from Eq. (9), but because of the cone effect, the traditional scheme does not give complete correction for telescopes with aperture size bigger than 10 m. If the telescope pupil is divided into several subapertures with the size 282 d = 2 R l N = r'; =[-k2 6.88

jd@:({)]-3'5,

501

then after A 0 correction the whole receiving telescope aperture becomes coherent. Therefore increasing the partition number N for the telescope pupil and using reduced cones it is possible to compensate the focal anisoplanatism. Our results of analytical and numerical calculations have shown that the wavefront sensing scheme with a field stop and LGS formed by wide collimated beam can be more efficient than the traditional wavefront sensing scheme based on a single LGS focused on the Sodium layer. The algorithm of reconstructing local slopes intensity variations has to be developed, for practical implementation of the new scheme to be attractive. We intended to explore the properties of the filed-oriented wavefront sensor, in particular its fundamental limitations related to the small return photon flux available from the Sodium layer.

Acknowledg~eNts This research was partly supported by Science Foundation Ireland under Grant No. SFUOl/PI.2/B039C

eferences 1. Buscher D. F., Love G., and Myers R., Opt. Lett. 27 (2002), 149-151. 2. Bonaccini D. and Lukin V., Frontiers in Optics 2006. (Rochester, USA, 2006), 129. 3. Bolbasova L., Goncharov A., Lukin V., 6th InternationuZ Workshop for Industry and Medicine, (Galway, Ireland, 2007), 174-175. 4. Gurvich A. S . , Kon A.I., Mironov V. L., and Khmelevtsov S . S . , Laser radiation in turbulent atmosphere (Nauka, Moscow, 1976). 5. Lukin V. P., Adaptive Optics. OSA Technical Digest Series 13 (1996), 35-1 -35-5. 6. Beland R.R., in The Infrared and Electro-Optical Systems Handbook, ed. Smith F. G. (WA: SPIE, Bellingham, 1993).