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and Pattern Formationin Semiconductors and DevicesEditor: F.-J. Niedernostheide

80 Computer Simulation Studiesin Condensed-Matter Physics VIIIEditors: D.P. Landau, K.K. Mon,and H.-B. Schuttler

81 Materials and Measurementsin Molecular ElectronicsEditors: K. Kajimura and S. Kuroda

82 Computer Simulation Studiesin Condensed-Matter Physics IXEditors: D.P. Landau, K.K. Mon,and H.-B. Schuttler

83 Computer Simulation Studiesin Condensed-Matter Physics XEditors: D.P. Landau, K.K. Mon,and H.-B. Schuttler

84 Computer Simulation Studiesin Condensed-Matter Physics XIEditors: D.P. Landau and H.-B. Schuttler

85 Computer Simulation Studiesin Condensed-Matter Physics XIIEditors: D.P. Landau, S.P. Lewis,and H.-B. Schuttler

86 Computer Simulation Studiesin Condensed-Matter Physics XIIIEditors: D.P. Landau, S.P. Lewis,and H.-B. Schuttler

87 Proceedingsof the 25th International Conferenceon the Physics of SemiconductorsEditors: N. Miura and T. Ando

88 Starburst GalaxiesNear and FarEditors: L. Tacconi and D. Lutz

89 Computer Simulation Studiesin Condensed-Matter Physics XIVEditors: D.P. Landau, S.P. Lewis,and H.-B. Schuttler

90 Computer Simulation Studiesin Condensed-Matter Physics XVEditors: D.P. Landau, S.P. Lewis,and H.-B. Schuttler

91 The Dense Interstellar Mediumin GalaxiesEditors: S. Pfalzner, C. Kramer,C. Straubmeier, and A. Heithausen

92 Beyond the Standard Model 2003Editor: H.V. Klapdor-Kleingrothaus

93 ISSMGEExperimental StudiesEditor: T. Schanz

94 ISSMGENumerical and Theoretical ApproachesEditor: T. Schanz

95 Computer Simulation Studiesin Condensed-Matter Physics XVIEditors: D.P. Landau, S.P. Lewis,and H.-B. Schuttler

96 Electromagnetics in a Complex WorldEditors: I.M. Pinto, V. Galdi,and L.B. Felsen

97 Fields, Networks,Computational Methods and Systemsin Modern ElectrodynamicsA Tribute to Leopold B. FelsenEditors: P. Russer and M. Mongiardo

98 Particle Physics and the UniverseProceedings of the 9th Adriatic Meeting,Sept. 2003, DubrovnikEditors: J. Trampetic and J. Wess

99 Cosmic ExplosionsOn the 10th Anniversary of SN1993J(IAU Colloquium 192)Editors: J. M. Marcaide and K. W. Weiler

100 Lasers in the Conservation of ArtworksLACONA V Proceedings,Osnabruck, Germany, Sept. 15–18, 2003Editors: K. Dickmann, C. Fotakis,and J.F. Asmus

101 Progress in TurbulenceEditors: J. Peinke, A. Kittel, S. Barth,and M. Oberlack

102 Adaptive Opticsfor Industry and MedicineProceedingsof the 4th International WorkshopEditor: U. Wittrock

Volumes 50–78 are listed at the end of the book.

U. Wittrock (Ed.)

Adaptive Opticsfor Industryand MedicineProceedings

Munster, Germany, Oct. 19–24, 2003

With 283 Figures

123

4of the th International Workshop

Professor Dr. Ulrich WittrockMunster

Stegerwaldst r. 39, 48565 Steinfurt, GermanyE-mail: wittrock@fh-muenster.de

ISSN 0930-8989

ISBN-10 3-540-23978-2 Springer Berlin Heidelberg New York

Library of Congress Control Number: 2004115731

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Preface

The 4th International Workshop on Adaptive Optics for Industry and Medi-cine took place in Munster, Germany, from October 19 to October 24, 2003.The series of International Workshops on Adaptive Optics for Industry andMedicine began with the first workshop in Shatura/Russia in 1997, the secondworkshop took place in Durham/England in 1999, and the third workshopwas held in Albuquerque/USA in 2001. The workshop series started out asa true grassroots movement and kept an informal spirit throughout all fourworkshops. Many personal friendships and scientific collaborations have beenformed at these meetings.

This fourth workshop was supposed to be held in Beijing, China. How-ever, the program committee decided in May 2003 to move the workshopto Munster due the general perception that the SARS (Severe Acute Res-piratory Syndrome) cases reported in China could lead to a large epidemic.Despite this rather short notice the workshop in Munster was attended byabout 70 people. Incidentally, the workshop coincided with the 50th anniver-sary of adaptive optics, because it was October 1953 when Horace Babcockpublished his famous paper “The possibilities of compensating astronomicalseeing” in the Publications of the Astronomical Society of the Pacific.

For years, adaptive optics has been synonymous for correction of at-mospheric aberrations, but many more applications have emerged in recentyears. Examples of fairly novel applications are imaging of the retina, confo-cal microscopy, laser resonators, dispersion compensation in ultrafast lasers,and free space optical communication. At the same time, significant progresshas been made in reducing the cost of adaptive optics components such asdeformable mirrors, driver electronics, or wavefront sensors. These factors areexpected to lead to much more widespread applications of adaptive optics inthe near future.

The workshops have never been associated with any of the big scientificsocieties. While this kept the cost for attendees low, it also meant that a lotof work had to be done by the local organizing committee. I’m very gratefulto Agnes Frieling, Ivo Buske, Hagen Zimer, Hans Heuck, and Petra Welp fortheir great enthusiasm in organizing this workshop.

VI Preface

The attendees at the workshop in Munster voted to hold the 5th Inter-national Workshop on Adaptive Optics for Industry and Medicine in Beijingin 2005. I wish the organizers well in their undertakings and look forward tomeeting many old and new friends in Beijing!

Munster, May 2005 Ulrich Wittrock

Contents

Part I Wavefront Correctors and Mirror Control

1 Micromachined Membrane Deformable MirrorsG. Vdovin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 The Development and Optimisationof High Bandwidth Bimorph Deformable MirrorsD. Rowe, L. Laycock, M. Griffith, N. Archer . . . . . . . . . . . . . . . . . . . . . . . 9

3 Deformable Mirrors with Thermal ActuatorsG. Vdovin, M. Loktev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Technology and Operationof a Liquid Crystal Modal Wavefront CorrectorM. Loktev, G. Vdovin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Aberration Compensation Using Nematic Liquid CrystalsS. Somalingam, M. Hain, T. Tschudi, J. Knittel, H. Richter . . . . . . . . . 35

6 Wireless Control of an LC Adaptive LensG. Vdovin, M. Loktev, X. Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7 Summary of Adaptive Optics at StanfordP. Lu, Y.-A. Peter, E. Carr, U. Krishnamoorty, I.-W. Jung,O. Solgaard, R. Byer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

8 Control of a Thermal Deformable Mirror: Correction of a StaticDisturbance with Limited Sensor InformationM. de Boer, K. Hinnen, M. Verhaegen, R. Fraanje, G. Vdovin,N. Doelman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

9 A Novel Microprocessor-Controlled High-Voltage Driverfor Deformable MirrorsH.-M. Heuck, I. Buske, U. Buschmann, H. Krause, U. Wittrock . . . . . . . 73

10 Preliminary Investigation of an Electrostatically ActuatedLiquid-Based Deformable MirrorE.M. Vuelban, N. Bhattacharya, J.M. Braat . . . . . . . . . . . . . . . . . . . . . . . . 83

VIII Contents

11 Interferometer-Based Adaptive Optical SystemO. Soloviev, G. Vdovin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Part II Wavefront Sensors

12 Extended Hartmann–Shack Wavefront SensorB. Schafer, K. Mann, M. Dyba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

13 High Resolution Wavefront SensingJ.E. Oti, V.F. Canales, M.P. Cagigal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

14 Distorted Grating Wavefront Sensing in the Midwave InfraredD.M. Cuevas, L.J. Otten, P. Harrison, P. Fournier . . . . . . . . . . . . . . . . . 119

15 Comparative Results from Shack–Hartmann and Distorted GratingWavefront Sensors in Ophthalmic ApplicationsP. Harrison, G.R.G. Erry, P. Fournier, D.M. Cuevas, L.J. Otten,A. Larichev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

16 Shack–Hartmann Sensors for Industrial Quality AssuranceJ. Pfund, M. Beyerlein, R. Dorn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

17 Single-Chip Neural Network Modal Wavefront Reconstructionfor Hartmann–Shack Wavefront SensorsT. Nirmaier, G. Pudasaini, C. Alvarez Diez, J. Bille,D.W. de Lima Monteiro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

18 CMOS Technology in Hartmann–Shack Wavefront SensingD.W. de Lima Monteiro and T. Nirmaier . . . . . . . . . . . . . . . . . . . . . . . . . . 163

19 Generalised Phase Diversity Wavefront SensorA.H. Greenaway, H.I. Campbell, S. Restaino . . . . . . . . . . . . . . . . . . . . . . . 177

20 Generalised Phase Diversity: Initial TestsS. Zhang, H.I. Campbell, A.H. Greenaway . . . . . . . . . . . . . . . . . . . . . . . . . 187

21 Prime Microlens Arrays for Hartmann–Shack Sensors:An Economical Fabrication TechnologyD.W. de Lima Monteiro, O. Akhzar-Mehr, G. Vdovin . . . . . . . . . . . . . . . 197

22 A Proposal for Wavefront Retrieval from Hartmann Test DataV.M. Duran-Ramirez, D. Malacara-Doblado, D. Malacara-Hernandez,D.P. Salas-Peimbert, G. Trujillo-Shiaffino . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Contents IX

Part III Laser Resonators and Laser Amplifiers

23 Use of Intracavity Adaptive Opticsin Solid-State Lasers Operation at 1 µmW. Lubeigt, P. van Grol, G. Valentine, D. Burns . . . . . . . . . . . . . . . . . . . 217

24 Intracavity Use of Membrane Mirrors in a Nd:YVO4 LaserP. Welp, I. Buske, U. Wittrock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

25 Adaptive Optics for High-Power Laser Beam ControlA. Kudryashov, V. Samarkin, A. Alexandrov, A. Rukosuev,V. Zavalova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

26 Aberrations of a Master-Oscillator-Power-Amplifier Laserwith Adaptive Optics CorrectionI. Buske, H.-M. Heuck, P. Welp, U. Wittrock . . . . . . . . . . . . . . . . . . . . . . . 249

27 Dynamic Aberrations Correction in an ICF Laser SystemY. Zhang, Z. Yang, C. Guan, H. Wang, P. Jiang, B. Xu, W. Jiang . . . 261

28 Adaptive Shaping of High-Power Broadband FemtosecondLaser PulsesT. Witting, G. Tsilimis, J. Kutzner, H. Zacharias, M. Koller,H. Maurer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

29 Wavefront Measurement and Adaptive Opticsat the PHELIX LaserH.-M. Heuck, U. Wittrock, C. Hafner, S. Borneis, E. Gaul, T. Kuhl,P. Wiewior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

30 ISTC Projects from RFNC-VNIIEFDevoted to Improving Laser Beam QualityF. Starikov, G. Kochemasov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

Part IV Medical Applications

31 Adaptive Optical Systemfor Retina Imaging Approaches Clinic ApplicationsN. Ling, Y. Zhang, X. Rao, C. Wang, Y. Hu, W. Jiang, C. Jiang . . . . . 305

32 Adaptive Optics to Simulate Visionwith a Liquid Crystal Spatial Light ModulatorS. Manzanera, P.M. Prieto, J. Salort, E.J. Fernandez, P. Artal . . . . . . . 317

33 Confocal Scanning Retinal Imaging with Adaptive OpticsI. Iglesias, B. Vohnsen, P. Artal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

X Contents

34 A High-Resolution Adaptive Optics Fundus ImagerG.R.G. Erry, L.J. Otten, A. Larichev, N. Irochnikov . . . . . . . . . . . . . . . . 333

35 Perceived Image Quality Improvementsfrom the Application of Image Deconvolutionto Retinal Images from an Adaptive Optics Fundus ImagerP. Soliz, S.C. Nemeth, G.R.G. Erry, L.J. Otten, S.Y. Yang . . . . . . . . . . 343

36 Adaptive Aberrometerfor Acuity Measurements and TestingA. Larichev, N. Irochnikov, S. Gorbunov . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

Part V Atmospheric Propagation

37 Adaptive Optics with Strong Scintillationand Optical Vortices for Optical CommunicationC. Paterson, C.R. Walker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

38 Wavefront Measurement over an Extended Horizontal PathUsing a Wavefront Curvature SensorJ. Burnett, S. Woods, A. Turner, A. Scott . . . . . . . . . . . . . . . . . . . . . . . . . 377

39 The Detection of Atmospheric Tip-Tiltand its Program Construction in Lunar Laser RangingG. Rui, X. Yaoheng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

List of Contributors

O. Akhzar-MehrDelft University of TechnologyEEMCSElectronic InstrumentationLaboratoryMekelweg 4, 2628 CD DelftThe Netherlandso.mehr@gmx.de

A. AlexandrovRussian Academy of SciencesILITAdaptive Optics for Industrial andMedical Applications GroupSvyatoozerskaya 1Shatura 140700, Russia

N. ArcherBAE SystemsProduct Assurance GroupWest Hanningfield RoadChelmsford, Englandnick.archer@baesystems.com

P. ArtalUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spainpablo@um.es

M. BeyerleinOptocraft GmbH Optical MetrologyHofmannstraße 11891052 Erlangen, Germany

N. BhattacharyaDelft University of TechnologyDepartment of Imaging Science andTechnologyOptics Research GroupLorentzweg 1, DelftThe Netherlands

J. BilleUniversity of HeidelbergKirchhoff Institute of PhysicsIm Neuenheimer Feld 22769120 Heidelberg, Germany

M. de BoerDelft University of TechnologyDelft Center of Systems and ControlMekelweg 2, 2628 CD DelftThe Netherlands

S. BorneisGesellschaft furSchwerionenforschung mbHPlanckstr. 1, 64291 DarmstadtGermany

J.M. BraatDelft University of TechnologyDepartment of Imaging Science andTechnologyOptics Research GroupLorentzweg 1, DelftThe Netherlands

XII List of Contributors

J. BurnettQinetiQ Ltd.Malvern Technology CentreSt Andrews RoadMalvern, Worcs WR14 3PS, UKjgburnett@QinetiQ.com

D. BurnsUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NW, Scotland

U. BuschmannMunster Universityof Applied SciencesPhotonics LaboratoryStegerwaldstr. 3948565 Steinfurt, Germany

I. BuskeMunster Universityof Applied SciencesPhotonics LaboratoryStegerwaldstr. 3948565 Steinfurt, Germanybuske@fh-muenster.de

R. ByerStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USA

M.P. CagigalUniversidad de CantabriaDepartamento de Fısica AplicadaAvda. Los Castros S/N39005 Santander, Spain

H.I. CampbellHeriot-Watt UniversityDepartment of PhysicsRiccartonEdinburgh, EH14 4AS, UKH.I.Campbell@hw.ac.uk

V.F. CanalesUniversidad de CantabriaDepartamento de Fısica AplicadaAvda. Los Castros S/N39005 Santander, Spain

E. CarrStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USA

D.M. CuevasKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USAdcuevas@kestrelcorp.com

C. Alvarez DiezUniversity of HeidelbergKirchhoff Institute of PhysicsIm Neuenheimer Feld 22769120 Heidelberg, Germany

N. DoelmanTNO TPDStieltjesweg 12628 CK DelftThe Netherlandsdoelman@tpd.tno.nl

R. DornOptocraft GmbH Optical MetrologyHofmannstraße 11891052 Erlangen, Germanydorn@optocraft.de

V.M. Duran-RamirezCentro de Investigaciones en OpticaLoma del Bosque 115Leon, Gto, Mexicovicdur@cio.mx

List of Contributors XIII

M. DybaMPI fur Biophysikalische ChemieAm Fassberg 1137077 Gottingen, Germanymdyba@gwdg.de

G.R.G. ErryKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USAgerry@kestrelcorp.com

E.J. FernandezUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spainenriquej@um.es

R. FraanjeUniversity of TwenteFaculty of Applied Physics, EnschedeThe Netherlands

P. FournierKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USA

E. GaulGesellschaft furSchwerionenforschung mbHPlanckstr. 1, 64291 DarmstadtGermany

S. GorbunovIPLIT RASPionerskaya 2Troick, Moscow region 142092Russia

A.H. GreenawayHeriot-Watt UniversityDepartment of PhysicsRiccartonEdinburgh, EH14 4AS, UKa.h.greenaway@hw.ac.uk

M. GriffithBAE SystemsAdvanced Technology CentreWest Hanningfield RoadChelmsford, England

P. van GrolUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NW, Scotland

C. GuanChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

C. HafnerGesellschaft furSchwerionenforschung mbHPlanckstr. 1, 64291 DarmstadtGermany

M. HainTechnische Universitat DarmstadtHochschulstr. 664289 Darmstadt, Germany

P. HarrisonKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USApharrison@kestrelcorp.com

H.-M. HeuckMunster Universityof Applied SciencesPhotonics LaboratoryStegerwaldstr. 3948565 Steinfurt, Germanyheuck@fh-muenster.de

XIV List of Contributors

K. HinnenDelft University of TechnologyDelft Center of Systems and ControlMekelweg 22628 CD DelftThe Netherlandsk.j.g.hinnen@dcsc.tudelft.nl

Y. HuChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

I. IglesiasUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spainiic@um.es

N. IrochnikovM.V. Lomonosov Moscow StateUniversityFaculty of PhysicsLeninskiye GoryMoscow 119992, Russia

C. JiangE&ENT Hospitalof Fudan UniversityShanghai, PR China

P. JiangChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

W. JiangChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

I.-W. JungStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USA

M. KollerWestfalische Wilhelms-UniversitatMunsterInstitut fur Numerische undinstrumentelle MathematikEinsteinstr. 6248149 Munster, Germanykollerma@math.uni-muenster.de

J. KnittelDeutsche Thomson Brandt GmbHHermann-Schwer-Str. 378048 Villingen–SchwenningenGermanyjoachim.knittel@thomson.net

G. KochemasovRussian Federal Nuclear Center –VNIIEFSarov, Nizhny NovgorodReg. 607190, Russia

H. KrauseMunster Universityof Applied SciencesPhotonics LaboratoryStegerwaldstr. 3948565 Steinfurt, Germany

U. KrishnamoortyStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USA

T. KuhlGesellschaft furSchwerionenforschung mbHPlanckstr. 1, 64291 DarmstadtGermany

List of Contributors XV

A. KudryashovRussian Academy of SciencesILITAdaptive Optics for Industrial andMedical Applications GroupSvyatoozerskaya 1Shatura 140700, Russiakud@laser.ru

J. KutznerWestfalische Wilhelms-UniversitatMunsterPhysikalisches InstitutWilhelm-Klemm-Str. 1048149 Munster, Germany

A. LarichevM.V. Lomonosov Moscow StateUniversityCenter of Medical PhysicsLeninskiye GoryMoscow 119992, Russialarichev@optics.ru

L. LaycockBAE SystemsAdvanced Technology CentreWest Hanningfield RoadChelmsford, England

D.W. de Lima MonteiroDelft University of TechnologyEEMCSElectronic InstrumentationLaboratoryMekelweg 4, 2628 CD DelftThe Netherlandsdavies@titus.et.tudelft.nl

N. LingChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

M. LoktevDelft University of TechnologyEEMCSElectronic InstrumentationLaboratoryMekelweg 4, 2628 CD DelftThe Netherlandsm.loktev@ewi.tudelft.nl

P. LuStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USApatlu@Stanford.EDU

W. LubeigtUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NW, Scotlandwalter.lubeigt@strath.ac.uk

D. Malacara-DobladoCentro de Investigaciones en OpticaLoma del Bosque 115Leon, Gto, Mexicodmalacdo@cio.mx

D. Malacara-HernandezCentro de Investigaciones en OpticaLoma del Bosque 115Leon, Gto, Mexicodmalacara@cio.mx

K. MannLaser Laboratorium GottingenHans-Adolf-Krebs-Weg 137077 Gottingen, Germanykmann@llg.gwdg.de

S. ManzaneraUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spainsilmanro@um.es

XVI List of Contributors

H. MaurerWestfalische Wilhelms-UniversitatMunsterInstitut fur Numerische undinstrumentelle MathematikEinsteinstr. 6248149 Munster, Germany

S.C. NemethKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USA

T. NirmaierUniversity of HeidelbergKirchhoff Institute of PhysicsIm Neuenheimer Feld 22769120 Heidelberg, Germanynirmaier@kip.uni-heidelberg.de

J.E. OtiUniversidad de CantabriaDepartamento de Fısica AplicadaAvda. Los Castros S/N39005 Santander, Spainotije@unican.es

L.J. OttenKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USAljotten@kestrelcorp.com

C. PatersonImperial CollegeThe Blackett LaboratoryLondon, SW7 2BW, UKcarlp@imperial.ac.uk

Y.-A. PeterStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USA

J. PfundOptocraft GmbH Optical MetrologyHofmannstraße 11891052 Erlangen, Germany

P.M. PrietoUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spainpegrito@um.es

G. PudasainiUniversity of HeidelbergKirchhoff Institute of PhysicsIm Neuenheimer Feld 22769120 Heidelberg, Germanygopal@kip.uni-heidelberg.de

X. RaoChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

S. RestainoNaval Research LaboratoryRemote Sensing Division, Code 721Kirtland Airforce BaseAlbuquerque, NM, USA

H. RichterDeutsche Thomson Brandt GmbHHermann-Schwer-Str. 378048 Villingen–SchwenningenGermany

D. RoweBAE SystemsAdvanced Technology CentreWest Hanningfield RoadChelmsford, Englandduncan.rowe@baesystems.com

List of Contributors XVII

G. RuiNational Astronomical ObservatoriesCASYunnan Observatorygr806@tom.com

A. RukosuevRussian Academy of SciencesILITAdaptive Optics for Industrial andMedical Applications GroupSvyatoozerskaya 1Shatura 140700, Russia

D.P. Salas-PeimbertInstituto Tecnologico de Chihuahua31310 Chihuahua, Chih., Mexicodsalas@itchihuahua.edu.mx

J. SalortUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spainsalort@um.es

V. SamarkinRussian Academy of Sciences,ILITAdaptive Optics for Industrial andMedical Applications GroupSvyatoozerskaya 1Shatura 140700, Russiasamarkin@laser.ru

B. SchaferLaser Laboratorium GottingenHans-Adolf-Krebs-Weg 137077 Gottingen, Germanybschae@llg.gwdg.de

A. ScottQinetiQ Ltd.Malvern Technology CentreSt Andrews RoadMalvern, Worcs WR14 3PS, UK

O. SolgaardStanford UniversityGinzton Laboratory450 Via PalouStanford, CA 94305-4088, USA

P. SolizKestrel Corporation3815 Osuna Road NEAlbuquerque, NM 87109, USApsoliz@kestrelcorp.com

O. SolovievDelft University of TechnologyElectronic InstrumentationLaboratoryMekelweg 4, 2628 CD, DelftThe NetherlandsO.Soloviev@EWI.TUDelft.nl

S. SomalingamTechnische Universitat DarmstadtHochschulstr. 664289 Darmstadt, Germanysomalin@prp.physik.tu-darmstadt.de

F. StarikovRussian Federal Nuclear Center –VNIIEFSarov, Nizhny Novgorod Reg.607190, Russiastarikov@otd13.vniief.ru

T. TschudiTechnische Universitat DarmstadtHochschulstr. 664289 Darmstadt, Germany

G. Trujillo-ShiaffinoInstituto Tecnologico de Chihuahua31310 Chihuahua, Chih., Mexico

XVIII List of Contributors

G. TsilimisWestfalische Wilhelms-UniversitatMunsterPhysikalisches InstitutWilhelm-Klemm-Str. 1048149 Munster, Germany

A. TurnerQinetiQ Ltd.Malvern Technology CentreSt Andrews RoadMalvern, Worcs WR14 3PS, UKajturner2@qinetiq.com

G. ValentineUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NW, Scotlandgareth.valentine@strath.ac.uk

G. VdovinDelft University of TechnologyEEMCSElectronic InstrumentationLaboratoryMekelweg 4, 2628 CD DelftThe Netherlandsgleb@ei.et.tudelft.nlandOKO TechnologiesPO Box 5812600 AN DelftThe Netherlandsgleb@okotech.com

M. VerhaegenDelft University of TechnologyDelft Center of Systems and ControlMekelweg 2, 2628 CD DelftThe Netherlands

B. VohnsenUniversidad de MurciaLaboratorio de OpticaCampus de Espinardo Ed. C.30071 Murcia, Spain

E.M. VuelbanDelft University of TechnologyDepartment of Imaging Science andTechnologyOptics Research GroupLorentzweg 1, DelftThe Netherlandse.vuelban@tnw.tudelft.nl

C.R. WalkerImperial CollegeThe Blackett LaboratoryLondon, SW7 2BW, UK

C. WangChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

H. WangChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

P. WelpMunster Universityof Applied SciencesPhotonics LaboratoryStegerwaldstr. 3948565 Steinfurt, Germanypetrawelp@fh-muenster.de

P. WiewiorJulius Maximilian UniversitatWurzburg97703 Wurzburg, Germany

List of Contributors XIX

T. WittingWestfalische Wilhelms-UniversitatMunsterPhysikalisches InstitutWilhelm-Klemm-Str. 1048149 Munster, Germanytwitting@nwz.uni-muenster.de

U. WittrockMunster Universityof Applied SciencesPhotonics LaboratoryStegerwaldstr. 3948565 Steinfurt, Germanywittrock@fh-muenster.de

S. WoodsQinetiQ Ltd.Malvern Technology CentreSt Andrews RoadMalvern, Worcs WR14 3PS, UKscwoods@taz.qinetiq.com

B. XuChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR China

X. YaohengNational Astronomical ObservatoriesCASYunnan Observatoryyozsx@public.km.yn.cn

S.Y. YangTexas Tech UniversityLubbock, TX, USAgzsyyang@yahoo.com

Z. YangChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR Chinazpyang@ioe.ac.cn

H. ZachariasWestfalische Wilhelms-UniversitatMunsterPhysikalisches InstitutWilhelm-Klemm-Str. 1048149 Munster, Germanyhzach@uni-muenster.de

V. ZavalovaRussian Academy of SciencesILITAdaptive Optics for Industrial andMedical Applications GroupSvyatoozerskaya 1Shatura 140700, Russia

S. ZhangHeriot-Watt UniversityDepartment of PhysicsRiccartonEdingburgh, EH14 4AS, UKsijiong.zhang@hw.ac.uk

X. ZhangDelft University of TechnologyEEMCSElectronic InstrumentationLaboratoryMekelweg 4, 2628 CD DelftThe Netherlands

Y. ZhangChinese Academy of SciencesInstitute of Optics and ElectronicsPO Box 350, ShuangliuChengdu 610209, PR Chinaydzhang@ioe.ac.cn

Part I

Wavefront Correctors and Mirror Control

1 Micromachined MembraneDeformable Mirrors

G. Vdovin

Delft University of Technology, EEMCS, Electronic Instrumentation LaboratoryMekelweg 4, 2628 CD Delft, The NetherlandsandOKO TechnologiesPO Box 581, 2600AN Delft, The Netherlands

Summary. Development of adaptive optics, initiated 50 years ago with the articleof Babcock [1], resulted in impressive technical and scientific results in military andastronomical applications. These results were obtained on a high price using custom-developed complex adaptive optical systems. Adaptive optics has a great potentialto be applied in a range of optical systems, including imaging, ophthalmic, laser,optical communications and information processing. These systems are marketedwidely and use relatively inexpensive parts with high performance. This articlepresents a fragmentary analysis of the current state and possible future developmentof inexpensive deformable mirrors for the industry and medicine. The analysis ismainly based on the results obtained by the author and his colleagues at the TUDelft and OKO Technologies during 1993–2003.

1.1 Design and Parameters

A Micromachined Membrane Deformable Mirror (MMDM) [2] consists of athin stretched membrane suspended over an array of electrostatic electrodes.The membrane is fabricated by LPCVD deposition of a thin ≈ 0.5 µm layerof tensile stressed silicon nitride SinNm, followed by anisotropic etching ofbulk silicon to release the membrane. Pure nitride membranes are sufficientlystrong for mirrors with a diameter of up to 25 mm, larger membranes – up to50 mm – can be fabricated by sandwiching a relatively thick – up to 10 µm –layer of epitaxial polysilicon between two nitride layers.

In the simplest case the membrane is coated by a thin layer of metal –aluminum or gold – providing sufficiently reflective broadband coatings inthe visible (Al) and infrared (gold) regions. In case a higher reflectivity isrequired (for instance for laser intracavity applications), the membrane canbe coated with Cr/Ag composition followed by up to 12 dielectric layers,resulting in reflectivity of up to 99.8% in a narrow spectral region. Multilayercoated mirrors reported to work with laser loads of up to 550 W in a 5 mmcircular beam at λ = 1.06 µm. The typical parameters of a standard MMDMproduced by OKO Technologies are shown in Table 1.1.

The initially flat membrane can be deformed only towards the electrostaticactuators because the electrostatic force can be only attractive. This limits

4 G. Vdovin

Table 1.1. MMDM technical data

Parameter Value

Aperture shape approximately circularMirror coating Al, Au, HR (R ≈ 99.9%)Aperture diameter 15–50mmNumber of electrodes 37–79Control voltages Vc 0 . . . 300VInitial rms deviation from plane less than 0.3 µmMain initial aberration 1 fringe at 630 nmFrequency range 1000HzMaximum deflection of the mirror center 9–30 µm

the possible optical figures of the MMDM to be always concave. Since most ofthe applications require both convex and concave operation of the mirror, theinitial mirror figure is electrically biased to take a concave parabolic shape,median with respect to zero and maximum deflection. From this position, themirror can correct both concave and convex aberrations with relation to theparabolically biased figure. The typical response time is ∼ 1 ms, making themirror suitable for real-time control of turbulence-induced aberrations.

1.2 Limitations

Technology of MMDM has certain limitations. The technology is suited formembranes with diameters in the range of 0.4–5.0 cm. It is difficult to fab-ricate larger or smaller mirrors. The effective number of electrodes is alsolimited. Electrostatic actuators can be easily integrated in very dense grids,resulting in small area per actuator. The maximum response per actuator isproportional to the actuator area. Practically it does not make sense to haveactuators that produce maximum response of less than λ/4, which limits themaximum number of actuators to several hundreds for a 5 cm mirror. In prac-tice, the mirror substrate should have voids, that are necessary for reductionof the air damping of the membrane movement. These voids should be uni-formly spaced and they occupy a considerable area, even more reducing thepossible number of uniformly spaced actuators.

The mirror membrane is fixed along its edges. To eliminate the influence offixed boundary conditions, the light aperture should occupy approximatelythe central 50% of the mirror surface. For example, if a membrane mirrorhas an aperture of 15 mm, only the central area of 10 mm in diameter can beused for functional correction of wavefront aberrations. To ensure best spatialresolution, the array of electrostatic actuators is also placed under the centralarea of the membrane, occupying only about 60% of the membrane area.

1 Micromachined Membrane Deformable Mirrors 5

Fig. 1.1. A simplified cross-section of a MMDM (top) and complete 79-ch 50-mmMMDM coated for 1060 nm wavelength (bottom)

The design of a micromachined deformable mirror allows deflection of themirror surface only in the direction of the control electrodes, corresponding toa positive curvature of the mirror surface. To be able to correct an aberrationthat has both positive and negative curvature, the mirror surface should bepre-deformed to a concave spherical shape, having a weak positive opticalpower in the biased “zero” position. The surface displacement of the biasedmirror surface limits the amplitude of the corrected aberration, moreover thecorrection amplitude and precision depends on the characteristic size of theaberration to be corrected.

The bias curvature Cb = 1/Rb, where Rb is the radius of biased surface,should be equal to the half of the maximum achievable curvature Cmax =1/Rmax = 2/(Rb). The range of curvature control is limited by the curvatureof the biased membrane. The shape of the membrane s(x) – that is needed

6 G. Vdovin

to correct for a hypothetic harmonic aberration – can be described by aharmonic function with a period T and amplitude A: s(x) = A sin(2πx/T )– for simplicity we consider a one-dimensional case. The curvature of themembrane C(x) = 4π2A/T 2 sin(2πx/T ) is limited by the value of 4π2 A/T2.This value (positive or negative) cannot exceed the absolute value of the biascurvature given by |1/Rb|. The amplitude of achievable harmonic deformationof the membrane mirror is given by

Am =T 2

4π2Rb, (1.1)

where T defines the characteristic size of the aberration to becorrected. Fi-nally the achievable P–V correction amplitude in terms of wavefront defor-mation will be four times larger (P–V amplitude of a harmonic function istwo times larger than its amplitude, further the phase deformation equals todoubled mirror surface deformation), yielding for P–V amplitude of wave-front correction:

Awf =T 2

π2Rb=

1π2fRb

, (1.2)

where f is the spatial frequency of the surface deformation. For aberrationswith a spatial period smaller than the mirror aperture, the membrane correc-tor represents a low-frequency filter, with a maximum amplitude of correctedaberration decreasing with aberration spatial frequency by 40 dB per decadeor 12 dB per octave. For the typical values of our system T = 1 cm andRb = 4 m – aberration over the whole aperture – the maximum amplitudeof correction equals 2 µm while for a local aberration with T = 5 mm themaximum amplitude of correction is almost an order of magnitude lower andequals only 0.5 µm.

Equation 1.2 defines the maximum amplitude of the wavefront that canbe corrected as a function of the aberration period T . A is the maximumamplitude of a wavefront with a spatial period of Tmin, that still can becorrected by the mirror. Wavefronts with larger amplitude and/or smallerperiods cannot be corrected.

Tmin = π√

RbA . (1.3)

Assuming the mirror diameter is D and we need at least 4 actuators tocorrect an aberration with a spatial period T , the total number of actuatorsproviding correction with amplitude precision A and period Tmin

N =16D2

π2RbA. (1.4)

For a deformable mirror with light aperture of D = 10 mm, Rb = 5 m andA = 10−7 m we have Tmin ≈ 2 mm and N ≈ 300. For comparison, the realdevice has only N = 37 actuators. For a mirror with D = 35 mm, Rb = 20 mand A = 10−7m we obtain Tmin ≈ 4.5 mm and N ≈ 1000.

1 Micromachined Membrane Deformable Mirrors 7

As we made no assumption about the nature of the deformable mirrorresponse, this analysis is valid in general for any curvature-limited deformablemirror device.

1.3 Applications

Since the technology of MMDM is based completely on inorganic materials,devices were demonstrated to work in vacuum at cryogenic temperaturesdown to T = 78 K [3], which makes them potentially suitable for space-basedadaptive optics.

MMDM is reported to be successfully used for real-time correction ofphase aberrations in laboratory and in a one meter telescope at Apache Point,New Mexico [4]. In particular, the Strehl ratio was improved in average from0.08 to 0.48 for simulated turbulence in the laboratory, and from 0.04 to 0.1in a 10-exposure field experiment with Altair image.

Small size, quick response, high density of actuators, smooth modal re-sponse and hysteresis-free operation make MMDM highly suitable for feed-forward correction using control approach based on a combination of opti-mization with program control. In the beginning, the voltage vector appliedto the mirror electrodes is optimized to obtain the maximum of the appro-priate quality parameter – brightness for laser systems, sharpness and imagequality for imaging systems, pulse duration for ultrafast lasers. The optimiza-tion process can take up to several thousand iterations and usually resultsin significant improvement of the quality of the optical system. The controlvector is written in the memory of the computer and can be recalled everytime the control situation repeats.

Based on this approach, a wide field correction of scanning optical micro-scope was demonstrated in [5]. The scanning beam quality was individuallyoptimized for each point in the field of view and the lookup table of MMDMcontrol vectors was stored in the computer. In the operation mode, the scan-ning beam was corrected “on the fly” for each scan position, resulting indrastic improvement of the microscope resolution over the whole field.

Another example of the optimization approach combined with a lookuptable is given in [6] – where the authors report on a 1×N optical switch withMMDM used to improve coupling efficiency in each switch channel of a fiberswitch by pre-setting the mirror shape in accordance with the lookup table.

Optimization approach proved very efficient in numerous experimentswith compression and optimization of ultrafast optical pulses. A specialMMDM was developed for one-dimensional correction of phase aberrationsalong a single line. These devices are usually used in a stretcher of ultrafastlaser to balance phase delays of spectral components. Optimization of thespectral phase resulted in efficient compression of femtosecond pulses andeven in improvement of the efficiency of a EUV plasma source [7–9].

8 G. Vdovin

Fig. 1.2. Typical interferometric pattern of a 37-ch 15mm MMDM: zero voltageapplied, control byte 180 applied to all actuators, control byte 255 applied to alland to some actuators (left to right)

MMDMs were also successfully used for wavefront correction in terawattlasers [10] and for intracavity control of high-power industrial lasers [11,12].

Finally, MMDM are suitable for real-time correction of the aberrationsof the human eye, making possible “electronic spectacles” for real-time im-provement of the visio nacuity [13].

Compactness, simplicity and high optical quality make MMDM the deviceof choice for a number of optical applications in the laser optics, imaging,optical testing and astronomy.

References

1. H.W. Babcock: The possibility of compensating astronomical seeing. Publica-tions of the astronomical society of Pacific 65, 229 (1953)

2. G.V. Vdovin, S. Middelhoek, P.M. Sarro: Opt. Eng. 36, 1382 (1997)3. H.M. Dyson, R.M. Sharples, N.A. Dipper, G.V. Vdovin: Opt. Express 8(1)

(2001)4. D. Dayton, S. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne,

S. Rogers, M. Vaidyanathan, M. Shilko: Opt. Comm. 176, 339 (2000)5. O. Albert, L. Sherman, G. Mourou, T.B. Norris, G. Vdovin: Opt. Lett. 25(1),

52 (2000)6. F. Gonte, A. Courteville, R. Dandliker: Opt. Eng. 41(5), 1073 (2002)7. E. Zeek, R. Bartels, M.M. Murnane, H.C. Kapteyn, S. Backus, G. Vdovin:

Opt. Lett. 25(8), 587 (2000)8. A. Baltuska, T. Fuji, T. Kobayashi: Opt. Lett. 27(5), 306 (2002)9. R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I.P. Christov, M.M.

Murnane, H.C. Kapteyn: Nature 406, 164 (2000)10. F. Druon, G. Cheraux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G.

Mourou, J.C. Chanteloup, G. Vdovin: Opt. Lett. 23, 1043 (1998)11. G. Vdovin, V. Kiyko: Opt. Lett. 26(11), 798 (2001)12. W. Lubeigt, G. Valentine, J. Girkin, E. Bente, D. Burns: Opt. Express 10(13),

550 (2002)13. E. Fernandez, I. Iglesias, P. Artal: Opt. Lett. 26(10) 746 (2001)

2 The Development and Optimisationof High Bandwidth BimorphDeformable Mirrors

D. Rowe1, L. Laycock1, M. Griffith1, and N. Archer2

1 BAE Systems Advanced Technology CentreWest Hanningfield Road, Chelmsford, England

2 BAE Systems Product Assurance GroupWest Hanningfield Road, Chelmsford, England

Summary. Our first mirror designs were based on a standard bimorph construc-tion and exhibited a resonant frequency of 1 kHz with a maximum stroke of ±5 µm.These devices were limited by the requirement to have a “dead space” between theinner active area and the mirror boundary. This was necessary to ensure that therequirements for both the stroke and the static boundary conditions at the edgeof the mirror could be met simultaneously, but there was a significant penalty topay in terms of bandwidth, which is inversely proportional to the square of the fullmirror diameter. In a series of design iteration steps, we have created mountingarrangements that seek not only to reduce dead space, but also to improve rugged-ness and temperature stability through the use of a repeatable and reliable assemblyprocedure. As a result, the most recently modeled mirrors display a resonance inexcess of 5 kHz, combined with a maximum stroke in excess of ±10 µm. This hasbeen achieved by virtually eliminating the “dead space” around the mirror. Bycareful thermal matching of the mirror and piezoelectric substrates, operation overa wide temperature range is possible. This paper will discuss the outcomes fromthe design study and present our initial experimental results for the most recentlyassembled mirror.

2.1 Introduction

The BAE SYSTEMS Advanced Technology Centre has been involved in asystems study to investigate the use of deformable mirrors to correct fordistortions in atmospheric imaging and laser beam propagation. Typical ap-plications include thermal imaging and laser remote sensing.

For correcting atmospheric distortions, the bandwidth required for thecontrol system is typically 1 kHz. This means that the deformable mirror’sresonant frequency needs to be > 1 kHz. In terms of stroke, the correction ofmoderate turbulence (D/r0 = 10, where D is the diameter of the aperture andr0 is the coherence length), requires the capability to provide a movement of0.5 µm (λ = 1 µm) over the mirror’s active surface. We have used these twobasic parameters as the target requirements in the development of a numberof prototype bimorph mirrors.

c© BAE SYSTEMS 2003. All rights reserved

10 D. Rowe et al.

2.2 1st Iteration Flexure

2.2.1 Design and Fabrication

The first bimorph mirror fabricated was based on the standard scheme wherea glass/PZT sandwich is supported rigidly around its edge. While this schemeis robust, the total substrate diameter is typically twice that of the requiredactive area. Since the resonant frequency of this device is inversely propor-tional to the square of the mirror diameter, reducing the “dead” space at theperiphery of the mirror was regarded as a prime objective. One way that thishas been achieved in the past is to support the periphery of the mirror withan o-ring. This prevents any vertical displacement at the edge, but does en-able a non-zero gradient. However, achieving an even pressure over the entireo-ring is difficult and requires careful adjustment of the clamping screws toavoid introducing mirror distortions. For this reason, we devised the 1st iter-ation flexure mount as an alternative mounting scheme. The flexures create arobust support which nevertheless enables a non-zero gradient at the mirroredge. This reduces the proportion of the mirror which is outside the mainpupil.

Analytical modeling [1] was used to provide an initial estimate of therequired substrate thickness. The trade off between the mirror stroke andresonant frequency is shown in Fig. 2.1.

The mirror was then drawn in Pro-Engineer, and transferred to Pro-Mechanica for finite element analysis. The electrode pattern chosen was basedon the work carried out by Edric Mark Ellis in his thesis [1]. A photographof the back of the mirror showing the flexures and electrode pattern, alongwith a picture of the fully assembled mirror is given in Fig. 2.2.

Fig. 2.1. Analytical plot of mirror resonance and maximum displacement as afunction of mirror substrate thickness

2 High Bandwidth Bimorph Deformable Mirrors 11

Table 2.1. Comparison of modelled and measured results

Stroke (300 V pk–pk) Resonant Frequency

Modelleda) ±7.3 µm 3.37 kHzFinal Mounted Mirror ±5 µm 2.7 kHz% Achieved 62 80a) The glue layer has not been taken into account in the modelled performance

Fig. 2.2. Photographs of the back of the mirror, showing the flexures and electrodepattern, and the fully assembled mirror

Fig. 2.3. Schematic of laser vibrometer test set-up

2.2.2 Performance

A laser vibrometer (see Fig. 2.3 for schematic) was used to determine the res-onant frequency and maximum stroke of the assembled device. A comparisonof the modelled and measured results is given in Table 2.1.

From the table it can be seen that the measured resonant frequency isclose to that predicted. The stroke achieved is only 60% of that predicted,but the model does not include the glue layer between the mirror substrateand PZT elements.

2.3 2nd Iteration Flexure

2.3.1 Design

While the 1st iteration flexure enabled a non-zero gradient at the mirrorperiphery, the unused portion of the mirror could be reduced even furtherif some vertical (piston) displacement were also possible. The 2nd iterationflexure is designed to provide this.

12 D. Rowe et al.

Fig. 2.4. Exaggerated 3D plots, and plots of mirror displacement for the 8 nodeand 16 node cases

Fig. 2.5. Bias voltages used to generate the 8 and 16 node patterns

Again, the mirror was drawn in Pro-Engineer, and transferred to Pro-Mechanica for finite element analysis, and the same 45 element electrodepattern was employed. This mirror was smaller than the 1st iteration design,and the substrate was fabricated from borosilicate glass. The PZT chosenmatches the thermal expansion of the glass to within 0.25 ppm/◦K. If youassume that no more than 10% of the maximum stroke should be used tocompensate for thermal distortions, then the effective temperature range forthe bimorph is ±64◦C. This, in conjunction with suitable choice of epox-ies and a PZT Curie temperature of > 200◦C, gives the mirror a potentialoperating temperature range of between −40◦C and +80◦C.

Figure 2.4 shows the results of modelling the mirror, while Fig. 2.5 showsthe bias voltages used to create the nodal patterns.