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SPIE PRESS | Field Guide FFiieelldd GGuuiiddee ttoo AAddaappttiivvee OOppttiiccss SSeeccoonndd EEddiittiioonn Robert K. Tyson Benjamin W. Frazier FG24 covers and title.indd 1 2/23/12 8:51 AM Field Guide to Adaptive Optics Second Edition Robert K. Tyson Benjamin W. Frazier SPIE Field Guides Volume FG24 John E. Greivenkamp, Series Editor Bellingham, Washington USA Library of Congress Cataloging-in-Publication Data Tyson, Robert K., 1948- Field guide to adaptive optics / Robert K. Tyson, Benjamin W. Frazier. -- 2nd ed. p. cm. -- (SPIE field guide series ; v. FG24) Includes bibliographical references and index. ISBN 978-0-8194-9017-9 1. Optics, Adaptive. 2. Optical detectors. 3. Optical measurements. I. Frazier, Benjamin W. (Benjamin West) II. Title. TA1522.T93 2012 621.36'9--dc23 2011050389 Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1.360. 676.3290 Fax: +1.360.647.1445 Email: [email protected] Web: http://spie.org Copyright © 2012 Society of Photo-Optical Instrumentation Engineers (SPIE) All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. For the latest updates about this title, please visit the book’s page on our website. Printed in the United States of America. First printing IntroductiontotheSeries Welcome to the SPIE Field Guides—a series of publica- tions written directly for the practicing engineer or sci- entist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including def- initions and descriptions, key equations, illustrations, ap- plication examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page,andprovidesfullcoverageofthattopiconthatpage. Highlights, insights and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships and alternative methods. Whilecompleteintheircoverage,theconcisepresentation maynotbeappropriateforthosenewtothefield. The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics aswellaswhatmaterialshouldbeaddedtoanindividual volume to make these Field Guides more useful to you. Pleasecontactusatfi[email protected]. JohnE.Greivenkamp,SeriesEditor CollegeofOpticalSciences TheUniversityofArizona FieldGuidetoAdaptiveOptics,2nd Ed. TheFieldGuideSeries Keepinformationatyourfingertipswithallofthetitlesin theFieldGuideSeries: AdaptiveOptics,SecondEdition,RobertK.Tyson& BenjaminW.Frazier AtmosphericOptics,LarryC.Andrews BinocularsandScopes,PaulR.Yoder,Jr.& DanielVukobratovich DiffractiveOptics,YakovG.Soskind GeometricalOptics,JohnE.Greivenkamp Illumination,AngeloArecchi,TaharMessadi,& R.JohnKoshel ImageProcessing,KhanM.Iftekharuddin&AbdulA. Awwal InfraredSystems,Detectors,andFPAs,SecondEdition, ArnoldDaniels InterferometricOpticalTesting,EricP.Goodwin& JamesC.Wyant LaserPulseGeneration,RüdigerPaschotta Lasers,RüdigerPaschotta Microscopy,TomaszTkaczyk OpticalFabrication,RayWilliamson OpticalFiberTechnology,RüdigerPaschotta OpticalLithography,ChrisA.Mack OpticalThinFilms,RonaldR.Willey Polarization,EdwardCollett Probability, Random Processes, and Random Data Analysis,LarryC.Andrews&RonaldL.Phillips Radiometry,BarbaraG.Grant SpecialFunctionsforEngineers,LarryC.Andrews Spectroscopy,DavidW.Ball VisualandOphthalmicOptics,JimSchwiegerling WaveOptics,DanSmith FieldGuidetoAdaptiveOptics,2nd Ed. FieldGuidetoAdaptiveOptics,SecondEdition There have been a number of books and thousands of papers published with descriptions and mathematical expressions regarding adaptive optics. The material in this Field Guide is a summary of the methods for determining the requirements of an adaptive optics system,theperformanceofthesystem,andrequirements forthecomponentsofthesystem.Thissecondeditionhas agreatlyexpandedpresentationofadaptiveopticscontrol system design and operation. Discussions of control models are accompanied by various recommendations for implementingthealgorithmsinhardware. This book is not just another book on adaptive optics. There are already many fine volumes. This volume is intended for students, researchers, and practicing engineers who want a “go to” book when the calculation was “needed yesterday” (by a customer who won’t be payingforituntilthenextfiscalyear). Many of the expressions are in the form of integrals. When that is the case, we show the results graphically for a variety of practical values. Some of the material in this volume duplicates similar expressions found in other volumes of the Field Guide series. We have attempted to remain consistent with symbols of the other volumes. In some cases, however, we chose different symbols because theyarewellknownwithintheadaptiveopticsliterature. Descriptions of the operation of subsystems and compo- nents and specific engineering aspects remain in the cita- tionsoftheBibliography. This Field Guide is dedicated to the late Horace Babcock, whosepioneeringideascreatedthefieldofadaptiveoptics. RobertK.Tyson UniversityofNorthCarolinaatCharlotte BenW.Frazier AOAXinetics, NorthropGrummanAerospaceSystems FieldGuidetoAdaptiveOptics,SecondEdition vii TableofContents Glossary x Introduction 1 ConventionalAdaptiveOpticsSystem 1 ImageSpreadwithAtmosphericTurbulence 2 ThePrincipleofPhaseConjugation 3 Point Spread Function for an Astronomical Telescope 4 ModelingtheEffectofAtmospheric Turbulence 5 Fried’sCoherenceLength 5 IsoplanaticAngle 6 KolmogorovModel 7 AtmosphericTurbulenceModels 8 CoherenceLengthforVariousWavelengths andTurbulenceModels 9 GreenwoodFrequency 10 WindModels 11 Scintillation 12 ZernikePolynomials 13 LegendrePolynomials 15 Angle of Arrival (Tilt) Fluctuations (Image Motion) 17 ModulationTransferFunction 18 BeamPropagation 19 SystemPerformanceEstimation 19 ModalandZonalFittingError 20 WavefrontSensors 21 PartialCorrection 21 Shack–HartmannWavefrontSensor andError 22 Shack–HartmannLensletArraySelection 24 CurvatureWavefrontSensorandError 25 PyramidWavefrontSensorandError 26 DeformableMirrors 27 Photodiodes 27 PhotodiodeNoise 28 Lateral-EffectPosition-SensingDetectors 29 FieldGuidetoAdaptiveOptics,2nd Ed. viii TableofContents QuadCells 30 NoiseEquivalentAngle 32 The Strehl Ratio: Laser Beam Propagation to theFarFieldwithWavefrontError 33 StrehlRatio 34 Laser“Brightness” 35 LaserBeamQuality 36 Astronomical“Brightness” 37 SpotSizeforaGaussianBeam 38 SpotSizeforaUniformCircularAperture 39 TemporalError 40 FocalAnisoplanatism(the“ConeEffect”) 41 LaserGuideStars 42 Subsystem Requirements: The Wavefront Sensor 44 AngularIsoplanaticError 45 SubsystemRequirements:TiltMirror 46 Subsystem Requirements: How Many Actua- tors?ZonalorModalControl 47 SubsystemRequirements:DeformableMirror 48 DeformableMirrorActuatorConfigurations 49 FerroelectricActuators 50 ElectrostaticActuators 52 VoiceCoilActuators 53 DeformableMirrorInfluenceFunctionModels 54 BimorphandMEMSMirrors 55 SegmentedDeformableMirrors 56 ControlandReconstruction 57 ActuatorandWavefrontSensorLayouts 57 CorrectabilityandFlatteningofaDeformable Mirror 58 AdaptiveOpticsSystemFeedback Configuration 59 DeformableMirrorDynamicModel 60 ControllerDynamicModel 61 WavefrontSensorDynamicModel 62 Latency 63 One-DimensionalSampling 64 Two-DimensionalSampling 66 TemporalSamplingRateSelection 67 SystemStability 68 GeneralControl-SystemParameters 69 FieldGuidetoAdaptiveOptics,2nd Ed. ix TableofContents SensitivityFunctions 70 BandwidthEstimationfromControllerGains 72 PokeMatrix 73 ExampleSystemGeometry 74 Singular-Value Decomposition of the Poke Matrix 76 ActuatorandSubapertureObservability 77 IdentificationofActuatorLocations 79 PokeMatrixSmoothing 80 ActuatorSlaving:ActiveActuator Identification 81 ActuatorSlaving:SlaveLogic 82 AddingSlavingintotheReconstructor 83 TiltRemoval 84 PistonandWaffleRemoval 85 ReconstructorGeneration:LeastSquares 86 ReconstructorGeneration:Regularization 87 T-Filter 89 ModalSuppression 90 InteractuatorShearSuppression 91 NullspaceSuppression 92 WeightingMatrices 93 ModalFeedback 94 ReconstructorGeneration:Procedure 96 ReconstructorComparison 97 SlopeDiscrepancy 98 OffloadsandWoofer-TweeterSystems 99 Open-LoopWavefrontEstimation 100 KalmanFiltering 101 MultivariableSystemPerformance 102 DisturbanceInjection 104 WavefrontSensorCalibration 105 CentroidingandThresholding 106 Misregistration 107 SubapertureSpillover 108 EquationSummary 109 Bibliography 117 Index 121 FieldGuidetoAdaptiveOptics,2nd Ed.