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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 guides 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: books@spie.org Web: http://spie.org 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 Introduction to the SeriesWelcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. 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 definitions and descriptions, key equations, illustrations, application 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, and provides full coverage of that topic on that page. 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. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. 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 as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org. John E. Greivenkamp, Series Editor College of Optical Sciences The University of Arizona The Field Guide SeriesKeep information at your fingertips with all of the titles in the Field Guide Series: Adaptive Optics, Second Edition, Robert K. Tyson & Benjamin W. Frazier Atmospheric Optics, Larry C. Andrews Binoculars and Scopes, Paul R. Yoder, Jr. & Daniel Vukobratovich Diffractive Optics, Yakov G. Soskind Geometrical Optics, John E. Greivenkamp Illumination, Angelo Arecchi, Tahar Messadi, & R. John Koshel Image Processing, Khan M. Iftekharuddin & Abdul A. Awwal Infrared Systems, Detectors, and FPAs, Second Edition, Arnold Daniels Interferometric Optical Testing, Eric P. Goodwin & James C. Wyant Laser Pulse Generation, Rüdiger Paschotta Lasers, Rüdiger Paschotta Microscopy, Tomasz Tkaczyk Optical Fabrication, Ray Williamson Optical Fiber Technology, Rüdiger Paschotta Optical Lithography, Chris A. Mack Optical Thin Films, Ronald R. Willey Polarization, Edward Collett Probability, Random Processes, and Random Data Analysis, Larry C. Andrews & Ronald L. Phillips Radiometry, Barbara G. Grant Special Functions for Engineers, Larry C. Andrews Spectroscopy, David W. Ball Visual and Ophthalmic Optics, Jim Schwiegerling Wave Optics, Dan Smith Field Guide to Adaptive Optics, Second EditionThere 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, the performance of the system, and requirements for the components of the system. This second edition has a greatly expanded presentation of adaptive optics control system design and operation. Discussions of control models are accompanied by various recommendations for implementing the algorithms in hardware. 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 paying for it until the next fiscal year). 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 they are well known within the adaptive optics literature. Descriptions of the operation of subsystems and components and specific engineering aspects remain in the citations of the Bibliography. This Field Guide is dedicated to the late Horace Babcock, whose pioneering ideas created the field of adaptive optics. Robert K. Tyson University of North Carolina at Charlotte Ben W. Frazier AOA Xinetics, Northrop Grumman Aerospace Systems Table of ContentsGlossary x Introduction 1 Conventional Adaptive Optics System 1 Image Spread with Atmospheric Turbulence 2 The Principle of Phase Conjugation 3 Point Spread Function for an Astronomical Telescope 4 Modeling the Effect of Atmospheric Turbulence 5 Fried’s Coherence Length 5 Isoplanatic Angle 6 Kolmogorov Model 7 Atmospheric Turbulence Models 8 Coherence Length for Various Wavelengths and Turbulence Models 9 Greenwood Frequency 10 Wind Models 11 Scintillation 12 Zernike Polynomials 13 Legendre Polynomials 15 Angle of Arrival (Tilt) Fluctuations (Image Motion) 17 Modulation Transfer Function 18 Beam Propagation 19 System Performance Estimation 19 Modal and Zonal Fitting Error 20 Wavefront Sensors 21 Partial Correction 21 Shack–Hartmann Wavefront Sensor and Error 22 Shack–Hartmann Lenslet Array Selection 24 Curvature Wavefront Sensor and Error 25 Pyramid Wavefront Sensor and Error 26 Deformable Mirrors 27 Photodiodes 27 Photodiode Noise 28 Lateral-Effect Position-Sensing Detectors 29 Quad Cells 30 Noise Equivalent Angle 32 The Strehl Ratio: Laser Beam Propagation to the Far Field with Wavefront Error 33 Strehl Ratio 34 Laser “Brightness” 35 Laser Beam Quality 36 Astronomical “Brightness” 37 Spot Size for a Gaussian Beam 38 Spot Size for a Uniform Circular Aperture 39 Temporal Error 40 Focal Anisoplanatism (the “Cone Effect”) 41 Laser Guide Stars 42 Subsystem Requirements: The Wavefront Sensor 44 Angular Isoplanatic Error 45 Subsystem Requirements: Tilt Mirror 46 Subsystem Requirements: How Many Actuators? Zonal or Modal Control 47 Subsystem Requirements: Deformable Mirror 48 Deformable Mirror Actuator Configurations 49 Ferroelectric Actuators 50 Electrostatic Actuators 52 Voice Coil Actuators 53 Deformable Mirror Influence Function Models 54 Bimorph and MEMS Mirrors 55 Segmented Deformable Mirrors 56 Control and Reconstruction 57 Actuator and Wavefront Sensor Layouts 57 Correctability and Flattening of a Deformable Mirror 58 Adaptive Optics System Feedback Configuration 59 Deformable Mirror Dynamic Model 60 Controller Dynamic Model 61 Wavefront Sensor Dynamic Model 62 Latency 63 One-Dimensional Sampling 64 Two-Dimensional Sampling 66 Temporal Sampling Rate Selection 67 System Stability 68 General Control-System Parameters 69 Sensitivity Functions 70 Bandwidth Estimation from Controller Gains 72 Poke Matrix 73 Example System Geometry 74 Singular-Value Decomposition of the Poke Matrix 76 Actuator and Subaperture Observability 77 Identification of Actuator Locations 79 Poke Matrix Smoothing 80 Actuator Slaving: Active Actuator Identification 81 Actuator Slaving: Slave Logic 82 Adding Slaving into the Reconstructor 83 Tilt Removal 84 Piston and Waffle Removal 85 Reconstructor Generation: Least Squares 86 Reconstructor Generation: Regularization 87 T-Filter 89 Modal Suppression 90 Interactuator Shear Suppression 91 Nullspace Suppression 92 Weighting Matrices 93 Modal Feedback 94 Reconstructor Generation: Procedure 96 Reconstructor Comparison 97 Slope Discrepancy 98 Offloads and Woofer-Tweeter Systems 99 Open-Loop Wavefront Estimation 100 Kalman Filtering 101 Multivariable System Performance 102 Disturbance Injection 104 Wavefront Sensor Calibration 105 Centroiding and Thresholding 106 Misregistration 107 Subaperture Spillover 108 Equation Summary 109 Bibliography 117 Index 121 Glossarya Width of segment gap A Structure constant at the surface ADC Analog-to-digital converter AInfl Influence function amplitude a0 Piezoelectric constant b Size of mirror segment B Laser brightness BAstro Astronomical brightness B Poke matrix Bc Calibrated poke matrix Br Reduced poke matrix Bs Smoothed poke matrix c Speed of light (=3×108 m/s) ca Interactuator coupling cnm Fourier–Legendre coefficient Atmospheric turbulence structure constant CCD Charge-coupled device d Size of subaperture (in object space) d Separation of the membrane and the addressing electrode d0 Characteristic distance of a laser guide star D Aperture diameter DAC Digital-to-analog converter d Vector of wavefront disturbances e Vector of calculated wavefront errors E Pulse energy of laser en Read-noise in electrons per pixel f Focal length fBW Closed-loop bandwidth fc Crossover frequency fG Greenwood frequency F Focal length of the system FRayleigh Return flux for Rayleigh guide star FSodium Return flux for sodium guide star g1 Loop gain g2 Leak gain G Gain G Generalized system plant model h Planck’s constant (=6.626×10−34 J s) h Altitude HT Height of the tropopause H–V Hufnagel–Valley I(r) Intensity distribution IAper Intensity at the circular aperture Id Dark current IGap Diffracted energy from gaps IJ Johnson noise current In Noise current Ip Photocurrent Is Shot noise current I0 On-axis intensity I Identity matrix J1 Bessel function k Wavenumber k Sample time index kB Boltzmann constant (= 1.38 × 10−23 J/K) K Aperture shape parameter for beam propagation Kg Increase in error at the null K Controller model l0 Inner scale of turbulence L Propagation distance LT Thickness of the tropopause L0 Outer scale of turbulence m Azimuthal index for Zernike polynomials m Number of wavefront measurements in influence matrix mv Visual magnitude of a star M Magnification M2 Beam quality M Modal feedback matrix Mr Reduced modal feedback matrix MTF Modulation transfer function n Radial index for Zernike polynomials n Vector of measurement noise na Number of actuators nB Number of detected background photo-electrons per subaperture nm Number of measurements np Number of detected photoelectrons per subaperture ns Number of slaved actuators nv Number of active actuators nR Rayleigh scattering density NAct Number of actuators ND Number of pixels in a subaperture NEA Noise equivalent angle NEP Noise equivalent power Np Photon count NZern Number of Zernike modes O Offload matrix OPD Optical path difference p Curvature sensor image plane offset P Optical power Pn Legendre polynomial of order n P Error propagation covariance matrix Pp Piston projection matrix Pt Tilt projection matrix Pw Waffle projection matrix PSD Position sensing detector PSF Point spread function q Electron charge (= 1.6 × 10−19 C) Qd Atmospheric disturbance covariance Qn Measurement noise covariance r Radial coordinate ra Actuator pad radius rc Interactuator spacing rm Mirror radius rs Radius of supporting ring r0 Coherence length of the atmosphere RMS Root mean square r Vector coordinate in the wavefront R Radius of circle R Photodiode responsivity R Reconstructor Rr Reduced reconstructor RSS Root sum square Zernike radial polynomial s Shear distance s Summing index in the Zernike radial polynomial s Laplace transform variable sAct Distance between actuators S Strehl ratio S Sensitivity function Sd Slope discrepancy matrix Sl Slave logic matrix Sw/jit Strehl ratio including effects of jitter SLC Strategic laser communications SNR Signal-to-noise ratio SVD Singular value decomposition t Thickness of the bimorph td Latency T Matrix transpose operator T Transmission of the optics T Complementary sensitivity function TA Transmission of the atmosphere Tm Tension of the membrane Ts Sampling time u Vector of actuator commands vG Wind velocity at low altitude vT Wind velocity at the tropopause vw Wind velocity as a function of altitude v(z)Bufton Wind velocity of the Bufton model V Applied voltage w Gaussian beam radius w0 Gaussian beam waist W(x, y) Wavefront W Wind velocity aloft W Weighting matrix WCE Wavefront control experiment WFS Wavefront sensor x, y Cartesian coordinates y Corrected output wavefront z Coordinate along propagation path z Altitude (if propagation path is vertical) z Z-transform variable αjit Root-mean-square average jitter Wavefront error variance (distance squared) δ Hartmann spot shift Δλ Spectral bandwidth ε0 Permittivity Phase Deformable mirror influence function (surface deflection) Wind direction relative to the telescope aperture Φ(r) Phase η Detector efficiency κ Fitting constant λ Wavelength λLGS Laser wavelength ν Spatial frequency νG Wind velocity at low altitude θ Angular size of reference source θd Half-angle beam divergence θ0 Isoplanatic angle ρ Discrete-time equivalent latency ρCol Sodium column abundance σfitting Wavefront fitting error σNa Resonant backscatter cross section σR Rayleigh scattering cross section σTemp Temporal wavefront error σTilt Wavefront tilt σWFS Wavefront sensor measurement error σ2 Wavefront error variance (radians squared) Intensity variance Measurement error variance Log-amplitude variance Root-mean-square wavefront error over a subaperture τ Actuator rise time ΩN Nyquist frequency ζ Zenith angle |
CITATIONS
Adaptive optics
Actuators
Performance modeling
Deformable mirrors
Wavefront sensors
Atmospheric modeling
Atmospheric optics
