Aero-Optical Effects: Physics, Analysis and Mitigation

286 Pages·2023·20.676 MB·English

by  Stanislav Gordeyev, Eric Jumper, Matthew Whiteley

Aero-Optical Effects
WILEY SERIES IN PURE AND APPLIED OPTICS
Founded by Stanley S. Ballard, University of Florida
EDITOR: Glenn Boreman, University of North Carolina at Charlotte
ASSANTO · Nematicons: Spatial Optical Solitons in Nematic Liquid Crystlas
BARRETT AND MYERS · Foundations of Image Science
BEISER · Holographic Scanning
BERGER-SCHUNN · Practical Color Measurement
BOYD · Radiometry and The Detection of Optical Radiation
BUCK · Fundamentals of Optical Fibers, Second Edition
CATHEY · Optical Information Processing and Holography
CHUANG · Physics of Optoelectronic Devices
DELONE AND KRAINOV · Fundamentals of Nonlinear Optics of Atomic Gases
DERENIAK AND BOREMAN · Infrared Detectors and Systems
DERENIAK AND CROWE · Optical Radiation Detectors
DE VANY · Master Optical Techniques
ERSOY · Diffraction, Fourier Optics and Imaging
GASKILL · Linear Systems, Fourier Transform, and Optics
GOODMAN · Statistical Optics
GROBE AND EISELT · Wavelength Division Multiplexing: A Practical Engineering Guide
HOBBS · Building Electro-Optical Systems: Making It All Work, Second Edition
HUDSON · Infrared System Engineering
IIZUKA · Elements of Photonics, Volume I: In Free Space and Special Media
IIZUKA · Elements of Photonics, Volume II: For Fiber and Integrated Optics
JUDD AND WYSZECKI · Color in Business, Science, and Industry,Third Edition
KAFRI AND GLATT · The Physics of Moire Metrology
KAROW · Fabrication Methods for Precision Optics
KASUNIC · Optomechanical Systems Engineering
KLEIN AND FURTAK · Optics, Second Edition
MA AND ARCE · Computational Lithography
MALACARA · Optical Shop Testing, Third Edition
MILONNI AND EBERLY · Lasers
NASSAU · The Physics and Chemistry of Color: The Fifteen Causes of Color, Second Edition
NIETO-VESPERINAS · Scattering and Diffraction in Physical Optics
OSCHE · Optical Detection Theory for Laser Applications
O’SHEA · Elements of Modern Optical Design
OZAKTAS · The Fractional Fourier Transform
PRATHER, SHI, SHARKAWY, MURAKOWSKI, AND SCHNEIDER · Photonic Crystals: Theory, Applications,
and Fabrication
SALEH AND TEICH · Fundamentals of Photonics,Second Edition
SCHUBERT AND WILHELMI · Nonlinear Optics and Quantum Electronics
SHEN · The Principles of Nonlinear Optics
STEGEMAN AND STEGEMAN · Nonlinear Optics: Phenomena, Materials, and Devices
UDD · Fiber Optic Sensors: An Introduction for Engineers and Scientists
UDD · Fiber Optic Smart Structures
VANDERLUGT · Optical Signal Processing
VEST · Holographic Interferometry
VINCENT · Fundamentals of Infrared Detector Operation and Testing
VINCENT, HODGES, VAMPOLA, STEGALL, AND PIERCE · Fundamentals of Infrared and Visible Detector
Operation and Testing, Second Edition
WEINER · Ultrafast Optics
WILLIAMS AND BECKLUND · Introduction to the Optical Transfer Function
WU AND REN · Introduction to Adaptive Lenses
WYSZECKI AND STILES · Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition
XU AND STROUD · Acousto-Optic Devices
YAMAMOTO · Coherence, Amplification, and Quantum Effects in Semiconductor Lasers
YARIV AND YEH · Optical Waves in Crystals
YEH · Optical Waves in Layered Media
YEH · Introduction to Photorefractive Nonlinear Optics
YEH AND GU · Optics of Liquid Crystal Displays, Second Edition
GORDEYEV, JUMPER, AND WHITELEY · Aero-Optical Effects: Physics, Analysis and Mitigation
Aero-Optical Effects
Physics, Analysis and Mitigation
Stanislav Gordeyev
Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN, USA
Eric J. Jumper
Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN, USA
Matthew R. Whiteley
MZA Associates Corporation
Dayton, OH, USA
Copyright © 2023 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or
otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright
Act, without either the prior written permission of the Publisher, or authorization through
payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222
Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the web at
www.copyright.com. Requests to the Publisher for permission should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030,
[phone], fax [phone], or online at http://www.wiley.com/go/permission.
Trademarks: Wiley and the Wiley logo are trademarks or registered trademarks of John
Wiley & Sons, Inc. and/or its affiliates in the United States and other countries and may
not be used without written permission. All other trademarks are the property of their
respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor
mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their
best efforts in preparing this book, they make no representations or warranties with
respect to the accuracy or completeness of the contents of this book and specifically
disclaim any implied warranties of merchantability or fitness for a particular purpose. No
warranty may be created or extended by sales representatives or written sales materials.
The advice and strategies contained herein may not be suitable for your situation. You
should consult with a professional where appropriate. Neither the publisher nor author
shall be liable for any loss of profit or any other commercial damages, including but not
limited to special, incidental, consequential, or other damages. Further, readers should be
aware that websites listed in this work may have changed or disappeared between when
this work was written and when it is read. Neither the publisher nor authors shall be
liable for any loss of profit or any other commercial damages, including but not limited to
special, incidental, consequential, or other damages.
For general information on our other products and services or for technical support,
please contact our Customer Care Department within the United States at [phone],
outside the United States at [phone] or fax [phone].
Wiley also publishes its books in a variety of electronic formats. Some content that appears
in print may not be available in electronic formats. For more information about Wiley
products, visit our web site at www.wiley.com.
A catalogue record for this book is available from the Library of Congress
Hardback ISBN: 9781119037170; ePub ISBN: 9781119037217; ePDF ISBN: 9781119037156;
oBook ISBN: 9781119037064
Cover image: Courtesy of Aero-Optics group
Cover design: Wiley
Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India
v
Contents
Acknowledgements ix
1 Introduction 1
1.1 Motivation for Revisiting Aero-Optics 2
2 Fundamentals 7
2.1 Wavefronts and Index of Refraction 7
2.2 Huygens’ Principle 8
2.3 Basic Equations and Optical Path Difference 11
2.4 Linking Equation 15
2.5 Image at a Focal Plane (Far-field Propagation) 17
2.6 Far-field Intensity in the Presence of Near-field Distortions 20
2.6.1 Temporal Intensity Variation 25
2.7 Wavefront Components 26
3 Measuring Wavefronts 31
3.1 Interferometry Methods 31
3.2 Wavefront Curvature Methods 33
3.3 Gradient-based Wavefront Sensors 35
3.3.1 Shack-Hartmann Wavefront Sensor 37
3.3.1.1 Wavefront Reconstruction Algorithm 41
3.3.2 Malley Probe 43
3.3.3 SABT Sensor 46
3.4 Typical Optical Set-Ups 47
4 Data Reduction and Interpretation 55
4.1 Statistical Analysis 56
4.1.1 Temporal and Spatial OPD 56
rms
4.1.2 Histograms and Higher-Moment Statistics 58
vi Contents
4.2 Spectral Analysis 60
4.2.1 Relation between the Deflection Angle Spectrum and the Wavefront
Statistics 62
4.2.2 Dispersion Analysis 63
4.3 Modal Analysis 65
4.3.1 Zernike Functions 66
4.3.2 Proper Orthogonal Decomposition (POD) 70
4.3.2.1 Direct Method 73
4.3.2.2 Snapshot Method 74
4.3.3 Dynamic Mode Decomposition (DMD) 82
4.4 Cross-correlation-based Techniques 85
4.4.1 Local Convective Speeds 85
4.4.2 Multi-point Malley Probe Analysis 89
4.4.3 Spatially Varying 2-D Convective Velocity 92
5 Aperture Effects 97
6 Typical Aero-Optical Flows 105
6.1 Scaling Arguments 105
6.2 Free Shear Layers 106
6.2.1 Shear-Layer Physics 106
6.2.2 Aero-Optical Effects 109
6.2.3 Historical Shear Layer Measurements in AEDC 110
6.2.4 Weakly Compressible Model 114
6.3 Boundary Layers 118
6.3.1 Model of Aero-optical Distortions for Boundary Layers
with Adiabatic Walls 122
6.3.2 Angular Dependence 130
6.3.3 Finite Aperture Effects 132
6.3.4 Nonadiabatic Wall Boundary Layers 133
6.3.5 Instantaneous Far-Field Intensity Drop-Outs 142
6.3.5.1 Absolute SR Threshold 147
6.3.5.2 Relative Intensity Variation 150
6.4 Turrets 152
6.4.1 AAOL 154
6.4.2 Flow Topology and Dynamics 159
6.4.3 Steady-lensing Effects at Forward-looking Angles 167
6.4.4 Aero-optical Environment at Back-looking Angles 169
6.4.5 Shock-effects at Transonic Speeds 172
Contents vii
7 Aero-Optical Jitter 179
7.1 Local and Global Jitter 180
7.1.1 Local Jitter 180
7.1.2 Global Jitter 180
7.2 Subaperture Effects 183
7.3 Techniques to Remove the Mechanically Induced Jitter 183
7.3.1 Cross-correlation Techniques 184
7.3.2 Large-Aperture Experiments 186
7.3.3 Stitching Method 187
8 Applications to Adaptive Optics 195
8.1 Beam-Control Components 195
8.2 How Much Correction Is Needed 198
8.3 Flow-Control Mitigation 198
8.3.1 Non-Flow-Control Mitigation 199
8.3.2 Some Qualities of Separated Shear Layers 200
8.3.3 Using the POD Analysis to Develop Requirements 204
8.4 Proper Number of Wavefront Sensor Subapertures
to Actuator Ratio 208
8.4.1 Numerical Simulation 209
8.4.2 Simulation Results 211
8.4.3 Conclusion from the Simulation Results 213
9 Adaptive Optics for Aero-Optical Compensation 217
9.1 Analogies from Free-Stream Turbulence Compensation 217
9.1.1 Statistical Optics Theoretical Considerations 217
9.1.2 Power-Law Observations from Aero-Optical Wavefront Data 219
9.2 Compensation Scaling Laws for Aero-Optics 222
9.2.1 Adaptive Optics Control Law and Error Rejection Transfer
Function 222
9.2.2 Asymptotic Results for Aero-Optics Compensation 223
9.2.3 Aero-Optics Compensation Frequency 225
9.2.4 Relation of Aero-Optics Scaling Laws to Free-Stream Turbulence 227
9.3 Spatial and Temporal Limitations of Adaptive Optics 228
9.3.1 Framework for Analysis of Aero-Optical Compensation 228
9.3.2 Deformable Mirror Fitting Error for Aero-Optical POD Modes 229
9.3.3 Decomposition of Correctable and Uncorrectable Power Spectrum 233
9.3.3.1 DM Sensitivity Transfer Function 233
9.3.4 Closed-Loop Residual Wavefront Error 234
viii Contents
9.3.5 Effect of Latency in Aero-Optics Compensation 236
9.4 Application to System Performance Modeling 238
9.4.1 Scaling of Aero-Optical Statistics to Flight Conditions 239
9.4.2 Joint Variations in Adaptive Optics Bandwidth and Actuator
Density 239
9.4.3 Relative Impact of Aero-Optics with Other Propagation
and System Effects 244
9.4.3.1 Comparing Aero-Optics to Free-Stream Turbulence Propagation 245
9.4.3.2 Comparing Aero-Optics to System Optical Jitter 246
9.4.4 Tracker Performance Degradations Related to Aero-Optics 248
9.4.4.1 Track Sensor Aero-Optical Imaging Resolution Degradation 249
9.4.4.2 Illuminator Propagation and Active Imaging through Aero-Optics 250
10 Concluding Remarks 255
References 259
Index 271
ix
Acknowledgements
No research effort can proceed without financial support. There are many
program managers in the Air Force Research Laboratory (AFRL), the Air Force
Office of Naval Research (AFOSR), the Office of Naval Research (ONR), the Naval
Air Warfare Center Weapons Division (NAWCWD), the Defense Advanced
Research Projects Agency (DARPA), the High Energy Laser Joint Technology
Office (HEL JTO) and the Directed Energy Joint Transition Office (DE JTO) to
which we are thankful; however, we are particularly thankful to a few key indi-
viduals for their financial and moral support at critical points in the long research
history from which the contents of this book came. First among these is Dr. James
McMichael at the Air Force Office of Scientific Research, who supported our early
efforts at Notre Dame. This support was continued under Dr. Thomas Beutner
with follow-on support later in our research with his move to the Office of Naval
Research. The biggest growth in our efforts came with a large grant through Mark
Neice, then director of the High-Energy Laser Joint Technology Office. In recent
years, that funding has continued due to the ardent support from Dr. Lawrence
Grimes, heading the office under the name change to Directed Energy Joint
Transition Office. Under the Office of Naval Research, we owe a special thanks to
Dr. Lewis DeSandre in Washington and Dr. C Denton Marrs at the Naval Warfare
Center at China Lake. We would also like to send our special thanks to Dr. Bill
Bower at Boeing Corporation for supporting many turret-related studies. Finally,
it is impossible to not acknowledge the special working relationship we have had
with the Dayton office of MZA Associates Corporation.