100,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley Series in Pure and Applied Optics
- Sprache: Englisch
AERO-OPTICAL EFFECTS Explore the newest techniques and technologies used to mitigate the effects of air flow over airborne laser platforms Aero-Optical Effects: Physics, Analysis and Mitigation delivers a detailed and insightful introduction to aero-optics and fully describes the current understanding of the physical causes of aero-optical effects from turbulent flows at different speeds. In addition to presenting a thorough discussion of instrumentation, data reduction, and data analysis, the authors examine various approaches to aero-optical effect mitigation using both flow control and adaptive optics approaches. The book explores the sources, characteristics, measurement approaches, and mitigation means to reduce aero-optics wavefront error. It also examines the precise measurements of aero-optical effects and the instrumentation of aero-optics. Flow control for aero-optical applications is discussed, as are approaches like passive flow control, active and hybrid flow control, and closed-loop flow control. Readers will benefit from discussions of the applications of aero-optics in relation to fields like directed energy and high-speed communications. Readers will also enjoy a wide variety of useful features and topics, including: * Comprehensive discussions of both aero-effects, which include the effects that air flow has over a beam director mounted on an aircraft, and aero-optics, which include atmospheric effects that degrade the ability of an airborne laser to focus a beam * A treatment of air buffeting and its effects on beam stabilization and jitter * An analysis of mitigating impediments to the use of high-quality laser beams from aircraft as weapons or communications systems * Adaptive optics compensation for aero-optical disturbances Perfect for researchers, engineers, and scientists involved with laser weapon and beam control systems, Aero-Optical Effects: Physics, Analysis and Mitigation will also earn a place in the libraries of principal investigators in defense contract work and independent research and development.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 404
Veröffentlichungsjahr: 2023
Ähnliche
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, (978) 750-8400, fax (978) 750-4470, 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, (201) 748-6011, fax (201) 748-6008, 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 (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.
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
Contents
Cover
Serious page
Title page
Copyright
Acknowledgements
1 Introduction
1.1 Motivation for Revisiting Aero-Optics
2 Fundamentals
2.1 Wavefronts and Index of Refraction
2.2 Huygens’ Principle
2.3 Basic Equations and Optical Path Difference
2.4 Linking Equation
2.5 Image at a Focal Plane (Far-field Propagation)
2.6 Far-field Intensity in the Presence of Near-field Distortions
2.6.1 Temporal Intensity Variation
2.7 Wavefront Components
3 Measuring Wavefronts
3.1 Interferometry Methods
3.2 Wavefront Curvature Methods
3.3 Gradient-based Wavefront Sensors
3.3.1 Shack-Hartmann Wavefront Sensor
3.3.1.1 Wavefront Reconstruction Algorithm
3.3.2 Malley Probe
3.3.3 SABT Sensor
3.4 Typical Optical Set-Ups
4 Data Reduction and Interpretation
4.1 Statistical Analysis
4.1.1 Temporal and Spatial OPDrms
4.1.2 Histograms and Higher-Moment Statistics
4.2 Spectral Analysis
4.2.1 Relation between the Deflection Angle Spectrum and the Wavefront Statistics
4.2.2 Dispersion Analysis
4.3 Modal Analysis
4.3.1 Zernike Functions
4.3.2 Proper Orthogonal Decomposition (POD)
4.3.2.1 Direct Method
4.3.2.2 Snapshot Method
4.3.3 Dynamic Mode Decomposition (DMD)
4.4 Cross-correlation-based Techniques
4.4.1 Local Convective Speeds
4.4.2 Multi-point Malley Probe Analysis
4.4.3 Spatially Varying 2-D Convective Velocity
5 Aperture Effects
6 Typical Aero-Optical Flows
6.1 Scaling Arguments
6.2 Free Shear Layers
6.2.1 Shear-Layer Physics
6.2.2 Aero-Optical Effects
6.2.3 Historical Shear Layer Measurements in AEDC
6.2.4 Weakly Compressible Model
6.3 Boundary Layers
6.3.1 Model of Aero-optical Distortions for Boundary Layers with Adiabatic Walls
6.3.2 Angular Dependence
6.3.3 Finite Aperture Effects
6.3.4 Nonadiabatic Wall Boundary Layers
6.3.5 Instantaneous Far-Field Intensity Drop-Outs
6.3.5.1 Absolute SR Threshold
6.3.5.2 Relative Intensity Variation
6.4 Turrets
6.4.1 AAOL
6.4.2 Flow Topology and Dynamics
6.4.3 Steady-lensing Effects at Forward-looking Angles
6.4.4 Aero-optical Environment at Back-looking Angles
6.4.5 Shock-effects at Transonic Speeds
7 Aero-Optical Jitter
7.1 Local and Global Jitter
7.1.1 Local Jitter
7.1.2 Global Jitter
7.2 Subaperture Effects
7.3 Techniques to Remove the Mechanically Induced Jitter
7.3.1 Cross-correlation Techniques
7.3.2 Large-Aperture Experiments
7.3.3 Stitching Method
8 Applications to Adaptive Optics
8.1 Beam-Control Components
8.2 How Much Correction Is Needed
8.3 Flow-Control Mitigation
8.3.1 Non-Flow-Control Mitigation
8.3.2 Some Qualities of Separated Shear Layers
8.3.3 Using the POD Analysis to Develop Requirements
8.4 Proper Number of Wavefront Sensor Subapertures to Actuator Ratio
8.4.1 Numerical Simulation
8.4.2 Simulation Results
8.4.3 Conclusion from the Simulation Results
9 Adaptive Optics for Aero-Optical Compensation
9.1 Analogies from Free-Stream Turbulence Compensation
9.1.1 Statistical Optics Theoretical Considerations
9.1.2 Power-Law Observations from Aero-Optical Wavefront Data
9.2 Compensation Scaling Laws for Aero-Optics
9.2.1 Adaptive Optics Control Law and Error Rejection Transfer Function
9.2.2 Asymptotic Results for Aero-Optics Compensation
9.2.3 Aero-Optics Compensation Frequency
9.2.4 Relation of Aero-Optics Scaling Laws to Free-Stream Turbulence
9.3 Spatial and Temporal Limitations of Adaptive Optics
9.3.1 Framework for Analysis of Aero-Optical Compensation
9.3.2 Deformable Mirror Fitting Error for Aero-Optical POD Modes
9.3.3 Decomposition of Correctable and Uncorrectable Power Spectrum
9.3.3.1 DM Sensitivity Transfer Function
9.3.4 Closed-Loop Residual Wavefront Error
9.3.5 Effect of Latency in Aero-Optics Compensation
9.4 Application to System Performance Modeling
9.4.1 Scaling of Aero-Optical Statistics to Flight Conditions
9.4.2 Joint Variations in Adaptive Optics Bandwidth and Actuator Density
9.4.3 Relative Impact of Aero-Optics with Other Propagation and System Effects
9.4.3.1 Comparing Aero-Optics to Free-Stream Turbulence Propagation
9.4.3.2 Comparing Aero-Optics to System Optical Jitter
9.4.4 Tracker Performance Degradations Related to Aero-Optics
9.4.4.1 Track Sensor Aero-Optical Imaging Resolution Degradation
9.4.4.2 Illuminator Propagation and Active Imaging through Aero-Optics
10 Concluding Remarks
References
Index
End User License Agreement
List of Illustrations
CHAPTER 01
Figure 1.1 Airborne Laser Laboratory...
Figure 1.2 (a) Ratio of...
CHAPTER 02
Figure 2.1 Distortions of monochromatic...
Figure 2.2 Hyugens’ principle...
Figure 2.3 Distortions imposed on...
Figure 2.4 Schematic of the...
Figure 2.5 Schematic of the...
Figure 2.6 Diffraction-limited intensity...
Figure 2.7 Spatial occurrences of...
Figure 2.8 Far-field intensity...
Figure 2.9 Left: Nominal optical...
Figure 2.10 Time-averaged diffraction...
CHAPTER 03
Figure 3.1 (a) Michelson-type...
Figure 3.2 (a) The principle...
Figure 3.3 Schematic of the...
Figure 3.4 (a) A knife...
Figure 3.5 Schematic of the...
Figure 3.6 Principle of deflection...
Figure 3.7 Principle of operation...
Figure 3.8 Image of a...
Figure 3.9 (a) Cell geometry...
Figure 3.10 Single-beam Malley...
Figure 3.11 Principle of operation...
Figure 3.12 Position detectability for...
Figure 3.13 Schematic of a...
Figure 3.14 Schematic of the...
Figure 3.15 Schematic of the...
Figure 3.16 Schematic of the...
Figure 3.17 (Cont’d...
Figure 3.18 Relation between the...
Figure 3.19 Object and image...
Figure 3.20 Wavefront, reimaged from...
CHAPTER 04
Figure 4.1 Examples of the...
Figure 4.2 Examples of P...
Figure 4.3 Aperture-averaged wavefront...
Figure 4.4 Wavefront spatial wavenumber...
Figure 4.5 First several Zernike...
Figure 4.6 Far-field images...
Figure 4.7 Example wavefronts, and...
Figure 4.8 Re-numerating the...
Figure 4.9 POD analysis, applied...
Figure 4.10 POD analysis of...
Figure 4.11 The normalized and...
Figure 4.12 The representative instantaneous...
Figure 4.13 Selected POD modes...
Figure 4.14 DMD analysis of...
Figure 4.15 (a) DMD spectrum...
Figure 4.16 (a) Concept of...
Figure 4.17 (a) Phase plot...
Figure 4.18 Example of multi...
Figure 4.19 (a) Schematic of...
Figure 4.20 Local phase convective...
CHAPTER 05
Figure 5.1 Examples of the...
Figure 5.2 Aperture transfer function...
Figure 5.3 The only-piston...
CHAPTER 06
Figure 6.1 Examples of shear...
Figure 6.2 Schematic of the...
Figure 6.3 AEDC ART Facility...
Figure 6.4 AEDC wavefront data...
Figure 6.5 Variation of the...
Figure 6.6 Comparison of the...
Figure 6.7 Scaled aero-optical...
Figure 6.8 Large-scale vortical...
Figure 6.9 Some of early...
Figure 6.10 Different choices of...
Figure 6.11 Mach dependent function...
Figure 6.12 A comparison of...
Figure 6.13 Experimentally measured normalized...
Figure 6.14 Streamwise evolution of...
Figure 6.15 Normalized deflection angle...
Figure 6.16 Beam traveling through...
Figure 6.17
B(γ
) for single-boundary-layer...
Figure 6.18 Predicted and measured...
Figure 6.19 Normalized mean component...
Figure 6.20 (a) D1 versus...
Figure 6.21 (a)
OPD
rms
normalized by...
Figure 6.22 Instantaneous far-field...
Figure 6.23 PDF for the...
Figure 6.24 (a) PDF of...
Figure 6.25 The temporal mean...
Figure 6.26 CCDF of a...
Figure 6.27 Probability of the...
Figure 6.28 (a) as a function of...
Figure 6.29 Definitions of different...
Figure 6.30 (a) All available...
Figure 6.31 Airborne Aero-optics...
Figure 6.32 Various turret geometries...
Figure 6.33 A picture and...
Figure 6.34 Schematic of the...
Figure 6.35 (a) Pressure coefficients...
Figure 6.36 Spatial distributions of...
Figure 6.37 Conceptual description of...
Figure 6.38 First six dominant...
Figure 6.39 Schematics of shifting...
Figure 6.40 Spectra of POD...
Figure 6.41 Normalized steady-lending...
Figure 6.42 Normalized
Figure 6.43 (a) Normalized...
Figure 6.44 Transonic flow features...
Figure 6.45 Normalized...
Figure 6.46 The top view...
Figure 6.47 Normalized aperture-averaged...
CHAPTER 07
Figure 7.1 (a) Global jitter...
Figure 7.2 Example of jitter...
Figure 7.3 Variable apertures, applied...
Figure 7.4 Normalized global jitter...
Figure 7.5 Two successive wavefronts...
Figure 7.6 Two successive wavefronts...
Figure 7.7 PDFs of the...
Figure 7.8 A portion of...
Figure 7.9 Normalized values of...
CHAPTER 08
Figure 8.1 Target closed-loop...
Figure 8.2 Effect on Strehl...
Figure 8.3 (a) Schematic of...
Figure 8.4 A phase-averaged...
Figure 8.5 Effect of phase...
Figure 8.6 First 16 POD...
Figure 8.7 Demonstration of how...
Figure 8.8 The first 4...
Figure 8.9 POD temporal coefficients...
Figure 8.10 Reoriented POD modes...
Figure 8.11 Comparison between the...
Figure 8.12 Illustration of small...
Figure 8.13 Illustration of small...
Figure 8.14 System gain as...
Figure 8.15 System gain as...
Figure 8.16 System gain as...
CHAPTER 09
Figure 9.1 Example of power...
Figure 9.2 Power law fits...
Figure 9.3 Normalized residual phase...
Figure 9.4 Power-law fitting...
Figure 9.5 Empirical fit for...
Figure 9.6 Aero-optics compensation...
Figure 9.7 Aero-optical severity...
Figure 9.8 Analytic framework for...
Figure 9.9 Residual wavefront variance...
Figure 9.10 Normalized residual phase...
Figure 9.11 (a) Fit power...
Figure 9.12 Decomposition of the...
Figure 9.13 DM sensitivity transfer...
Figure 9.14 Example AO error...
Figure 9.15 Effect of AO...
Figure 9.16 Adaptive optics residual...
Figure 9.17 Residual wavefront error...
Figure 9.18 Compensated Strehl ratio...
Figure 9.19 Comparison between compensated...
Figure 9.20 Comparison between compensated...
Figure 9.21 Normalized MTF for...
Figure 9.22 Image of a...
Figure 9.23 (a) Target illumination...
Figure 9.24 Active imaging with...
Guide
Cover
Serious page
Title page
Copyright
Table of Contents
Acknowledgements
Begin Reading
References
Index
End User License Agreement
Pages
i
ii
iii
iv
v
vi
vii
viii
ix
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
Acknowledgments
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 individuals 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.
1 Introduction
We considered the title Modern Aero-Optics, but because we believe that this book will become a quintessential reference far into the future, the term “modern” would quickly lose its significance. What we have done here is gathered what is now known about the field of Aero-Optics, including how to measure it, how to estimate its deleterious effects on laser beams, and a discussion of how to mitigate these effects. Any attempt to do this must begin by defining what is meant and what is not meant by aero-optics. In the strictest sense, the term aero-optics refers to the optical effects that a variable-index-of-refraction flow has on the wavefront figure of a laser beam. In aero-optics we are concerned with laser beam propagated through variable-index flows with the understanding that the extent of the propagation through the flow is on the order of the beam’s aperture. This assumes that the extent of the variable-index flow is from one to ten times the beam’s diameter. This last supposition is what distinguishes aero-optics from atmospheric propagation. For atmospheric propagation, the propagation path through the atmosphere ranges from kilometers to hundreds of kilometers, and the optical-turbulence structures as large as hundreds of meters in size (Tatarski 1961; etc.). In fact, because of this it is important to note that it is not possible to cast aero-optical environments into the theoretical constructs of atmospheric optical turbulence. The variability in index-of-refraction of the flow can be caused by any number of conditions that range from the mixing of streams of fluid with different indexes of refraction, to compressibility effects due to the acceleration and deceleration of the flow. In general, aero-optics deals with what is known in atmospheric turbulence as the “outer scale,” that is to say the turbulence has not cascaded to the “inertial range” of the turbulence; thus, cannot be used to quantify aero-optical turbulence. Of course, the fundamental understanding of aero-optics is as applicable to imaging as it is to laser propagation, but from an analytic point of view it is more straightforward to confine our discussion in this book to laser propagation. Although in its strict definition aero-optics refers to propagation through the variable-index flow, we will also include another aero-induced effect referred to as aero buffet, which causes considerable forcing on a beam director. The unsteady force imposed on the beam director results in beam jitter, which directly causes a time-averaged reduction in intensity in the far-field. The most common applications where aero-optics/aero effects play a critical performance role are airborne laser systems and airborne laser free-space communication; thus, some of the material in this book is also applicable to communication.
This is not the first book to deal with aero-optics. The American Institute of Aeronautics and Astronautics published a Progress in Astronautics and Aeronautics Series Volume in 1982, Aero-Optical Phenomena, edited by K.G. Gilbert and L.J. Otten (Gilbert and Otten 1982). That book was made up of a collection of individual chapters written by various authors active in the field in the 1970s. To this day, there is useful information in that book; however, most of the information and data presented in it has been proven to be incorrect, primarily due to the instrumentation limitations and methods of reducing data available at the time. We hope that this book will replace the ubiquitous use of the information in the previous book, much of which is not only incorrect but also misleading.
It is interesting to note that essentially all funding in aero-optics had ended by the end of the 1980s because the work performed in the area was considered mature and could not be further extended due to limited measurement methods. In the early 1990s a new initiative at the Air Force Office of Scientific Research (AFOSR) began to revisit aero-optics. What would become the Aero-Optics Group at Notre Dame was the first to receive funding in AFOSR’s decision to again fund the topic. In this chapter, we will discuss the rationale for revisiting the topic of aero-optics.
1.1 Motivation for Revisiting Aero-Optics
The original motivation for emphasizing aero-optics in the 1970s was to support the first airborne directed-energy system, The Airborne Laser Laboratory or ALL (Duffner 1997), shown in a top left picture in Figure 1.1. A rotating turret, mounted on top of the aircraft, was used to point the laser beam in a desired direction. Lasers had only recently been demonstrated, and the first truly high-energy laser was the Carbon Dioxide Gas Dynamic Laser, GDL, developed by AVCO, which lased at a wavelength of 10.6 μm. The aero-optics book edited by Gilbert and Otten was based solely on work funded in support of the ALL program. What we now refer to as aero-optics was first addressed by Liepmann in 1952 to assess the effect of high-speed boundary layers in supersonic tunnels to investigate the sharpness of schlieren images (Leipmann 1952). In the mid-1950s, Stine and Winovich performed experiments attempting to validate Liepmann’s theory (Stine and Winovich 1956). Early papers on aero-optics in support of the ALL made use of methods introduced by Tatarski (Tatarski 1961; Sutton 1969). It should be noted that virtually all the theoretical constructs for estimating aero-optical effects were for attached turbulent boundary layers, but were applied to shear layers by default. Near the end of the 1980s, a memo was circulated inside the Air Force Weapons Laboratory that categorically stated that aero-optic aberrations for a short-wavelength (i.e., lasing at a wavelengths much smaller than 10 microns) laser-beam directed from an aircraft flying at Mach 0.8 and 33,000 ft would suffer a reduction in intensity due to aero-optic effects of about 5 percent at the most. At the same time, several prominent people in the field of aero-optics had suggested that the field of aero-optics was essentially mature, and that the opportunities for further research were to polish up the techniques already in existence and maybe apply them to a few more flows (Sutton 1985). Thus, aero-optics was considered simply irrelevant. Others were willing to assume that aero-optical effects may have degraded the performance of the ALL at certain pointing directions, but results showed only between 1 and 10 percent reduction in intensity at the target. However, aero-optical effects strongly depend on the laser wavelength. While all these estimates were correct for the long laser wavelength of 10.6 μm, for shorter wavelengths, the aero-effects result in much more severe intensity reduction; however, misguided by the circulating memo, a system hit of let’s only about 5% was adapted for system performance predictions.
Figure 1.1 Airborne Laser Laboratory (ALL) (USAF Museum / Wikimedia Commons), Airborne Laser Testbed (formally AirBorne Laser or ABL) (Bobby Jones / Wikimedia Commons Public domain) and Advanced Tactical Laser (ATL) (U.S. Air Force / Wikimedia Commons Public domain).
While the ALL was shown to be effective at shooting down surface-skimming cruise missiles and missiles shot directly at it (i.e., self-defense), range was a concern. The damage mechanism for a laser weapon is producing and maintaining an average intensity, , at the aim point on a target above a minimum threshold and maintaining it for sufficient time, , to exceed a minimum accumulated fluence (Bloembergen et al. 1987). The diffraction-limited intensity is the highest physically possible intensity, achievable only when no optical distortions are present along the propagation of the laser beam. For a diffraction-limited laser beam, the maximum intensity on the target is
where is the power, is the diameter of the beam aperture at the exit pupil of the beam director, is the range (effective focal length) and is the laser wavelength. (Equation 1.1) is fully derived in Chapter 2, Equation (2.25). The effect of wavelength has clear implications. First, for the same power and beam diameter decreasing the wavelength directly increases the range to obtain the same maximum intensity. But, it also implies that for the same range, the required power is dramatically reduced. So, under the misimpression that aero-optics would reduce the intensity on target by 5%, at most, the emphasis was placed on developing a high-power laser at shorter wavelength. In fact, the Chemical Oxygen-Iodine Laser, COIL, which lased at 1.315 μm, developed in the late 1980s and early 1990s, met that goal.
In the same memo circulating in the late 1980s that categorically stated that aero-optical effects would reduce performance above 33,000 ft by 5% at most, based on “measurements,” also stressed the importance of reducing imperfections of the optical components in the beam-control system to a very small number (Gilbert 2013). To address this concern, it is necessary to make use of some terms and equations that will be addressed in more detail in Chapter 2. The first of these is the definition of Strehl Ratio, , which is defined as the instantaneous intensity on the target in the far-field, , or its time average, divided by the maximum value of so-called diffraction-limited intensity, . A simple estimate based on is given by the Large-Aperture Approximation,
where is a time average of the spatial rms of the optical path difference, OPD, over the aperture. The optical path difference will be properly defined in Chapter 2; however, here consider it a measure of the magnitude of the aberrations present. More discussion about the assumptions behind (Equation 1.2) will also be provided in Chapter 2.
New funding made available by AFOSR in the early 1990s addressed the possibility that the aero-optic effects, assumed to reduce the intensity by 5% at most, might be wrong. Without any of the new information we now have, it is instructive to plot these two equations and examine their implications. To do this, let us suppose that the maximum intensity of the 10.6 μm for CO2 Gas Dynamic Laser (GDL), was reduced by 5% due to aero-optical effects from the flow over the beam director. Figure 1.2 plots first the effect of reducing the wavelength for a diffraction-limited beam, given by (Equation 1.1); the second plot is the effect the same aberrations that reduced the 10.6 μm performance by 5% has on the shorter wavelengths, given by (Equation 1.2). The wavelength of various types of lasers are also marked on the figures, CO2, Hydrogen-Fluoride (HF), Deuterium-Fluoride (DF) and the Chemical Oxygen-Iodine Laser (COIL). It should be noted that COIL laser with its wavelength of 1.315 μm, was the High Energy Laser (HEL) used in 2000s in both the AirBorne Laser (ABL), shown in Figure 1.1, and Advanced Tactical Laser (ATL), also shown in Figure 1.1. The ABL used a nose-mounted turret and the ATL used a side-mounted turret underneath the aircraft. Solid-state lasers at this writing have wavelengths of approximately 1 μm. Figure 1.2, clearly shows that a laser wavelength near 1 μm would drive the Strehl ratio to near zero.
Figure 1.2 (a) Ratio of maximum diffraction limited intensity on target to that for a laser with the wavelength of 1 μm based on (Equation 1.1). Source: Jumper et al. (2013) / With permission of SPIE. (b) Strehl ratio as a function of the laser wavelength, (Equation 1.2),based on optical aberrations at the exit pupil that degrade the intensity on target by 5% for a 10.6 μm laser. Source: Jumper et al. (2013) / With permission of SPIE.
Until the early 1990s, the Weapons Laboratory memo from the 1980s made consideration of aero-optics for new airborne laser systems a simple 5% Strehl ratio budget hit. In 1992, Notre Dame received a small grant from AFOSR to try to measure the amplitude, temporal and spatial frequency content of aero-optical flows of various types. This led to new types of wavefront sensors based on small-aperture laser beams, which will be discussed in Chapter 3. A serendipitous opportunity to make wavefront measurements in a Mach 0.8 shear layer at the Arnold Engineering Development Center (AEDC) found that rather than being relatively benign, the shear layer, which will always be present for flows separating off a turret, produced devastating aero-optical effects that had high spatial and temporal frequencies (Jumper and Fitzgerald 2001; Wang et al. 2012; Jumper and Gordeyev 2017). The AEDC experiment turned out to be the single most important aero-optical experiment to date. The data showed that the for an aperture of at least 20 cm was 0.43 μm. For a 1 μm laser wavelength this would result in a Strehl ratio of only 0.0007! Thus, began a now 25-year program of research that has moved from basic laboratory research to flight testing.
2 Fundamentals
This chapter gives a minimal background in optics to understand the aero-optics material to follow in later chapters. We will introduce wavefront distortions and their components, and quantitative ways to characterize them and several definitions. We will discuss far-field intensity patterns on a target, and how different wavefront components affect it. We will also derive several useful relationships between the density field, wavefronts and the resulting far-field intensity.
2.1 Wavefronts and Index of Refraction
There are many excellent textbooks on the development of propagation rules for electromagnetic waves; see Klein (1970), for instance. Analysis shows that light propagates in a medium at some velocity, v, which is a property of the medium. Light always travels slower in a medium, where the photons are constantly absorbed and re-emitted an instant later by atoms or molecules. In a vacuum, the speed of light is constant, (approximately, m/s). Since the speed in vacuum is constant and known, index-of-refraction, , is defined as the ratio of the speed in vacuum divided by the speed of light, , in the medium, . Consequently, the index-of-refraction is always greater than or equal to unity, .
Consider light propagating through a medium of variable index-of-refraction. For simplicity, consider a monochromatic point light source emitting electromagnetic waves at a wavelength, , and a frequency, , as schematically shown in Figure 2.1. By definition, a wavefront is a simply connected surface of the constant phase at some fixed moment of time, . For example, the solid and dashed lines in Figure 2.1 represent the connected points where the light amplitude reaches either a maximum or a minimum. When light propagates outward, points on the wavefront propagate with the local speed of light. If there is vacuum between points A and Aʹ, it would take time to get from point A to point Aʹ. If a different point B at the same wavefront surface travels through a region of some media, with , for the same traveled time, , the wavefront will travel less distance, , compared to the would-have-been undistorted wavefront, indicated as a dotted-dashed green line in Figure 2.1. Thus, the otherwise spherical wavefront becomes distorted in space. The distortions are always negative (lagging), compared to the undistorted wavefront in vacuum.
Figure 2.1 Distortions of monochromatic light wavefronts.
For compressible flows the index-of-refraction depends on the media density, ρ, via the Gladstone-Dale relation (Gladstone and Dale 1863),
where KGD is the Gladstone-Dale constant. This constant depends on the gas mixture and the laser wavelength (Gardiner et al. 1980); for dry air over the infrared, visible and into the infrared range KGD for room temperatures can be approximated by the following equation (Barrell and Sears 1939),
For the double-frequency Yag:Nd laser, nm, , and for a laser with μm, .
2.2 Huygens’ Principle
For distorted wavefronts, light travels along the original undistorted straight lines but changes its local direction. This phenomenon is known as refraction. For instance, a lens can change a divergent beam into a beam with a plane wavefront, often called a collimated beam, as different parts of the wavefront travel through the parts of the lens with different thicknesses. The refraction is a consequence of the Huygens Principle, which states that a wavefront propagating through a variable index-of-refraction media can be broken up into an infinite number of self-emitting point sources along the wavefront surface, as shown in Figure 2.2. After a small increment time, Δt, the sources of the radiating spheres, according to wave optics, sum into a surface of constant phase exactly parallel to the previous surface aberrated only by any speeding up or slowing down of the local spherical waves emanating from each point source. A shorthand version of Huygens’ principle is that a wavefront always propagates locally normal to itself.
Figure 2.2 Hyugens’ principle.
As mentioned before, a wavefront is defined as a surface of the constant phase, . It is more convenient, however, to define the wavefront as a distance from a known surface, usually a -plane with a fixed . An example for a collimated beam is shown in Figure 2.3. Let us say it takes an amount of time, , for the light to travel to the -surface in a vacuum. If the medium with is present along the beam, during the same time the light will travel the smaller distance, . Thus, the distance from the -plane to the wavefront surface will be
Figure 2.3 Distortions imposed on the collimated beam.
Using the definition of the index-of-refraction and recalling that , this equation can be re-written as
Finally, using the Gladstone-Dale relation, (Equation 2.2), it can be written as
Here, we allowed the density field to depend on time, as the turbulent field can be safely treated as a frozen medium during beam propagation.
As mentioned previously, Huygens’ principle states that, locally, the wavefront always travels normal to itself. Another consequence is that the local direction of the propagation of light, relative to the undistorted direction, z, is given by an outward normal vector, indicated in Figure 2.2, which is equal to a local gradient of the wavefront,
In the case of a collimated beam, shown in Figure 2.3, it is easy to see that the phase function is related to the wavefront, , as
Plugging this equation into (Equation 2.5) gives the components of the normal vector as
It is convenient to define the local direction of the light as the angles between the z-direction and the normal vector; these angles are known as the local deflection angles, and ,
In most cases, the distorted wavefronts are on the order of a micron or less, while all typical scales in the -plane are on the order of a millimeter or more. Thus, the partial derivatives in the above equation are small and the tangent function can be dropped to get the final set of equations, relating the wavefront and the local deflection angles,
(Equation 2.6) forms a mathematical background for several types of the wavefront sensors, such as a Shack-Hartmann wavefront sensor and a Malley probe. See Chapter 3 for a detailed discussion of their principle of operation.
2.3 Basic Equations and Optical Path Difference
Aero-optics involves the refracting effect on a laser’s wavefront as it propagates through a variable density flow field. The theoretical foundation for electromagnetic wave propagation in a turbulent medium can be found in Monin and Yaglom (1975). Here we briefly outline a basic derivation, assumptions and definitions in the context of aero-optics. In the most general sense, the propagation of electromagnetic waves is governed by the Maxwell equations. For aero-optical problems, the timescale for optical propagation is negligibly short relative to flow timescales, and hence optical propagation can be solved under the assumption of frozen flow at each time instant. If the optical wavelength is much shorter than the smallest flow scale (Kolmogorov scale), which is generally the case, and the effect of depolarization is negligible, the Maxwell equations are reduced to a vector wave equation in which all three components of the electromagnetic field, , are decoupled. In particular, a scalar component of the electric field at a fixed frequency, , becomes where the spatial distribution of the electric field, , is governed by the following equation,
Here again, is the index-of-refraction and is the speed of light in vacuum. Unless stated otherwise, in this book we will denote the direction of the beam propagation as the z-direction and the -plane as the plane normal to the z-direction, as shown in Figure 2.4. If the beam amplitude does not change significantly over the wavelength, which is almost always the case in practical applications, the electric field can be approximated as a fast-changing component in the z-direction, multiplied by a slowly changing envelope function, , (the so-called paraxial approximation),
Figure 2.4 Schematic of the aero-optical problem due to the turbulent flow around an aircraft.
where , and is the wavenumber. Substituting this approximation into (Equation 2.7) gives the following equation for the A-function,
