Optical Beam Control
Imaging Satellites and Laser Systems
1st Edition
Published on 21. October 2025
Book
Hardback
352 pages
978-1-119-83024-5 (ISBN)
Description
OPTICAL BEAM CONTROL
Imaging Satellites and Laser Systems
The authors have designed this timely new book in response to the need for up-to-date and complete coverage of multi-disciplinary basic principles of optical beam control for imaging satellites and laser systems. As the uses of imaging satellites and laser systems increase, optical beam control for these systems will occupy engineers and scientists for years to come. The book introduces space telescopes, ground telescopes, laser communications, and high energy laser systems, covering light sources, lenses, wave optics, diffraction, and polarization, as well as fine pointing control, classical control, modern control, Kalman filters, sensors, actuators, flexible control, slew maneuvers, and acquisition, tracking, and pointing.
The authors have over 30 years' experience in research, development, and testing of complex state-of-art systems, such as 3-meter diameter segmented mirror space telescopes and high energy laser beam control systems.
As a text and reference dealing with basics of optical beam control, this book includes information on:
Sources of aberrations, vibration and jitter, optical aberrations, air turbulence, and measure of optical aberrations
Vibration isolation and jitter control, active jitter control, strap down, and inertial stable platform
Adaptive optics, wavefront sensors, wavefront reconstruction, adaptive optics configurations, and control systems
Imaging satellites, telescope design, optical train components, image aberration, and performance analysis
Laser beam control hardware, laser aberration, and laser performance analysis
Optical Beam Control is an essential reference for engineers working in imaging satellites and laser systems along with electrical engineers focused on optics, satellites, lasers, and control systems. The text is also valuable for students taking courses on laser technology, satellite control, spacecraft design, and optics and photonics.
Imaging Satellites and Laser Systems
The authors have designed this timely new book in response to the need for up-to-date and complete coverage of multi-disciplinary basic principles of optical beam control for imaging satellites and laser systems. As the uses of imaging satellites and laser systems increase, optical beam control for these systems will occupy engineers and scientists for years to come. The book introduces space telescopes, ground telescopes, laser communications, and high energy laser systems, covering light sources, lenses, wave optics, diffraction, and polarization, as well as fine pointing control, classical control, modern control, Kalman filters, sensors, actuators, flexible control, slew maneuvers, and acquisition, tracking, and pointing.
The authors have over 30 years' experience in research, development, and testing of complex state-of-art systems, such as 3-meter diameter segmented mirror space telescopes and high energy laser beam control systems.
As a text and reference dealing with basics of optical beam control, this book includes information on:
Sources of aberrations, vibration and jitter, optical aberrations, air turbulence, and measure of optical aberrations
Vibration isolation and jitter control, active jitter control, strap down, and inertial stable platform
Adaptive optics, wavefront sensors, wavefront reconstruction, adaptive optics configurations, and control systems
Imaging satellites, telescope design, optical train components, image aberration, and performance analysis
Laser beam control hardware, laser aberration, and laser performance analysis
Optical Beam Control is an essential reference for engineers working in imaging satellites and laser systems along with electrical engineers focused on optics, satellites, lasers, and control systems. The text is also valuable for students taking courses on laser technology, satellite control, spacecraft design, and optics and photonics.
More details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 21 mm
Weight
826 gr
ISBN-13
978-1-119-83024-5 (9781119830245)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Brij N. Agrawal | Jae Jun Kim | Sachin Agrawal
Optical Beam Control
Imaging Satellites and Laser Systems
E-Book
11/2025
1st Edition
Wiley
€130.99
Available for download
Brij N. Agrawal | Jae Jun Kim | Sachin Agrawal
Optical Beam Control
Imaging Satellites and Laser Systems
E-Book
10/2025
1st Edition
Wiley
€130.99
Available for download
Persons
Dr. Brij N. Agrawal is a Distinguished Professor in the Department of Mechanical and Aerospace Engineering and Director of the Spacecraft Research and Design Center at Naval Postgraduate School (NPS).
Dr. Jae Jun Kim joined the NPS in 2005. He is currently a Research Associate Professor in the Department of Mechanical and Aerospace Engineering.
Sachin Agrawal is an Engineer who has worked on spacecraft guidance, navigation, and control at Maxar Technologies and Lockheed Martin.
Dr. Jae Jun Kim joined the NPS in 2005. He is currently a Research Associate Professor in the Department of Mechanical and Aerospace Engineering.
Sachin Agrawal is an Engineer who has worked on spacecraft guidance, navigation, and control at Maxar Technologies and Lockheed Martin.
Content
Preface xvii
Acknowledgments xix
1 Introduction 1
1.1 Optical Beam 1
1.2 Telescopes 2
1.2.1 Space Telescope 3
1.2.1.1 Hubble Space Telescope 3
1.2.1.2 James Webb Space Telescope 5
1.2.2 Ground Telescope 8
1.2.2.1 Keck Telescope 8
1.3 Laser Systems 10
1.3.1 High-power Laser Systems 11
1.3.1.1 Airborne Laser System 11
1.3.2 Low Power Laser Systems 12
1.3.2.1 Laser Communications Relay Demonstration 13
1.4 Optical Beam Control Challenges 15
2 Optics 17
2.1 Light Sources 17
2.1.1 Point Source and Extended Source 17
2.1.2 Coherent and Incoherent Light Sources 18
2.1.3 Polarized and Unpolarized Light Sources 19
2.1.4 Light Amplification by Stimulated Emission of Radiation 19
2.2 Properties of Light 21
2.2.1 Interference 21
2.2.2 Polarization 23
2.2.3 Doppler Effect 24
2.2.4 Light Propagation in Vacuum 24
2.2.5 Light Interaction with Different Media 25
2.2.6 Transmission and Reflection 25
2.2.7 Refraction 26
2.2.8 Diffraction 27
2.2.9 Absorption 28
2.2.10 Scattering 28
2.3 Geometric Optics 29
2.3.1 Lens 29
2.3.2 Mirrors 31
2.3.3 Image Formation Using Lenses and Mirrors 32
2.3.4 Geometric Optics for Telescopes and Microscopes 34
2.3.5 Geometric Optics for 4f Optical System 36
2.4 Physical Optics and Fourier Optics 37
2.4.1 Scalar Diffraction Theory 37
2.4.2 Fourier Optics 38
2.4.3 Amplitude Spread Function and Point Spread Function 39
2.4.4 Coherent and Incoherent Imaging System 40
2.4.5 Optical Transfer Function and Modulation Transfer Function 40
3 Feedback Control 43
3.1 Foundations of Classical Control 43
3.1.1 The Laplace Transform 43
3.1.2 The Inverse Laplace Transform 44
3.1.3 Transfer Functions, Zeros, Poles 44
3.1.3.1 dc Motor Dynamics Model 45
3.1.4 First-order Systems 47
3.1.5 Second-order Systems 47
3.1.5.1 Effect of Zeros on the Response 50
3.1.5.2 Bounded-Input Bounded-Output (BIBO) Stability 51
3.1.6 Basic Equations for Feedback 51
3.1.6.1 Tracking, Regulation, and Noise 53
3.1.7 System Type 53
3.1.8 Basic Feedback Controllers 54
3.1.8.1 Proportional Control 54
3.1.8.2 Integral Control 54
3.1.8.3 Derivative Control 55
3.1.8.4 Proportional-integral-derivative Control 56
3.1.8.5 Heuristic Tuning of the PID Controller 57
3.1.8.6 Velocity Feedback (Rate Feedback) Control 59
3.1.8.7 Feedforward Control 59
3.2 The Root Locus 60
3.2.1 The Root Locus Technique 60
3.3 Frequency Response Methods 65
3.3.1 Bode Plots 65
3.3.1.1 Bode Plot Construction 65
3.3.1.2 Non-minimum Phase Transfer Functions 68
3.3.1.3 Relating Root Locus to Bode Plots 70
3.3.2 Gain and Phase Margin 71
3.3.3 Lead and Lag Compensator Design 72
3.3.3.1 Pure Gain Compensation 72
3.3.3.2 Lead Compensation 73
3.3.3.3 Lag Compensation 76
3.3.3.4 Lead-lag Compensation 77
3.3.3.5 Summary of Lead and Lag Control Techniques 78
3.3.4 PID Compensation in the Frequency Domain 79
3.3.5 Time Delay on a Bode Plot 79
3.3.6 Summary of Classical Design Techniques 81
3.4 Flexible Control 83
3.4.1 Second-order Filters 86
3.4.2 Colocated Control Design 87
3.4.3 Non-colocated Control Design 91
3.4.4 Non-colocated Control Design Solution 92
3.5 State-space Models 94
3.5.1 Linearization of a System 97
3.5.2 The Matrix Exponential 102
3.5.2.1 Computing e At and Modal Interpretation 103
3.5.3 State-space Stability 105
3.5.3.1 Canonical Forms 106
3.5.4 State Feedback Design 108
3.5.5 Controllability 109
3.5.5.1 Pole-placement 111
3.5.6 Reference Input Design in State-space 113
3.5.7 Estimator Design in State-space 114
3.5.8 Observability 115
3.5.9 The Separation Theorem 117
3.5.9.1 Closed-loop Poles 119
3.6 Introduction to Discrete-time Systems 119
3.6.1 Discrete-time Linear Dynamical Systems 121
3.6.1.1 Solution of Discrete-time Linear Dynamical Systems 122
3.6.2 Block Toeplitz Matrices in Discrete-time Systems 123
3.7 Introduction to Optimal Control 123
3.7.1 Linear Algebra Review 123
3.7.1.1 Vector Operations 124
3.7.1.2 Matrix Multiplication 124
3.7.1.3 Subspaces 124
3.7.1.4 Range, Null Space, and Rank 125
3.7.1.5 Orthonormal Basis and Orthogonal Complement 126
3.7.1.6 Properties of Orthonormal Sets and Semi-orthogonal Matrices 126
3.7.1.7 Orthogonal Complement 126
3.7.2 Linear Equations 127
3.7.3 Symmetric Matrices, Positive Definiteness, and Ellipsoids 127
3.7.3.1 Ellipsoids 127
3.7.4 Estimation and Control Problems 127
3.7.5 Singular Value Decomposition 128
3.7.5.1 Control Ellipsoid 129
3.7.5.2 Condition Number 130
3.7.6 Least Squares Estimation 131
3.7.6.1 Derivation of Least Squares Solution 131
3.7.6.2 Linear Regression 132
3.7.7 Minimum-norm Optimization 132
3.7.8 Multiobjective Least Squares 136
3.7.9 Completing the Square 137
3.7.10 Block Matrix Inversion 137
3.7.11 The Linear Quadratic Regulator 138
3.7.11.1 Dynamic Programming Approach 138
3.7.11.2 Summary of LQR Solution via Dynamic Programming 140
3.7.11.3 Steady-state Regulator 140
3.7.12 Probability Review 142
3.7.12.1 Random Variables 143
3.7.12.2 Random Vectors 145
3.7.12.3 Marginal Distributions 147
3.7.12.4 Conditional Distributions 148
3.7.13 Mean Squared Error 149
3.7.14 Linear Model with Noise 150
3.7.15 MAP and MMSE Estimates 150
3.7.16 The Kalman Filter 150
3.7.16.1 State Estimation Notation 151
3.7.16.2 The Measurement Update 151
3.7.16.3 Time Update 152
3.7.16.4 Summary of the Kalman Filter Recursion 152
3.7.16.5 Riccati Recursion 152
3.7.16.6 Steady-state Kalman Filter 152
4 Sources of Aberrations 157
4.1 Vibration and Jitter 157
4.1.1 Platform Jitter 157
4.1.2 Atmospheric Jitter 158
4.2 Optical Aberrations 158
4.2.1 Defocus and Spherical Aberration 158
4.2.2 Coma Aberration 159
4.2.3 Astigmatism Aberration 159
4.2.4 Field Curvature 160
4.2.5 Image Distortion 161
4.2.6 Chromatic Aberration 161
4.2.7 Optical Surface Errors 161
4.3 Air Turbulence 162
4.3.1 Kolmogorov Theory 162
4.3.2 Air Turbulence Parameters 163
4.3.2.1 Refractive Index Structure Parameter 163
4.3.2.2 Fried's Atmospheric Coherence Length 165
4.3.2.3 Greenwood Frequency 166
4.3.2.4 Isoplanatic Angle 166
4.3.2.5 Rytov Parameter 167
4.3.3 Non-Kolmogorov Atmospheric Turbulence 167
4.3.4 Effect of Air Turbulence in Optical Beam Propagation 167
4.3.4.1 Beam Jitter 167
4.3.4.2 Beam Spreading 167
4.3.4.3 Scintillation 168
4.4 Measure of Aberrations 169
4.4.1 Point Spread Function 169
4.4.2 Optical Transfer Function and Modular Transfer Function 170
4.4.3 Encircled and Ensquared Energy 171
4.4.4 Wavefront Error 171
4.4.5 Strehl Ratio 172
5 Vibration Isolation and Jitter Control 175
5.1 Introduction 175
5.2 Passive Vibration and Jitter Control 177
5.2.1 Passive Vibration Control 178
5.2.1.1 Viscoelastic Devices 178
5.2.1.2 Viscous Devices 179
5.2.1.3 Magnetic Devices 180
5.2.1.4 Passive Piezoelectrics 181
5.2.1.5 Tuned Mass Dampers 181
5.3 Active Vibration and Jitter Control 184
5.3.1 Actuators 184
5.3.1.1 Voice Coils 184
5.3.1.2 Piezoceramic 184
5.3.1.3 Fast Steering Mirrors 188
5.3.1.4 Jitter Sensor 189
5.3.2 Control Algorithms 190
5.3.2.1 Transverse Filter 190
5.3.3 Active Optics Beam Jitter Control 191
5.3.3.1 Experimental Results 193
5.3.4 Slew Maneuvers 193
5.3.4.1 Bang-Bang Profile 194
5.3.4.2 Versine Profile 195
5.3.4.3 Input Shaping 195
5.3.5 Reference Laser Beam 197
5.4 Active Vibration Isolation 199
5.4.1 Ultra Quiet Platform 199
5.4.2 Precision Pointing Hexapod 201
6 Adaptive Optics 203
6.1 Introduction 203
6.2 Wave Front Sensors 205
6.2.1 Shack-Hartman Wavefront Sensor 205
6.2.2 Curvature Wavefront Sensor 206
6.2.2.1 Intensity Difference and Curvature 207
6.2.2.2 Poisson Equation for Wavefront Reconstruction 207
6.2.3 Pyramid Wavefront Sensor 207
6.2.3.1 Intensity Difference Calculation 208
6.2.3.2 Reconstructing the Wavefront Error 208
6.2.4 Choosing a Sensor 208
6.3 Wave Reconstruction 208
6.3.1 Zonal Method 209
6.3.1.1 Hudgin Grid Pattern 209
6.3.1.2 Southwell Grid Pattern 209
6.3.1.3 Fried Grid Pattern 209
6.3.2 Least Squares Solution 210
6.3.3 Modal Reconstruction 210
6.4 Fast Steering Mirrors and Deformable Mirrors 211
6.4.1 Fast Steering Mirrors 211
6.4.1.1 Voice Coil Actuated FSM 212
6.4.1.2 Piezoelectric Actuated Mirrors 212
6.4.1.3 Identification of the FSM Dynamics 213
6.4.2 Deformable Mirrors 213
6.4.2.1 DM Characteristics 214
6.4.2.2 Types of DMs 215
6.4.2.3 Comparison of DMs 217
6.4.2.4 DMs for NPS Multi-conjugate AO Testbed 218
6.5 AO Configurations 219
6.5.1 Conventional AO System 219
6.5.2 Laser Guide Star AO 220
6.5.3 Multi-conjugate AO System 221
6.5.4 Woofer-Tweeter AO System 223
6.5.5 Beaconless Target-in-the-loop System 225
6.6 AO Control 226
6.6.1 Influence Function and Influence Matrix 226
6.6.2 Closed-loop Feedback AO Control System Design 228
7 Imaging Satellites 233
7.1 Introduction 233
7.2 Telescope Designs 233
7.2.1 Optical Beam Aberrations 234
7.2.1.1 Spherical Aberration (Third Order) 234
7.2.1.2 Coma (Fifth Order) 234
7.2.1.3 Astigmatism (Seventh Order) 234
7.2.1.4 Curvature of Field (Ninth Order) 235
7.2.2 Telescopes 235
7.2.3 Cassegrain Telescopes 237
7.2.4 Ritchey-Chretien Telescope 238
7.2.5 Three-mirror Anastigmat Telescope 239
7.3 Telescope Performance 240
7.3.1 Diffraction 240
7.3.1.1 Beam Propagation 241
7.3.1.2 Modulation Transfer Function 243
7.3.1.3 Optical Transfer Function 245
7.3.1.4 Resolution 245
7.3.2 Object Image Generation 246
7.3.2.1 Digital Focal Plane 246
7.3.2.2 Ground Sampling Distance 247
7.3.2.3 Quality Factor 247
7.3.2.4 Ground Resolution Distance 248
7.3.2.5 Jitter Requirements 248
7.3.2.6 Pointing Accuracy 248
7.3.3 Example 249
7.3.4 Sampling MTF 250
7.3.5 Aliasing 250
7.4 Optical Components 252
7.4.1 Focal Plane 252
7.4.1.1 Focal Plane Technology 252
7.4.1.2 Focal Plane Devices 253
7.4.2 Operation Concepts 254
7.4.2.1 Pushbroom Scanner 256
7.4.2.2 Whiskbroom Scanner 256
7.4.2.3 Step-stare Scanner 256
7.4.2.4 Comparison of push broom and starring imaging 257
7.5 Image Aberration 257
7.5.1 Pointing, Jitter, and Smear 257
7.5.2 National Image Interpretability Rating Scale 259
7.5.2.1 Signal-to-noise Ratio 259
7.5.2.2 General Image Quality Equation 259
7.5.2.3 Edge Response Function 260
7.6 Space Telescopes 260
7.6.1 Segmented Mirror Telescope 260
7.6.1.1 Optical Configuration 261
7.6.1.2 Analytical Model 261
7.6.1.3 First-order Modeling to Develop Sensitivities 264
7.6.1.4 Experimental Verification 266
7.7 Telescope Design Example 268
7.7.1 Misson 268
7.7.1.1 Requirements 268
7.7.2 Trade Space 269
7.7.3 Optical Telescope Design 269
7.7.3.1 Image Collection 270
7.7.4 Telescope Components 273
8 Laser Systems 275
8.1 Laser Fundamentals 275
8.1.1 Stimulated Emission 275
8.1.2 Resonant Cavities 276
8.1.3 Laser Characteristics 277
8.1.3.1 Monochromaticity 277
8.1.3.2 Coherence 277
8.1.3.3 Polarization 277
8.1.3.4 Mode Shapes 277
8.1.4 Type of Lasers 278
8.1.4.1 Gas Lasers 278
8.1.4.2 Diode Lasers 278
8.1.4.3 Dye Lasers 278
8.1.4.4 Solid-state Lasers 278
8.1.4.5 Fiber Laser 278
8.1.4.6 Chemical Lasers 278
8.1.4.7 Free-electron Lasers 279
8.1.4.8 Continuous Wave Lasers 279
8.1.4.9 Pulsed Lasers 279
8.2 Laser Beam Profile 280
8.3 Laser Beam Aberrations 286
8.3.1 Laser Beam Aberration Metrics 286
8.3.2 Laser Beam Quality 287
8.3.3 Optical Component 288
8.3.4 Telescope Central Obscuration 288
8.3.5 Optical Jitter 289
8.3.6 Higher Order Aberrations 289
8.3.7 Atmospheric Transmission 290
8.3.8 Scintillation 290
8.3.9 Additional Sources of Laser Beam Aberrations 291
8.4 Laser Beam Control Components 292
8.4.1 Beam Director 292
8.4.2 Fast Steering Mirrors 293
8.4.3 Optical Inertial Reference Unit 295
8.4.4 Light Sensors 296
8.4.4.1 Photodiodes 297
8.4.4.2 Focal Plane Arrays 298
8.5 Visual Object Tracking 300
8.5.1 Centroid Algorithm 300
8.5.2 Correlation Tracker 301
8.6 Beam Control for Laser Systems 301
8.6.1 Acquisition, Tracking, and Pointing of Laser Systems 301
8.6.1.1 Acquisition and Coarse Tracking 302
8.6.1.2 Fine Tracking and Pointing 302
8.6.2 Optical Jitter Control for LOS Stabilization 304
8.6.3 Adaptive Optics for Laser Systems 304
8.7 Free-space Laser Communication System 304
8.7.1 Space Laser Communication Terminal 306
8.7.1.1 Telescope 306
8.7.1.2 Optical Beam Jitter Control for LOS Stabilization 307
8.7.1.3 Acquisition, Tracking, and Pointing 307
8.7.2 Optical Ground Stations 308
8.7.3 Optical Transmitter and Receiver Modem 310
8.7.3.1 Laser Source 310
8.7.3.2 Coding and Modulation 310
8.7.3.3 Fiber Amplifier 311
8.7.3.4 Demodulation 311
8.7.3.5 Detector 311
8.7.4 Optical Link Analysis 311
8.8 High-energy Laser Systems 312
8.8.1 Overview of High-energy Laser Beam Control 312
8.8.1.1 High-energy Laser Source 313
8.8.1.2 Acquisition, Tracking, and Pointing 314
8.8.1.3 Optical Jitter Control for LOS Stabilization 315
8.8.1.4 Atmospheric Turbulence Compensation 315
8.8.2 Airborne Laser System 315
8.8.2.1 Acquisition, Tracking, and Pointing of ABL System 317
8.8.2.2 LOS Stabilization of ABL System 318
Index 319
Acknowledgments xix
1 Introduction 1
1.1 Optical Beam 1
1.2 Telescopes 2
1.2.1 Space Telescope 3
1.2.1.1 Hubble Space Telescope 3
1.2.1.2 James Webb Space Telescope 5
1.2.2 Ground Telescope 8
1.2.2.1 Keck Telescope 8
1.3 Laser Systems 10
1.3.1 High-power Laser Systems 11
1.3.1.1 Airborne Laser System 11
1.3.2 Low Power Laser Systems 12
1.3.2.1 Laser Communications Relay Demonstration 13
1.4 Optical Beam Control Challenges 15
2 Optics 17
2.1 Light Sources 17
2.1.1 Point Source and Extended Source 17
2.1.2 Coherent and Incoherent Light Sources 18
2.1.3 Polarized and Unpolarized Light Sources 19
2.1.4 Light Amplification by Stimulated Emission of Radiation 19
2.2 Properties of Light 21
2.2.1 Interference 21
2.2.2 Polarization 23
2.2.3 Doppler Effect 24
2.2.4 Light Propagation in Vacuum 24
2.2.5 Light Interaction with Different Media 25
2.2.6 Transmission and Reflection 25
2.2.7 Refraction 26
2.2.8 Diffraction 27
2.2.9 Absorption 28
2.2.10 Scattering 28
2.3 Geometric Optics 29
2.3.1 Lens 29
2.3.2 Mirrors 31
2.3.3 Image Formation Using Lenses and Mirrors 32
2.3.4 Geometric Optics for Telescopes and Microscopes 34
2.3.5 Geometric Optics for 4f Optical System 36
2.4 Physical Optics and Fourier Optics 37
2.4.1 Scalar Diffraction Theory 37
2.4.2 Fourier Optics 38
2.4.3 Amplitude Spread Function and Point Spread Function 39
2.4.4 Coherent and Incoherent Imaging System 40
2.4.5 Optical Transfer Function and Modulation Transfer Function 40
3 Feedback Control 43
3.1 Foundations of Classical Control 43
3.1.1 The Laplace Transform 43
3.1.2 The Inverse Laplace Transform 44
3.1.3 Transfer Functions, Zeros, Poles 44
3.1.3.1 dc Motor Dynamics Model 45
3.1.4 First-order Systems 47
3.1.5 Second-order Systems 47
3.1.5.1 Effect of Zeros on the Response 50
3.1.5.2 Bounded-Input Bounded-Output (BIBO) Stability 51
3.1.6 Basic Equations for Feedback 51
3.1.6.1 Tracking, Regulation, and Noise 53
3.1.7 System Type 53
3.1.8 Basic Feedback Controllers 54
3.1.8.1 Proportional Control 54
3.1.8.2 Integral Control 54
3.1.8.3 Derivative Control 55
3.1.8.4 Proportional-integral-derivative Control 56
3.1.8.5 Heuristic Tuning of the PID Controller 57
3.1.8.6 Velocity Feedback (Rate Feedback) Control 59
3.1.8.7 Feedforward Control 59
3.2 The Root Locus 60
3.2.1 The Root Locus Technique 60
3.3 Frequency Response Methods 65
3.3.1 Bode Plots 65
3.3.1.1 Bode Plot Construction 65
3.3.1.2 Non-minimum Phase Transfer Functions 68
3.3.1.3 Relating Root Locus to Bode Plots 70
3.3.2 Gain and Phase Margin 71
3.3.3 Lead and Lag Compensator Design 72
3.3.3.1 Pure Gain Compensation 72
3.3.3.2 Lead Compensation 73
3.3.3.3 Lag Compensation 76
3.3.3.4 Lead-lag Compensation 77
3.3.3.5 Summary of Lead and Lag Control Techniques 78
3.3.4 PID Compensation in the Frequency Domain 79
3.3.5 Time Delay on a Bode Plot 79
3.3.6 Summary of Classical Design Techniques 81
3.4 Flexible Control 83
3.4.1 Second-order Filters 86
3.4.2 Colocated Control Design 87
3.4.3 Non-colocated Control Design 91
3.4.4 Non-colocated Control Design Solution 92
3.5 State-space Models 94
3.5.1 Linearization of a System 97
3.5.2 The Matrix Exponential 102
3.5.2.1 Computing e At and Modal Interpretation 103
3.5.3 State-space Stability 105
3.5.3.1 Canonical Forms 106
3.5.4 State Feedback Design 108
3.5.5 Controllability 109
3.5.5.1 Pole-placement 111
3.5.6 Reference Input Design in State-space 113
3.5.7 Estimator Design in State-space 114
3.5.8 Observability 115
3.5.9 The Separation Theorem 117
3.5.9.1 Closed-loop Poles 119
3.6 Introduction to Discrete-time Systems 119
3.6.1 Discrete-time Linear Dynamical Systems 121
3.6.1.1 Solution of Discrete-time Linear Dynamical Systems 122
3.6.2 Block Toeplitz Matrices in Discrete-time Systems 123
3.7 Introduction to Optimal Control 123
3.7.1 Linear Algebra Review 123
3.7.1.1 Vector Operations 124
3.7.1.2 Matrix Multiplication 124
3.7.1.3 Subspaces 124
3.7.1.4 Range, Null Space, and Rank 125
3.7.1.5 Orthonormal Basis and Orthogonal Complement 126
3.7.1.6 Properties of Orthonormal Sets and Semi-orthogonal Matrices 126
3.7.1.7 Orthogonal Complement 126
3.7.2 Linear Equations 127
3.7.3 Symmetric Matrices, Positive Definiteness, and Ellipsoids 127
3.7.3.1 Ellipsoids 127
3.7.4 Estimation and Control Problems 127
3.7.5 Singular Value Decomposition 128
3.7.5.1 Control Ellipsoid 129
3.7.5.2 Condition Number 130
3.7.6 Least Squares Estimation 131
3.7.6.1 Derivation of Least Squares Solution 131
3.7.6.2 Linear Regression 132
3.7.7 Minimum-norm Optimization 132
3.7.8 Multiobjective Least Squares 136
3.7.9 Completing the Square 137
3.7.10 Block Matrix Inversion 137
3.7.11 The Linear Quadratic Regulator 138
3.7.11.1 Dynamic Programming Approach 138
3.7.11.2 Summary of LQR Solution via Dynamic Programming 140
3.7.11.3 Steady-state Regulator 140
3.7.12 Probability Review 142
3.7.12.1 Random Variables 143
3.7.12.2 Random Vectors 145
3.7.12.3 Marginal Distributions 147
3.7.12.4 Conditional Distributions 148
3.7.13 Mean Squared Error 149
3.7.14 Linear Model with Noise 150
3.7.15 MAP and MMSE Estimates 150
3.7.16 The Kalman Filter 150
3.7.16.1 State Estimation Notation 151
3.7.16.2 The Measurement Update 151
3.7.16.3 Time Update 152
3.7.16.4 Summary of the Kalman Filter Recursion 152
3.7.16.5 Riccati Recursion 152
3.7.16.6 Steady-state Kalman Filter 152
4 Sources of Aberrations 157
4.1 Vibration and Jitter 157
4.1.1 Platform Jitter 157
4.1.2 Atmospheric Jitter 158
4.2 Optical Aberrations 158
4.2.1 Defocus and Spherical Aberration 158
4.2.2 Coma Aberration 159
4.2.3 Astigmatism Aberration 159
4.2.4 Field Curvature 160
4.2.5 Image Distortion 161
4.2.6 Chromatic Aberration 161
4.2.7 Optical Surface Errors 161
4.3 Air Turbulence 162
4.3.1 Kolmogorov Theory 162
4.3.2 Air Turbulence Parameters 163
4.3.2.1 Refractive Index Structure Parameter 163
4.3.2.2 Fried's Atmospheric Coherence Length 165
4.3.2.3 Greenwood Frequency 166
4.3.2.4 Isoplanatic Angle 166
4.3.2.5 Rytov Parameter 167
4.3.3 Non-Kolmogorov Atmospheric Turbulence 167
4.3.4 Effect of Air Turbulence in Optical Beam Propagation 167
4.3.4.1 Beam Jitter 167
4.3.4.2 Beam Spreading 167
4.3.4.3 Scintillation 168
4.4 Measure of Aberrations 169
4.4.1 Point Spread Function 169
4.4.2 Optical Transfer Function and Modular Transfer Function 170
4.4.3 Encircled and Ensquared Energy 171
4.4.4 Wavefront Error 171
4.4.5 Strehl Ratio 172
5 Vibration Isolation and Jitter Control 175
5.1 Introduction 175
5.2 Passive Vibration and Jitter Control 177
5.2.1 Passive Vibration Control 178
5.2.1.1 Viscoelastic Devices 178
5.2.1.2 Viscous Devices 179
5.2.1.3 Magnetic Devices 180
5.2.1.4 Passive Piezoelectrics 181
5.2.1.5 Tuned Mass Dampers 181
5.3 Active Vibration and Jitter Control 184
5.3.1 Actuators 184
5.3.1.1 Voice Coils 184
5.3.1.2 Piezoceramic 184
5.3.1.3 Fast Steering Mirrors 188
5.3.1.4 Jitter Sensor 189
5.3.2 Control Algorithms 190
5.3.2.1 Transverse Filter 190
5.3.3 Active Optics Beam Jitter Control 191
5.3.3.1 Experimental Results 193
5.3.4 Slew Maneuvers 193
5.3.4.1 Bang-Bang Profile 194
5.3.4.2 Versine Profile 195
5.3.4.3 Input Shaping 195
5.3.5 Reference Laser Beam 197
5.4 Active Vibration Isolation 199
5.4.1 Ultra Quiet Platform 199
5.4.2 Precision Pointing Hexapod 201
6 Adaptive Optics 203
6.1 Introduction 203
6.2 Wave Front Sensors 205
6.2.1 Shack-Hartman Wavefront Sensor 205
6.2.2 Curvature Wavefront Sensor 206
6.2.2.1 Intensity Difference and Curvature 207
6.2.2.2 Poisson Equation for Wavefront Reconstruction 207
6.2.3 Pyramid Wavefront Sensor 207
6.2.3.1 Intensity Difference Calculation 208
6.2.3.2 Reconstructing the Wavefront Error 208
6.2.4 Choosing a Sensor 208
6.3 Wave Reconstruction 208
6.3.1 Zonal Method 209
6.3.1.1 Hudgin Grid Pattern 209
6.3.1.2 Southwell Grid Pattern 209
6.3.1.3 Fried Grid Pattern 209
6.3.2 Least Squares Solution 210
6.3.3 Modal Reconstruction 210
6.4 Fast Steering Mirrors and Deformable Mirrors 211
6.4.1 Fast Steering Mirrors 211
6.4.1.1 Voice Coil Actuated FSM 212
6.4.1.2 Piezoelectric Actuated Mirrors 212
6.4.1.3 Identification of the FSM Dynamics 213
6.4.2 Deformable Mirrors 213
6.4.2.1 DM Characteristics 214
6.4.2.2 Types of DMs 215
6.4.2.3 Comparison of DMs 217
6.4.2.4 DMs for NPS Multi-conjugate AO Testbed 218
6.5 AO Configurations 219
6.5.1 Conventional AO System 219
6.5.2 Laser Guide Star AO 220
6.5.3 Multi-conjugate AO System 221
6.5.4 Woofer-Tweeter AO System 223
6.5.5 Beaconless Target-in-the-loop System 225
6.6 AO Control 226
6.6.1 Influence Function and Influence Matrix 226
6.6.2 Closed-loop Feedback AO Control System Design 228
7 Imaging Satellites 233
7.1 Introduction 233
7.2 Telescope Designs 233
7.2.1 Optical Beam Aberrations 234
7.2.1.1 Spherical Aberration (Third Order) 234
7.2.1.2 Coma (Fifth Order) 234
7.2.1.3 Astigmatism (Seventh Order) 234
7.2.1.4 Curvature of Field (Ninth Order) 235
7.2.2 Telescopes 235
7.2.3 Cassegrain Telescopes 237
7.2.4 Ritchey-Chretien Telescope 238
7.2.5 Three-mirror Anastigmat Telescope 239
7.3 Telescope Performance 240
7.3.1 Diffraction 240
7.3.1.1 Beam Propagation 241
7.3.1.2 Modulation Transfer Function 243
7.3.1.3 Optical Transfer Function 245
7.3.1.4 Resolution 245
7.3.2 Object Image Generation 246
7.3.2.1 Digital Focal Plane 246
7.3.2.2 Ground Sampling Distance 247
7.3.2.3 Quality Factor 247
7.3.2.4 Ground Resolution Distance 248
7.3.2.5 Jitter Requirements 248
7.3.2.6 Pointing Accuracy 248
7.3.3 Example 249
7.3.4 Sampling MTF 250
7.3.5 Aliasing 250
7.4 Optical Components 252
7.4.1 Focal Plane 252
7.4.1.1 Focal Plane Technology 252
7.4.1.2 Focal Plane Devices 253
7.4.2 Operation Concepts 254
7.4.2.1 Pushbroom Scanner 256
7.4.2.2 Whiskbroom Scanner 256
7.4.2.3 Step-stare Scanner 256
7.4.2.4 Comparison of push broom and starring imaging 257
7.5 Image Aberration 257
7.5.1 Pointing, Jitter, and Smear 257
7.5.2 National Image Interpretability Rating Scale 259
7.5.2.1 Signal-to-noise Ratio 259
7.5.2.2 General Image Quality Equation 259
7.5.2.3 Edge Response Function 260
7.6 Space Telescopes 260
7.6.1 Segmented Mirror Telescope 260
7.6.1.1 Optical Configuration 261
7.6.1.2 Analytical Model 261
7.6.1.3 First-order Modeling to Develop Sensitivities 264
7.6.1.4 Experimental Verification 266
7.7 Telescope Design Example 268
7.7.1 Misson 268
7.7.1.1 Requirements 268
7.7.2 Trade Space 269
7.7.3 Optical Telescope Design 269
7.7.3.1 Image Collection 270
7.7.4 Telescope Components 273
8 Laser Systems 275
8.1 Laser Fundamentals 275
8.1.1 Stimulated Emission 275
8.1.2 Resonant Cavities 276
8.1.3 Laser Characteristics 277
8.1.3.1 Monochromaticity 277
8.1.3.2 Coherence 277
8.1.3.3 Polarization 277
8.1.3.4 Mode Shapes 277
8.1.4 Type of Lasers 278
8.1.4.1 Gas Lasers 278
8.1.4.2 Diode Lasers 278
8.1.4.3 Dye Lasers 278
8.1.4.4 Solid-state Lasers 278
8.1.4.5 Fiber Laser 278
8.1.4.6 Chemical Lasers 278
8.1.4.7 Free-electron Lasers 279
8.1.4.8 Continuous Wave Lasers 279
8.1.4.9 Pulsed Lasers 279
8.2 Laser Beam Profile 280
8.3 Laser Beam Aberrations 286
8.3.1 Laser Beam Aberration Metrics 286
8.3.2 Laser Beam Quality 287
8.3.3 Optical Component 288
8.3.4 Telescope Central Obscuration 288
8.3.5 Optical Jitter 289
8.3.6 Higher Order Aberrations 289
8.3.7 Atmospheric Transmission 290
8.3.8 Scintillation 290
8.3.9 Additional Sources of Laser Beam Aberrations 291
8.4 Laser Beam Control Components 292
8.4.1 Beam Director 292
8.4.2 Fast Steering Mirrors 293
8.4.3 Optical Inertial Reference Unit 295
8.4.4 Light Sensors 296
8.4.4.1 Photodiodes 297
8.4.4.2 Focal Plane Arrays 298
8.5 Visual Object Tracking 300
8.5.1 Centroid Algorithm 300
8.5.2 Correlation Tracker 301
8.6 Beam Control for Laser Systems 301
8.6.1 Acquisition, Tracking, and Pointing of Laser Systems 301
8.6.1.1 Acquisition and Coarse Tracking 302
8.6.1.2 Fine Tracking and Pointing 302
8.6.2 Optical Jitter Control for LOS Stabilization 304
8.6.3 Adaptive Optics for Laser Systems 304
8.7 Free-space Laser Communication System 304
8.7.1 Space Laser Communication Terminal 306
8.7.1.1 Telescope 306
8.7.1.2 Optical Beam Jitter Control for LOS Stabilization 307
8.7.1.3 Acquisition, Tracking, and Pointing 307
8.7.2 Optical Ground Stations 308
8.7.3 Optical Transmitter and Receiver Modem 310
8.7.3.1 Laser Source 310
8.7.3.2 Coding and Modulation 310
8.7.3.3 Fiber Amplifier 311
8.7.3.4 Demodulation 311
8.7.3.5 Detector 311
8.7.4 Optical Link Analysis 311
8.8 High-energy Laser Systems 312
8.8.1 Overview of High-energy Laser Beam Control 312
8.8.1.1 High-energy Laser Source 313
8.8.1.2 Acquisition, Tracking, and Pointing 314
8.8.1.3 Optical Jitter Control for LOS Stabilization 315
8.8.1.4 Atmospheric Turbulence Compensation 315
8.8.2 Airborne Laser System 315
8.8.2.1 Acquisition, Tracking, and Pointing of ABL System 317
8.8.2.2 LOS Stabilization of ABL System 318
Index 319