Free Space Optical Systems Engineering
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Preface xii
About the Companion Website xvi
1 Mathematical Preliminaries 1
1.1 Introduction 1
1.2 Linear Algebra 1
1.2.1 Matrices and Vectors 2
1.2.2 Linear Operations 2
1.2.3 Traces, Determinants, and Inverses 3
1.2.4 Inner Products, Norms, and Orthogonality 7
1.2.5 Eigenvalues, Eigenvectors, and Rank 8
1.2.6 Quadratic Forms and Positive Definite Matrices 8
1.2.7 Gradients, Jacobians, and Hessians 8
1.3 Fourier Series 9
1.3.1 Real Fourier Series 9
1.3.2 Complex Fourier Series 10
1.3.3 Effects of Finite Fourier Series Use 11
1.3.4 Some Useful Properties of Fourier Series 14
1.4 Fourier Transforms 15
1.4.1 Some General Properties 15
1.5 Dirac Delta Function 20
1.6 Probability Theory 21
1.6.1 Axioms of Probability 21
1.6.2 Conditional Probabilities 23
1.6.3 Probability and Cumulative Density Functions 25
1.6.4 Probability Mass Function 27
1.6.5 Expectation and Moments of a Scalar Random Variable 28
1.6.6 Joint PDF and CDF of Two Random Variables 29
1.6.7 Independent Random Variables 29
1.6.8 Vector-Valued Random Variables 30
1.6.9 Gaussian Random Variables 31
1.6.10 Quadratic and Quartic Forms 33
1.6.11 Chi-Squared Distributed Random Variable 34
1.6.12 Binomial Distribution 35
1.6.13 Poisson Distribution 37
1.6.14 Random Processes 38
1.7 Decibels 40
1.8 Problems 42
References 48
2 Fourier Optics Basics 51
2.1 Introduction 51
2.2 The Maxwell Equations 52
2.3 The Rayleigh-Sommerfeld-Debye Theory of Diffraction 55
2.4 The Huygens-Fresnel-Kirchhoff Theory of Diffraction 59
2.5 Fraunhofer Diffraction 68
2.6 Bringing Fraunhofer Diffraction into the Near Field 76
2.7 Imperfect Imaging 82
2.8 The Rayleigh Resolution Criterion 84
2.9 The Sampling Theorem 85
2.10 Problems 89
References 93
3 Geometrical Optics 95
3.1 Introduction 95
3.2 The Foundations of Geometrical Optics - Eikonal Equation and Fermat Principle 96
3.3 Refraction and Reflection of Light Rays 98
3.4 Geometrical Optics Nomenclature 101
3.5 Imaging System Design Basics 103
3.6 Optical Invariant 109
3.7 Another View of Lens Theory 111
3.8 Apertures and Field Stops 113
3.8.1 Aperture Stop 113
3.8.2 Entrance and Exit Pupils 114
3.8.3 Field Stop and Chief and Marginal Rays 115
3.8.4 Entrance and Exit Windows 117
3.8.5 Baffles 119
3.9 Problems 119
References 121
4 Radiometry 123
4.1 Introduction 123
4.2 Basic Geometrical Definitions 124
4.3 Radiometric Parameters 127
4.3.1 Radiant Flux (Radiant Power) 129
4.3.2 Radiant Intensity 130
4.3.3 Radiance 130
4.3.4 Étendue 132
4.3.5 Radiant Flux Density (Irradiance and Radiant Exitance) 135
4.3.6 Bidirectional Reflectance Distribution Function 135
4.3.7 Directional Hemispheric Reflectance 136
4.3.8 Specular Surfaces 136
4.4 Lambertian Surfaces and Albedo 137
4.5 Spectral Radiant Emittance and Power 138
4.6 Irradiance from a Lambertian Source 139
4.7 The Radiometry of Images 143
4.8 Blackbody Radiation Sources 145
4.9 Problems 151
References 151
5 Characterizing Optical Imaging Performance 153
5.1 Introduction 153
5.2 Linearity and Space Variance of the Optical System or Optical Channel 154
5.3 Spatial Filter Theory of Image Formation 156
5.4 Linear Filter Theory of Incoherent Image Formation 160
5.5 The Modulation Transfer Function 162
5.6 The Duffieux Formula 167
5.7 Obscured Aperture OTF 174
5.7.1 Aberrations 179
5.8 High-Order Aberration Effects Characterization 184
5.9 The Strehl Ratio 191
5.10 Multiple Systems Transfer Function 193
5.11 Linear Systems Summary 195
References 198
6 Partial Coherence Theory 201
6.1 Introduction 201
6.2 Radiation Fluctuation 202
6.3 Interference and Temporal Coherence 205
6.4 Interference and Spatial Coherence 214
6.5 Coherent Light Propagating Through a Simple Lens System 219
6.6 Partially Coherent Imaging Through any Optical System 231
6.7 Van Cittert-Zernike Theorem 233
6.8 Problems 235
References 237
7 Optical Channel Effects 239
7.1 Introduction 239
7.2 Essential Concepts in Radiative Transfer 239
7.3 The Radiative Transfer Equation 245
7.4 Mutual Coherence Function for an Aerosol Atmosphere 251
7.5 Mutual Coherence Function for a Molecular Atmosphere 255
7.6 Mutual Coherence Function for an Inhomogeneous Turbulent Atmosphere 256
7.7 Laser Beam Propagation in the Total Atmosphere 262
7.8 Key Parameters for Analyzing Light Propagation Through Gradient Turbulence 272
7.9 Two Refractive Index Structure Parameter Models for the Earth's Atmosphere 278
7.10 Engineering Equations for Light Propagation in the Ocean and Clouds 282
7.11 Problems 294
References 295
8 Optical Receivers 299
8.1 Introduction 299
8.2 Optical Detectors 300
8.2.1 Performance Criteria 300
8.2.2 Thermal Detectors 302
8.2.3 Photoemissive Detectors 302
8.2.4 Semiconductor Photodetectors 305
8.2.5 Photodiode Array and Charge-Coupled Devices 325
8.3 Noise Mechanisms in Optical Receivers 325
8.3.1 Shot Noise 326
8.3.2 Erbium-Doped Fiber Amplifier (EDFA) Noise 330
8.3.3 Relative Intensity Noise 331
8.3.4 More Conventional Noise Sources 333
8.4 Performance Measures 335
8.4.1 Signal-to-Noise Ratio 336
8.4.2 The Optical Signal-to-Noise Ratio 338
8.4.3 The Many Faces of the Signal-to-Noise Ratio 345
8.4.4 Noise Equivalent Power and Minimum Detectable Power 346
8.4.5 Receiver Sensitivity 347
8.5 Problems 350
References 353
9 Signal Detection and Estimation Theory 355
9.1 Introduction 355
9.2 Classical Statistical Detection Theory 356
9.2.1 The Bayes Criterion 358
9.2.2 The Minimax Criterion 360
9.2.3 The Neyman-Pearson Criterion 361
9.3 Testing of Simple Hypotheses Using Multiple Measurements 365
9.4 Constant False Alarm Rate (CFAR) Detection 374
9.5 Optical Communications 375
9.5.1 Receiver Sensitivity for System Noise-Limited Communications 375
9.5.2 Receiver Sensitivity for Quantum-Limited Communications 381
9.6 Laser Radar (LADAR) and LIDAR 389
9.6.1 Background 389
9.6.2 Coherent Laser Radar 392
9.6.3 Continuous Direct Detection Intensity Statistics 398
9.6.4 Photon-Counting Direct Detection Intensity Statistics 401
9.6.5 LIDAR 404
9.7 Resolved Target Detection in Correlated Background Clutter and Common System Noise 408
9.8 Zero Contrast Target Detection in Background Clutter 415
9.9 Multispectral Signal-Plus-Noise/Noise-Only Target Detection in Clutter 416
9.10 Resolved Target Detection in Correlated Dual-Band Multispectral Image Sets 427
9.11 Image Whitener 434
9.11.1 Orthogonal Sets 434
9.11.2 Gram-Schmidt Orthogonalization Theory 435
9.11.3 Prewhitening Filter Using the Gram-Schmidt Process 436
9.12 Problems 437
References 440
10 Laser Sources 443
10.1 Introduction 443
10.2 Spontaneous and Stimulated Emission Processes 444
10.2.1 The Two-Level System 444
10.2.2 The Three-Level System 451
10.2.3 The Four-Level System 453
10.3 Laser Pumping 454
10.3.1 Laser Pumping without Amplifier Radiation 454
10.3.2 Laser Pumping with Amplifier Radiation 455
10.4 Laser Gain and Phase-Shift Coefficients 456
10.5 Laser Cavity Gains and Losses 463
10.6 Optical Resonators 466
10.6.1 Planar Mirror Resonators - Longitudinal Modes 466
10.6.2 Planar Mirror Resonators - Transverse Modes 471
10.7 The ABCD Matrix and Resonator Stability 474
10.8 Stability of a Two-Mirror Resonator 477
10.9 Problems 479
References 482
Appendix A STATIONARY PHASE AND SADDLE POINT METHODS 485
A.1 Introduction 485
A.2 The Method of Stationary Phase 485
A.3 Saddle Point Method 487
Appendix B EYE DIAGRAM AND ITS INTERPRETATION 489
B.1 Introduction 489
B.2 Eye Diagram Overview 489
Appendix C VECTOR-SPACE IMAGE REPRESENTATION 491
C.1 Introduction 491
C.2 Basic Formalism 491
Reference 493
Appendix D PARAXIAL RAY TRACING - ABCD MATRIX 495
D.1 Introduction 495
D.2 Basic Formalism 495
D.2.1 Propagation in a Homogeneous Medium 497
D.2.2 Propagation Against a Curved Interface 498
D.2.3 Propagation into a Refractive Index Interface 499
References 502
Index 503
