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Free Space Optical Systems Engineering: Design and Analysis

ISBN: 978-1-119-27904-4
528 pages
March 2017
Free Space Optical Systems Engineering: Design and Analysis (1119279046) cover image

Description

Gets you quickly up to speed with the theoretical and practical aspects of free space optical systems engineering design and analysis

One of today's fastest growing system design and analysis disciplines is free space optical systems engineering for communications and remote sensing applications. It is concerned with creating a light signal with certain characteristics, how this signal is affected and changed by the medium it traverses, how these effects can be mitigated both pre- and post-detection, and if after detection, it can be differentiated from noise under a certain standard, e.g., receiver operating characteristic. Free space optical systems engineering is a complex process to design against and analyze. While there are several good introductory texts devoted to key aspects of optics—such as lens design, lasers, detectors, fiber and free space, optical communications, and remote sensing—until now, there were none offering comprehensive coverage of the basics needed for optical systems engineering. If you're an upper-division undergraduate, or first-year graduate student, looking to acquire a practical understanding of electro-optical engineering basics, this book is intended for you. Topics and tools are covered that will prepare you for graduate research and engineering in either an academic or commercial environment. If you are an engineer or scientist considering making the move into the opportunity rich field of optics, this all-in-one guide brings you up to speed with everything you need to know to hit the ground running, leveraging your experience and expertise acquired previously in alternate fields. Following an overview of the mathematical fundamentals, this book provides a concise, yet thorough coverage of, among other crucial topics:

  • Maxwell Equations, Geometrical Optics, Fourier Optics, Partial Coherence theory
  • Linear algebra, Basic probability theory, Statistics, Detection and Estimation theory, Replacement Model detection theory, LADAR/LIDAR detection theory, optical communications theory
  • Critical aspects of atmospheric propagation in real environments, including commonly used models for characterizing beam, and spherical and plane wave propagation through free space, turbulent and particulate channels
  • Lasers, blackbodies/graybodies sources and photodetectors (e.g., PIN, ADP, PMT) and their inherent internal noise sources

The book provides clear, detailed discussions of the basics for free space optical systems design and analysis, along with a wealth of worked examples and practice problems—found throughout the book and on a companion website. Their intent is to help you test and hone your skill set and assess your comprehension of this important area. Free Space Optical Systems Engineering is an indispensable introduction for students and professionals alike.

 

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Table of Contents

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

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Author Information

Larry B. Stotts, Ph.D., is a Resident Consultant at Science and Technology Associates in Arlington, Virginia. He received his B.A. in Applied Physics and Information Sciences and his Ph.D. in Electrical Engineering (Communications Systems), both from the University of California, San Diego. He has more than 40 years' experience in optical communications and remote sensing, optical systems engineering, avionics and optical navigation systems. Dr. Stotts is a Fellow of IEEE and SPIE, and a Senior Member of the Optical Society of America.

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