Free Space Optical Systems Engineering

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.

• Preface xiiAbout the Companion Website xvi1 Mathematical Preliminaries 11.1 Introduction 11.2 Linear Algebra 11.2.1 Matrices and Vectors 21.2.2 Linear Operations 21.2.3 Traces, Determinants, and Inverses 31.2.4 Inner Products, Norms, and Orthogonality 71.2.5 Eigenvalues, Eigenvectors, and Rank 81.2.6 Quadratic Forms and Positive Definite Matrices 81.2.7 Gradients, Jacobians, and Hessians 81.3 Fourier Series 91.3.1 Real Fourier Series 91.3.2 Complex Fourier Series 101.3.3 Effects of Finite Fourier Series Use 111.3.4 Some Useful Properties of Fourier Series 141.4 Fourier Transforms 151.4.1 Some General Properties 151.5 Dirac Delta Function 201.6 Probability Theory 211.6.1 Axioms of Probability 211.6.2 Conditional Probabilities 231.6.3 Probability and Cumulative Density Functions 251.6.4 Probability Mass Function 271.6.5 Expectation and Moments of a Scalar Random Variable 281.6.6 Joint PDF and CDF of Two Random Variables 291.6.7 Independent Random Variables 291.6.8 Vector-Valued Random Variables 301.6.9 Gaussian Random Variables 311.6.10 Quadratic and Quartic Forms 331.6.11 Chi-Squared Distributed Random Variable 341.6.12 Binomial Distribution 351.6.13 Poisson Distribution 371.6.14 Random Processes 381.7 Decibels 401.8 Problems 42References 482 Fourier Optics Basics 512.1 Introduction 512.2 The Maxwell Equations 522.3 The Rayleigh–Sommerfeld–Debye Theory of Diffraction 552.4 The Huygens–Fresnel–Kirchhoff Theory of Diffraction 592.5 Fraunhofer Diffraction 682.6 Bringing Fraunhofer Diffraction into the Near Field 762.7 Imperfect Imaging 822.8 The Rayleigh Resolution Criterion 842.9 The Sampling Theorem 852.10 Problems 89References 933 Geometrical Optics 953.1 Introduction 953.2 The Foundations of Geometrical Optics – Eikonal Equation and Fermat Principle 963.3 Refraction and Reflection of Light Rays 983.4 Geometrical Optics Nomenclature 1013.5 Imaging System Design Basics 1033.6 Optical Invariant 1093.7 Another View of Lens Theory 1113.8 Apertures and Field Stops 1133.8.1 Aperture Stop 1133.8.2 Entrance and Exit Pupils 1143.8.3 Field Stop and Chief and Marginal Rays 1153.8.4 Entrance and Exit Windows 1173.8.5 Baffles 1193.9 Problems 119References 1214 Radiometry 1234.1 Introduction 1234.2 Basic Geometrical Definitions 1244.3 Radiometric Parameters 1274.3.1 Radiant Flux (Radiant Power) 1294.3.2 Radiant Intensity 1304.3.3 Radiance 1304.3.4 Étendue 1324.3.5 Radiant Flux Density (Irradiance and Radiant Exitance) 1354.3.6 Bidirectional Reflectance Distribution Function 1354.3.7 Directional Hemispheric Reflectance 1364.3.8 Specular Surfaces 1364.4 Lambertian Surfaces and Albedo 1374.5 Spectral Radiant Emittance and Power 1384.6 Irradiance from a Lambertian Source 1394.7 The Radiometry of Images 1434.8 Blackbody Radiation Sources 1454.9 Problems 151References 1515 Characterizing Optical Imaging Performance 1535.1 Introduction 1535.2 Linearity and Space Variance of the Optical System or Optical Channel 1545.3 Spatial Filter Theory of Image Formation 1565.4 Linear Filter Theory of Incoherent Image Formation 1605.5 The Modulation Transfer Function 1625.6 The Duffieux Formula 1675.7 Obscured Aperture OTF 1745.7.1 Aberrations 1795.8 High-Order Aberration Effects Characterization 1845.9 The Strehl Ratio 1915.10 Multiple Systems Transfer Function 1935.11 Linear Systems Summary 195References 1986 Partial Coherence Theory 2016.1 Introduction 2016.2 Radiation Fluctuation 2026.3 Interference and Temporal Coherence 2056.4 Interference and Spatial Coherence 2146.5 Coherent Light Propagating Through a Simple Lens System 2196.6 Partially Coherent Imaging Through any Optical System 2316.7 Van Cittert–Zernike Theorem 2336.8 Problems 235References 2377 Optical Channel Effects 2397.1 Introduction 2397.2 Essential Concepts in Radiative Transfer 2397.3 The Radiative Transfer Equation 2457.4 Mutual Coherence Function for an Aerosol Atmosphere 2517.5 Mutual Coherence Function for a Molecular Atmosphere 2557.6 Mutual Coherence Function for an Inhomogeneous Turbulent Atmosphere 2567.7 Laser Beam Propagation in the Total Atmosphere 2627.8 Key Parameters for Analyzing Light Propagation Through Gradient Turbulence 2727.9 Two Refractive Index Structure Parameter Models for the Earth’s Atmosphere 2787.10 Engineering Equations for Light Propagation in the Ocean and Clouds 2827.11 Problems 294References 2958 Optical Receivers 2998.1 Introduction 2998.2 Optical Detectors 3008.2.1 Performance Criteria 3008.2.2 Thermal Detectors 3028.2.3 Photoemissive Detectors 3028.2.4 Semiconductor Photodetectors 3058.2.5 Photodiode Array and Charge-Coupled Devices 3258.3 Noise Mechanisms in Optical Receivers 3258.3.1 Shot Noise 3268.3.2 Erbium-Doped Fiber Amplifier (EDFA) Noise 3308.3.3 Relative Intensity Noise 3318.3.4 More Conventional Noise Sources 3338.4 Performance Measures 3358.4.1 Signal-to-Noise Ratio 3368.4.2 The Optical Signal-to-Noise Ratio 3388.4.3 The Many Faces of the Signal-to-Noise Ratio 3458.4.4 Noise Equivalent Power and Minimum Detectable Power 3468.4.5 Receiver Sensitivity 3478.5 Problems 350References 3539 Signal Detection and Estimation Theory 3559.1 Introduction 3559.2 Classical Statistical Detection Theory 3569.2.1 The Bayes Criterion 3589.2.2 The Minimax Criterion 3609.2.3 The Neyman–Pearson Criterion 3619.3 Testing of Simple Hypotheses Using Multiple Measurements 3659.4 Constant False Alarm Rate (CFAR) Detection 3749.5 Optical Communications 3759.5.1 Receiver Sensitivity for System Noise-Limited Communications 3759.5.2 Receiver Sensitivity for Quantum-Limited Communications 3819.6 Laser Radar (LADAR) and LIDAR 3899.6.1 Background 3899.6.2 Coherent Laser Radar 3929.6.3 Continuous Direct Detection Intensity Statistics 3989.6.4 Photon-Counting Direct Detection Intensity Statistics 4019.6.5 LIDAR 4049.7 Resolved Target Detection in Correlated Background Clutter and Common System Noise 4089.8 Zero Contrast Target Detection in Background Clutter 4159.9 Multispectral Signal-Plus-Noise/Noise-Only Target Detection in Clutter 4169.10 Resolved Target Detection in Correlated Dual-Band Multispectral Image Sets 4279.11 Image Whitener 4349.11.1 Orthogonal Sets 4349.11.2 Gram–Schmidt Orthogonalization Theory 4359.11.3 Prewhitening Filter Using the Gram–Schmidt Process 4369.12 Problems 437References 44010 Laser Sources 44310.1 Introduction 44310.2 Spontaneous and Stimulated Emission Processes 44410.2.1 The Two-Level System 44410.2.2 The Three-Level System 45110.2.3 The Four-Level System 45310.3 Laser Pumping 45410.3.1 Laser Pumping without Amplifier Radiation 45410.3.2 Laser Pumping with Amplifier Radiation 45510.4 Laser Gain and Phase-Shift Coefficients 45610.5 Laser Cavity Gains and Losses 46310.6 Optical Resonators 46610.6.1 Planar Mirror Resonators – Longitudinal Modes 46610.6.2 Planar Mirror Resonators – Transverse Modes 47110.7 The ABCD Matrix and Resonator Stability 47410.8 Stability of a Two-Mirror Resonator 47710.9 Problems 479References 482Appendix A STATIONARY PHASE AND SADDLE POINT METHODS 485A.1 Introduction 485A.2 The Method of Stationary Phase 485A.3 Saddle Point Method 487Appendix B EYE DIAGRAM AND ITS INTERPRETATION 489B.1 Introduction 489B.2 Eye Diagram Overview 489Appendix C VECTOR-SPACE IMAGE REPRESENTATION 491C.1 Introduction 491C.2 Basic Formalism 491Reference 493Appendix D PARAXIAL RAY TRACING – ABCD MATRIX 495D.1 Introduction 495D.2 Basic Formalism 495D.2.1 Propagation in a Homogeneous Medium 497D.2.2 Propagation Against a Curved Interface 498D.2.3 Propagation into a Refractive Index Interface 499References 502Index 503