Statistical Optics

This book discusses statistical methods that are useful for treating problems in modern optics, and the application of these methods to solving a variety of such problems This book covers a variety of statistical problems in optics, including both theory and applications. The text covers the necessary background in statistics, statistical properties of light waves of various types, the theory of partial coherence and its applications, imaging with partially coherent light, atmospheric degradations of images, and noise limitations in the detection of light. New topics have been introduced in the second edition, including: Analysis of the Vander Pol oscillator model of laser light Coverage on coherence tomography and coherence multiplexing of fiber sensors An expansion of the chapter on imaging with partially coherent light, including several new examples An expanded section on speckle and its properties New sections on the cross-spectrum and bispectrum techniques for obtaining images free from atmospheric distortions A new section on imaging through atmospheric turbulence using coherent light The addition of the effects of read noise to the discussions of limitations encountered in detecting very weak optical signals A number of new problems and many new references have been added Statistical Optics, Second Edition is written for researchers and engineering students interested in optics, physicists and chemists, as well as graduate level courses in a University Engineering or Physics Department.

This book discusses statistical methods that are useful for treating problems in modern optics, and the application of these methods to solving a variety of such problemsThis book covers a variety of statistical problems in optics, including both theory and applications. The text covers the necessary background in statistics, statistical properties of light waves of various types, the theory of partial coherence and its applications, imaging with partially coherent light, atmospheric degradations of images, and noise limitations in the detection of light. New topics have been introduced in the second edition, including:* Analysis of the Vander Pol oscillator model of laser light* Coverage on coherence tomography and coherence multiplexing of fiber sensors* An expansion of the chapter on imaging with partially coherent light, including several new examples* An expanded section on speckle and its properties* New sections on the cross-spectrum and bispectrum techniques for obtaining images free from atmospheric distortions* A new section on imaging through atmospheric turbulence using coherent light* The addition of the effects of "read noise" to the discussions of limitations encountered in detecting very weak optical signals* A number of new problems and many new references have been addedStatistical Optics, Second Edition is written for researchers and engineering students interested in optics, physicists and chemists, as well as graduate level courses in a University Engineering or Physics Department.

1 Introduction 11.1 Deterministic Versus Statistical Phenomena and Models 21.2 Statistical Phenomena in Optics 31.3 An Outline of the Book 52 Random Variables 62.1 Definitions of Probability and Random Variables 62.2 Distribution Functions and Density Functions 82.3 Extension to Two or More Joint Random Variables 122.4 Statistical Averages 142.5 Transformations of Random Variables 202.6 Sums of Real Random Variables 272.7 Gaussian Random Variables 322.8 Complex-Valued Random Variables 372.9 Random Phasor Sums 422.10 Poisson Random Variables 523 Random Processes 563.1 Definition and Description of a Random Process 563.2 Stationarity and Ergodicity 593.3 Spectral Analysis of Random Processes 643.4 Autocorrelation Functions and the Wiener-Khinchin Theorem 693.5 Cross-Correlation Functions and Cross-Spectral Densities 753.6 Gaussian Random Processes 783.7 Poisson Impulse Processes 803.8 Random Processes Derived from Analytic Signals 933.9 The Circular Complex Gaussian Random Process 1013.10 The Karhunen-Loève Expansion 1024 Some First-Order Statistical Properties of Light 1094.1 Propagation of Light 1104.2 Thermal Light 1144.3 Partially Polarized Thermal Light 1194.4 Single-Mode Laser Light 1304.5 Multimode Laser Light 1434.6 Pseudothermal Light Produced by Passing Laser Light Through a Changing Diffuser 1485 Temporal and Spatial Coherence of Optical Waves 1525.1 Temporal Coherence 1535.2 Spatial Coherence 1725.3 Separability of Spatial and Temporal Coherence Effects 1885.4 Propagation of Mutual Coherence 1915.5 Special Forms of the Mutual Coherence Function 1965.6 Diffraction of Partially Coherent Light by a Transmitting Structure 2025.7 The Van Cittert-Zernike Theorem 2085.8 A Generalized Van Cittert-Zernike Theorem 2145.9 Ensemble-Average Coherence 2186 Some Problems Involving Higher-Order Coherence 2276.1 Statistical Properties of the Integrated Intensity of Thermal or Pseudothermal Light 2286.2 Statistical Properties of Mutual Intensity with Finite Measurement Time 2436.3 Classical Analysis of the Intensity Interferometer 2497 Effects of Partial Coherence in Imaging Systems 2627.1 Preliminaries 2637.2 Space-Domain Calculation of Image Intensity 2697.3 Frequency Domain Calculation of the Image Intensity Spectrum 2747.4 The Incoherent and Coherent Limits 2807.5 Some Examples 2867.6 Image Formation as an Interferometric Process 2937.7 The Speckle Effect in Imaging 3088 Imaging Through Randomly Inhomogeneous Media 3238.1 Effects of Thin Random Screens on Image Quality 3248.2 Random-Phase Screens 3288.3 The Earth's Atmosphere as a Thick Phase Screen 3368.4 Electromagnetic Wave Propagation Through the Inhomogeneous Atmosphere 3448.5 The Long-Exposure OTF 3528.6 The Short-Exposure OTF 3758.7 Stellar Speckle Interferometry 3828.8 The Cross-Spectrum or Knox-Thompson Technique 3928.9 The Bispectrum Technique 3988.10 Adaptive Optics 4018.11 Generality of the Theoretical Results 4048.12 Imaging Laser-Illuminated Objects through a Turbulent Atmosphere 4069 Fundamental Limits in Photoelectric Detection of Light 4159.1 The Semiclassical Model for Photoelectric Detection 4169.2 Effects of Random Fluctuations of the Classical Intensity 4179.3 The Degeneracy Parameter 4299.4 Noise Limitations of the Amplitude Interferometer at Low Light Levels 4399.5 Noise Limitations of the Intensity Interferometer at Low Light Levels 4499.6 Noise Limitations in Stellar Speckle Interferometry 456Appendix A The Fourier Transform 471A.1 Fourier Transform Definitions 471A.2 Basic Properties of the Fourier Transform 473A.3 Tables of Fourier Transforms 476Appendix B Random Phasor Sums 478Appendix C The Atmospheric Filter Functions 484Appendix D Analysis of Stellar Speckle Interferometry 489Appendix E Fourth-Order Moment of the Spectrum of a Detected Speckle Image 493Bibliography 496Index 509