Modeling fluctuations in scattered waves

STATISTICAL PRELIMINARIES Introduction Random Variables Transformation of Variables Wiener-Khinchin Theorem The Karhunen-Loeve Expansion Statistical Independence Characteristic Functions and Generating Functions Detection References THE GAUSSIAN PROCESS Introduction Independent Gaussian Variables Correlated Gaussian Variables Higher-Order Correlations Gaussian Processes Complex Gaussian Processes Joint Statistical Properties Properties of the Derivative of a Complex Gaussian Process Joint Phase Derivative Statistics References PROCESSES DERIVED FROM GAUSSIAN NOTES Introduction Rice Variables Rice Processes Gamma Variables Gamma Processes Statistics of the Derivative of a Gamma Process Compound Variables Other Commonly Encountered Distributions References SCATTERING BY A COLLECTION OF DISCRETE OBJECTS: THE RANDOM WALK MODEL Introduction The Incident Wave Moments of the Field Scattered by a Fixed Number of Small Particles The Probability Distribution of the Scattered Wave Variations in Step Length: Illumination by a Gaussian Beam The Effect of Variations in Step Number Intensity Correlation Partially Developed Speckle References SCATTERING BY CONTINUOUS MEDIA: PHASE SCREEN MODELS Introduction Scattering Geometries Time-Dependent Scattering Scattering into the Fresnel Region Fraunhofer Scattering Scattering in Non-Gaussian Regimes Surface Scattering References SCATTERING BY SMOOTHLY VARYING PHASE SCREENS Introduction "Smooth" Models for the Phase Correlation Function Qualitative Features of Scattering by Smoothly Varying Phase Screens Calculation of the Scintillation Index in the Fresnel Region Predicted Behavior of the Scintillation Index in the Fresnel Region Higher-Order Statistics in the Fresnel Region Spatial Coherence Properties in the Fresnel Region Calculation of the Scintillation Index in the Fraunhofer Region Predicted Behavior of the Scintillation Index in the Far Field Higher-Order Statistical Properties in the Far Field Coherence Properties in the Far Field Phase Statistics References SCATTERING BY FRACTAL PHASE SCREENS Introduction Scattering into the Fresnel Region by a Fractal Phase Screen Scattering into the Fraunhofer Region by a Fractal Phase Screen Subfractal Phase Screens Ray Density Fluctuations beyond a Subfractal Phase Screen Coherence Properties of the Intensity Beyond a Subfractal Screen Outer Scale Effects Scattering into the Fraunhofer Region by a Subfractal Screen Concluding Remarks References OTHER PHASE SCREEN MODELS Introduction Scattering by Smoothly Varying Gamma Distributed Phase Screens Scattering by Fractal Gamma Distributed Phase Screens Telegraph Wave Phase Screens Scattering by Telegraph Wave Phase Screens Phase Statistics Concluding Remarks References PROPAGATION THROUGH EXTENDED INHOMOGENEOUS MEDIA Introduction Single Phase Screen Approximation Power-Law Models for the Refractive Index Spectrum Multiple Phase Screens Propagation of Electromagnetic Waves through Turbulence Intensity Fluctuations References MULTIPLE SCATTERING: FLUCTUATIONS IN DOUBLE PASSAGE AND MULTIPATH SCATTERING GEOMETRIES Introduction Multiple Scattering in Particulates Enhanced Backscattering through Continuous Media A Phase Screen Model for Enhanced Backscattering Fluctuations in Double Passage Configurations Multipath Near Surfaces References VECTOR SCATTERING: POLARIZATION FLUCTUATIONS Introduction The Polarization Characteristics of Gaussian Speckle Non-Gaussian Polarization Effects in Scattering by Particles Correlation of Stokes Parameters in Particle Scattering Scattering from Particles Near an Interface Polarization Fluctuations: Particles Near an Interface References K-DISTRIBUTED NOISE Introduction Experimental Evidence A Population Model for Scatterer Number Fluctuations Properties of the Scattered Intensity Related Distributions Statistical Mechanics References MEASUREMENT AND DETECTION Introduction Temporal Averaging of a Gamma-Lorentzian Process Approximations for the Effect of Temporal and Spatial Integration Averaging Signals with More than One Scale Enhancement of Fluctuations Caused by Filtering The Effect of Finite Dynamic Range The Effect of Finite Measurement Time Noise in Frequency Demodulation Detection Quantum Limited Measurements References NUMERICAL TECHNIQUES Introduction The Transformation of Random Numbers Gaussian Random Numbers The Telegraph Wave The Gaussian Random Process Non-Gaussian Processes Simulation of Wave Propagation Multiple Phase Screens References