Engineering Book from C.H.I.P.S.

Modeling Fluctuations in Scattered Waves
by Eric Jakeman

Modeling Fluctuations in Scattered Waves provides a practical guide to the phenomenology, mathematics, and simulation of non-Gaussian noise models and discusses how they can be used to characterize the statistics of scattered waves.


  • Covers practical problems encountered in optical and microwave remote sensing
  • Collects scattering results from random phase screens that provide an excellent model for many non-Gaussian scattering systems
  • Discusses K-distributed noise, the most widely used non-Gaussian model
  • Outlines some of the practical limitations encountered in experimental measurement and how they affect the interpretation of results, detection, and measurement accuracy
  • Provides over 130 figures of theoretical predictions as well as real and simulated data, including photographs of optical scattering patterns


Statistical Preliminaries

  • Random Variables
  • Transformation of Variables
  • Wiener-Khinchin Theorem
  • The Karhunen-Loeve Expansion
  • Statistical Independence
  • Characteristic Functions and Generating Functions
  • Detection

The Gaussian Process

  • 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

Processes Derived From Gaussian Notes

  • Rice Variables
  • Rice Processes
  • Gamma Variables
  • Gamma Processes
  • Statistics of the Derivative of a Gamma Process
  • Compound Variables
  • Other Commonly Encountered Distributions

Scattering by a Collection of Discrete Objects

  • 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

Scattering by Continuous Media: Phase Screen Models

  • Scattering Geometries
  • Time-Dependent Scattering
  • Scattering into the Fresnel Region
  • Fraunhofer Scattering
  • Scattering in Non-Gaussian Regimes
  • Surface Scattering

Scattering by Smoothly Varying Phase Screens

  • "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

Scattering by Fractal Phase Screens

  • 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

Other Phase Screen Models

  • 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

Propagation Through Extended Inhomogeneous Media

  • Single Phase Screen Approximation
  • Power-Law Models for the Refractive Index Spectrum
  • Multiple Phase Screens
  • Propagation of Electromagnetic Waves through Turbulence
  • Intensity Fluctuations

Multiple Scattering: Fluctuations in Double Passage and Multipath Scattering Geometries

  • Multiple Scattering in Particulates
  • Enhanced Backscattering through Continuous Media
  • A Phase Screen Model for Enhanced Backscattering
  • Fluctuations in Double Passage Configurations
  • Multipath Near Surfaces

Vector Scattering: Polarization Fluctuations

  • 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

K-Distributed Noise

  • Experimental Evidence
  • A Population Model for Scatterer Number Fluctuations
  • Properties of the Scattered Intensity
  • Related Distributions
  • Statistical Mechanics

Measurement and Detection

  • 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

Numerical Techniques

  • 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


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Modeling Fluctuations in Scattered Waves
by Eric Jakeman
2006 336 pages $128.95 + shipping
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