Wave Scattering from Rough Surfaces

1. Introduction.- 2. Scattering Amplitude and Its Properties.- 2.1 Formulation of Problem and Some Auxiliary Relations.- 2.2 Scattering Amplitude.- 2.3 Reciprocity Theorem and Unitarity Condition.- 2.4 Scattering Amplitude for Statistical Case.- 3. Helmholtz Formula and Rayleigh Hypothesis.- 3.1 Helmholtz Formula.- 3.2 Rayleigh Hypothesis.- 3.3 Analytical Properties of Surface Sources Density Function.- 3.4 Rayleigh Hypothesis and Lippman Argument: Completeness of Set of the Plane Waves.- 4. Small Perturbation Method.- 4.1 Dirichlet Problem.- 4.2 Small Perturbation Method and the Rayleigh Hypothesis.- 4.3 Neumann Problem.- 4.4 Scattering of Electromagnetic Waves at a Perfectly Conducting Boundary.- 4.5 Scattering of Sound Waves at the Interface Between Liquid Half-Spaces.- 4.6 Electromagnetic Wave Scattering at the Interface Between Two Dielectrics.- 5. Kirchhoff-Tangent Plane Approximation.- 5.1 Tangent Plane Approximation.- 5.2 Kirchhoff Approximation.- 5.3 Corrections to the Kirchhoff Approximation: Deterministic Case.- 5.4 Corrections to the Kirchhoff Approximation: Statistical Case.- 5.5 Two-Scale Model.- 6. "Nonclassical" Approaches to Wave Scattering at Rough Surfaces.- 6.1 Small Slope Approximation.- 6.2 Small Slope Approximation and Rayleigh Equation. Numerical Experiments.- 6.3 Phase Perturbation Technique.- 6.4 Phase Operator Method for Dirichlet Problem.- 6.5 Meecham-Lysanov Approach.- 6.6 Relation Between Bahar's Full Wave Approach and Small Slope Approximation.- 6.7 Operator Expansion Method.- 7. Waveguide with Statistically Rough Boundary in Noncorrelated Successive Reflections Approximation.- 7.1 Directional Source in the Waveguide with Rough Boundary: General Solution.- 7.2 Average Field.- 7.3 Correlation Function of the Field.- 7.4 RadiativeTransport Theory.- 7.5 Problem of Noise Surface Sources: Diffusion Approximation.- References.