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Wave Scattering From Rough Surfaces deals with a theory that has many important practical applications. The monograph considers the subject by using the concept of scattering amplitude, which allows one to simplify theoretical constructions and, more importantly, to consider different approaches within a single theoretical scheme. It emphasizes new theoretical approaches developed in this area during the last two decades. For the second edition, a special section was added to present one of the most powerful among recently developed methods, namely the operator expansion method.
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 Radiative Transport Theory.- 7.5 Problem of Noise Surface Sources: Diffusion Approximation.- References.