Abstract
Many previous analyzes of scattering by sinusoidal surfaces are based on the Helmholtz integral equation in two dimensions and assume that the incident energy is a plane wave. Some of these solutions are exact insofar as they do not use the Kirchhoff boundary value approximation. However, all of the analyzes are based on one or more commonly used scattering approximations. Analyses presented here are carried out in three dimensions and are based on an integral equation which is analogous to the Rayleigh integral formula. The scattering is restricted to the plane of incidence, but includes receiver grazing angles ranging from 0 to 180 deg. Both the Fresnel phase approximation and Gaussian source and receiver beam functions are used. One of the objectives of this study is to explore the validity of the Kirchhoff approximation, so shadowing and second order scattering are explicitly included. The surface heights and slopes are not restricted in any way, and the surface slope treatment is exact. The resulting expressions are used in the companion paper to explore various approximations and limiting cases that are often encountered in the scattering literature.
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