Rough-Surface Scattering: Shadowing, Multiple Scatter, and Energy Conservation

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Abstract
Multiple‐scatter and shadowing effects are included in an extended theory of high‐frequency scattering from a surface rough in one dimension. The single‐scatter probability of slopes relation, corrected for shadowing, is an immediate consequence for any stationary random process. The double‐scatter contribution (shadow corrected) is derived as well, and it provides a significant correction for surfaces with appreciable rms slope. The total power scattered by a perfectly reflecting rough surface is numerically evaluated as a test of energy conservation; the results show that the double‐scatter formulation is substantially more accurate than the conventional single‐scatter, unshadowed theory, particularly in the cases of large angles of incidence or very rough surfaces.

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