The earliest theories of the scattering of electromagnetic waves from randomly rough surfaces were single-scattering theories, such as small-amplitude perturbation theory and the Kirchhoff approximation. The incorporation of multiple scattering into theories of rough surface scattering has led to the prediction of several new effects, which have now been verified experimentally. The new multiple-scattering effects to be discussed in this paper include enhanced backscattering, which is the presnece of a well-defined peak in the retroreflection direction in the angular dependence of the intensity of the diffuse component of the light scattered from a random surface; enhanced transmission, which is the presnece of a peak in the antispecular direction in the angular dependence of the intensity of the diffuse component of the light transmitted through a thin metal film with a random-surface; satellite peaks that accompany the enhanced backscattering and transmision peaks when light is scattered from, and transmitted through,roug h dielectric or metallic films that support two or more surface or guided waves; changes in the spectrum of light scattered from random surfaces (the Wolf shift); and the scattering of light uniformly within a specified angular range and the absence of scattering outside this range. This paper concludes with some suggestions for directions that research in the area of rough surface scattering could take in the next few years.
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