The conventional Kirchhoff approximation for rough surface scattering does not reduce to perturbation results in the limit of small surface heights. It is shown here how to modify the conventional Kirchhoff approximation by using appropriate half-space Green’s functions. The resulting expressions for the differential cross section for scattering from rough surfaces reduce to the conventional Kirchhoff results and the perturbation results in the appropriate limits.
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Berman et al. (1985) studied this question.
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