<title>Modifying the Harvey-Shack surface scatter theory</title>

Abstract

The Rayleigh-Rice (R-R) vector perturbation theory agrees well with experimental wide-angle scatter measurements from 'smooth' surfaces for arbitrary incident angles. However, not all applications of interest satisfy the smooth surface approximation. The Beckmann-Kirchoff (B-K) scalar diffraction theory of surface scatter phenomena is valid for rougher surfaces; but contains a paraxial (small-angle) assumption that limits its ability to accurately handle wide-angle scattering and large angles of incidence. In 1979 Harvey and Shack formulated a scattering theory in a linear systems format. Harvey later generalized this Harvey-Shack (H-S) theory to include the effects of small-angle scatter caused by 'mid' spatial frequency surface irregularities, and the extremely large incident angles inherent to grazing incidence Wolter Type I x-ray telescopes. In this paper we extend the H- S theory to include large incidence angles and scatter angles. We demonstrate that the customary paraxial limitation imposed in most scalar diffraction treatments is completely unnecessary and the resulting calculations for diffracted radiance (not irradiance or radiant intensity) are shift- invariant in direction cosine space