An expression is derived for the mutual coherence function of laser radiation scattered from a rough surface. The rough surface is described by the superposition of two random-height distributions. The expression descibes the correlation of the radiation amplitude at spatially separated far-field points caused by the scattering from spatially separate surface elements. Numerical predictions of this mutual interaction or coherent contribution to the mutual coherence function are computed for a square surface area and typical values of the surface statistical parameters. These results are compared with the scattering cross section of a flat surface area and the degree of coherence of a perfectly diffuse surface. The functional form of the incoherent contribution to the mutual coherence function, resulting from the integration of the radiation that is diffracted by the surface irregularities, is deduced from an analysis of the single scale of roughness scattering problem. The derived mutual coherence function is shown to reduce to the proper functional form for the ideal limiting cases of a perfectly flat surface and a perfectly diffuse scattering area.
© 1976 Optical Society of America
J. Carl Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536-546 (1976)