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First-order perturbation theory is used to calculate the scattering of a plane wave from the surface of a semi-infinite medium, where the surface is slightly rough and the scattering medium is isotropic but has a dielectric permittivity which varies as a function of position. Both the roughness and dielectric permittivity perturbations, which are treated as random variables, can independently cause scattering, and there is generally interference between the two scattered fields. The scattering depends on the autocovariance functions for the surface roughness and dielectric fluctuations and their cross-correlation properties. Thus, the polarization ratio between the p and s angle resolved scattering components is found to be a variable that depends on the autocovariance functions of, and cross-correlation between, the surface roughness and dielectric fluctuations. This result is unlike predicted scattering caused by roughness or dielectric perturbations alone; in these cases, the polarization ratios do not depend on the statistical properties of the perturbation. Numerical results of the calculations of this work are consistent with some aspects of experimental measurements. In particular, measurements of the polarization ratio of light retroscattered from apparently identical silver films are seen to vary widely between samples and even from place to place on the same sample. The present work shows one physical mechanism as to how this can occur.
angle resolved scattering, BRDF, dielectric inhomogeneities, surface roughness
Michelson Laboratory, Physics Division Naval Weapons Center, China Lake, California