First-order perturbation theory is applied to calculate scattering of a plane wave from a planebounded, semi-infinite medium where the boundary surface has a roughness perturbation and the scattering medium consists of an isotropic perturbation of the dielectric permittivity. The dielectric perturbation is assumed to fluctuate randomly in the plane parallel to the surface and decay exponentially with depth into the surface. 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 scattered fields generally depend on the autocovariance functions of the surface roughness and dielectric fluctuations and on the crosscorrelation properties between them. For this reason, the polarization ratio of the $p$- and $s$- polarized scattered light fields depends on the autocovariance and cross-correlation statistical properties. This result is unlike the calculation of scattered fields caused by roughness or dielectric perturbations alone, since in this case the polarization ratios of the scattered fields do not depend on the statistical properties of the perturbation. The numerical results of this work are consistent with experimental measurements where the polarization ratio of light scattered from nominally identical silver films varies widely from surface to surface.

• Received 28 November 1983

DOI:https://doi.org/10.1103/PhysRevB.30.5460