title: Second-order perturbation theory for scattering from heterogeneous rough surfaces.
abstract: We propose a model to calculate scattering from inhomogeneous three-dimensional, rough surfaces on top of a stratified medium. The roughness is made up of an ensemble of deposits with various shapes and permittivities whose heights remain small with respect to the wavelength of the incident light. This geometry is encountered in the remote sensing of soil surfaces, or in optics wherever there are contaminated planar components. Starting from a volume-integral equation involving the Green's tensor of the stratified medium, we derive a height-perturbative expansion up to second-order. Our formulation, which depends explicitly on the profiles of each deposit and on the Fresnel coefficients of the layered substrate, accounts for double-scattering events and permits an evaluation of depolarization in the plane of incidence. Comparisons with rigorous calculations in the simplified case of two-dimensional geometries are presented. It is shown that the second-order scattering term can be much more important for heterogeneous surfaces than for their homogeneous counterparts.
authors.affiliation: Institut Fresnel, Unité Mixte de Recherche 6133, Centre National de la Recherche Scientifique, Faculté des Sciences de Saint-Jérôme, case 162, F-13397 Marseille, France. charles-antoine.guerin@fresnel.fr
authors.forename: Charles-Antoine
authors.initials: CA
authors.lastname: Guérin
authors.forename: Anne
authors.initials: A
authors.lastname: Sentenac