Nonparametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data: Application to computer-generated and experimental scattering data

An approach is introduced for the nonparametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface-height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step, the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface-height correlation function without initially assuming any particular form for this function (nonparametric inversion). The input data used to validate this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement is obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this is the case for both dielectric and metallic surfaces, for both p- and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust, and contactless method based on in-plane and co-polarized scattering data for the nonparametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surfaces.