A simple model of a one-dimensional, randomly rough, non-Gaussian surface

摘要

Several years ago Knotts, Michel, and O'Donnell (J. Opt. Soc. Am. A10, 928 (1993)) measured and calculated the independent elements of the Stokes matrix for in-plane scattering from a one-dimensional, randomly rough, metal surface. They found that the agreement between the computer simulation results and the experimental results for these matrix elements was significantly improved if the statistical properties of the surface profile function ζ(x_1) determined experimentally were used in the simulations instead of the commonly used assumption that ζ(x_1) is a stationary zero-mean, Gaussian random process with a Gaussian surface height autocorrelation function. Specifically, they found that while the probability density function (pdf) of ζ(x_1) for the surface studied was closely a Gaussian, with a correlation function that was also closely a Gaussian, the pdf of ζ′(x_1) was lower at the origin than predicted by a Gaussian expression, and the pdf of ζ″(x_1) was skewed in the direction of positive values of this function. By starting from a function H(x_1) that is a stationary, single-valued, zero-mean, Gaussian random process, with a Gaussian surface height autocorrelation function, we show how to construct surface profile functions ζ(x_1) of the form ζ(x_1) = [H(x_1) + F(H(x_1),H′(x_1), H″(x_1))] that have statistical properties of the kind displayed by the surface studied by Knotts et al.. Results of computer simulation calculations of the Stokes matrix elements on the basis of a surface defined by H(x_1) and on the basis of profile functions ζ(x_1) obtained from it show that some of the latter can be in qualitatively and quantitatively better agreement with the experimental results of Knotts et al. than the results based on H(x_1).