On the Co-Polarized Scattered Intensity Ratio of Rough Layered Surfaces: The Probability Law Derived From the Small Perturbation Method

We determine the probability law of the ratio between the co-polarized intensities scattered from a stack of two two-dimensional rough interfaces in the incidence plane. Calculations are carried out within the framework of the first-order small perturbation method. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters and has an infinite average and an infinite variance. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle and the cross-spectral density upon this probability law.