Résumé: Abstract—We propose a theoretical study on the electromagnetic wave scattering from three-dimensional layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not, isotropic or not. The electromagnetic field in each medium is represented by a continuum of plane waves and a perturbation theory is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitudes under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. We analyze with the small slope approximation model the combined influence of the anisotropy and cross-correlation upon the electromagnetic signature of a natural stratified structure. Index Terms—Rough layered surfaces, scattering amplitudes, small perturbation method, small slope approximation.

Résumé: Abstract|We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic field in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitude under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented.

Résumé: Abstract— A study of a response of a remote radar sensor by a rough natural structure of two dimensions is made. Using the model of the small slope approximation, our objective is to study the problem of the electromagnetic wave scattering by natural structures in normal incidence. Two configurations are used: Air/Ice/Sea and Air/Snow/Ice/sea, our goal was not only the analytical presentation of the expressions of coherent and incoherent intensities, but also to understand the influence of the layers thickness of snow and ice on the diffracted signal by simulation. Moreover, we study the effect of inhomogeneity of the snow layer on the coherent and incoherent intensities. Keywords— Rough Surfaces, scattering signal, small slope approximation method (SSA).

Résumé: Abstract— In The framework of the small perturbation method, we study the stationarity and the ergodicity of signal scattering by layered interfaces in the incidence plane. The random surfaces are represented by a stationary and ergodic Gaussian process to the second-order. These interfaces are not correlated. In the first instance, we demonstrate that under oblique incidence, the total field is not wide-sense stationary. For infinite extension surfaces, we derive the probability density functions (PDFs) for the modulus and phase of the total field components, we find that The modulus PDF is in the form of infinite sum of modified Bessel functions while the phase PDF is expressed in terms of the error function. For a given altitude, at normal incidence, the total field is a strict-sense stationary process. In the second instance, we determine the spatial moments of the total field. For a given altitude, we find that whatever the angle of incidence, the total field is an ergodic process in the second-order. Furthermore, the probability density functions (PDFs) for the modulus and phase of the total field follow the general laws. Keywords— Rough surfaces, scattered field, small perturbations method, stationarity, ergodicity.