Scattering of electromagnetic waves from a randomly perturbed quasiperiodic surface

Abstract

The scattering of electromagnetic waves from a randomly perturbed quasiperiodic surface is studied for active remote sensing of plowed fields. The Kirchoff approximation is used. The narrow-band Gaussian random variation around the spatial frequency of the sinusoidal variation is used to introduce the quasiperiodicity. The physical optics integral is evaluated to obtain closed form solutions for coherent and incoherent bistatic scattering coefficients. In the geometrical optics limit, it is shown that the bistatic scattering coefficients are proportional to the probability of the occurrence of the slopes which will specularly reflect the incident wave to the observation direction. The theoretical results are illustrated for the various cases by plotting backscattering cross sections as a function of the angle of incidence. It is shown that there is a large difference between the cases where the incident wave vector is parallel or perpendicular to the row direction. When the incident wave vector is perpendicular to the row direction, the maximum value of the backscattering cross section does not necessary occur at normal incidence. The scattering coefficients can be interpreted as a convolution of the scattering patterns for the sinusoidal and the random rough surfaces. For the backscattering cross sections we observe the occurrence of peaks whose relative magnitudes and the locations are explained in terms of the scattering patterns for sinusoidal surfaces.