Some Statistical and Spatial Properties of Signal Scattering by 2-D Slightly Rough Random Surfaces

Within the framework of the first-order small perturbation method (SPM), we establish some statistical and spatial properties of signal scattering by 2-D slightly rough random surfaces. The work concerns the total field within the intermediate field-zone for an ergodic and stationary Gaussian surface under illumination by a monochromatic plane wave. For infinite extension surfaces, we obtain the probability density functions (pdfs) for the modulus and phase of the total field components. The modulus pdf is expressed as an infinite sum of modified Bessel functions while the phase pdf is expressed in terms of the error function. Under oblique illumination, the total field is not wide-sense stationary. From a spatial point of view, for a given elevation and under all incidences, we show that the total field is ergodic to the second order. Under oblique incidence, the spatial distribution of the total field modulus is a Rayleigh law and the phase is uniform. Under normal incidence, we establish that the spatial and statistical distributions are interchangeable.