Statistical Distribution of Field Scattered by 1-dimensional Random Slightly rough Surfaces

Abstract

We consider a perfectly conducting plane with a local cylindrical perturbation illuminated by a monochromatic plane wave. The perturbation is represented by a random function assuming values with a Gaussian probability density. For each realization of the stochastic process, the spatial average value over the width of the modulated zone is zero. The mean value of the random function is also zero. Without any deformation, the total field is the sum of the incident field and the reflected field. For a locally deformed plane, we consider-in addition to the incident and reflected plane waves-a scattered field. Outside the modulated zone, the scattered field can be represented by a superposition of a continuous spectrum of outgoing plane waves. The method of stationary phase leads to the asymptotic field, the dependence angular of which is given by the scattering amplitudes of the propagating plane waves. Using the first-order small perturbation method, we show that the real part and the imaginary part of scattering amplitudes are uncorrelated Gaussian stochastic variables with zero mean values and unequal variances. Consequently, the probability density for the amplitude is given by the Hoyt distribution and the phase is not uniformly distributed between 0 and 2π. C(α) = −2jβ i +L/2 −L/2 a 0 (x) exp + j(α − α i)x dx (12)