Statistics of specular points on a non-Gaussian random surface

Abstract

The distribution of specular points (DSP) is derived in the case of wave scattering from a non-Gaussian rough surface. The probability-density function of the surface’s slopes is assumed to be represented by the Edgeworth series in two dimensions. The effect of the surface’s elevations on the DSP is neglected. The form of the DSP is obtained for various positions and altitudes of the source and the receiver. Some of the properties that characterize the DSP patterns when the surface’s statistical parameters are varied are studied. Knowledge of the DSP permits the quantitative examination of some of the most frequently used criteria for discriminating Fraunhofer- and Fresnel-type scatterings. A conclusion is drawn that for source and receiver altitudes that are small compared with the distance between them, the scattering cannot be described adequately as a Fraunhofer one. In addition, the DSP patterns show that for small rms slopes the frequently used cylindrical models are a conceivable approximation to the natural surfaces.