On the Use of Finite Surfaces in the Numerical Prediction of Rough Surface Scattering

Method of moments (MOM)-based Monte Carlo calculations are widely used in determining the average radar cross section of randomly rough surfaces. It is desirable in these numerical calculations to truncate the scattering surface into as short a length as possible to minimize the solution time. However, truncating the surface tends to change the solution for the surface fields near the truncation points and may alter the scattered far fields. In this paper, these end effect errors are examined for one-dimensional (i.e., grooved or corduroy) surfaces which are Gaussian distributed in height and have either a Gaussian or a Pierson–Moskowitz spectra. In the case of the Pierson–Moskowitz type surface, it is shown that a relatively short surface of 80–120 wavelengths can be used to obtain the average backscattered radar cross section for backscattering angles as large as 60 from normal. For a comparatively smooth Gaussian surface, on the other hand, its is shown that the truncation effects can be very significant at moderate backscattering angles. Also, great care should be taken when examining the scattering from Gaussian surfaces which are dominated by specular scattering. It is shown that in this situation, a very large number of calculations may be needed to obtain a good numerical average.