Backscattering cross section of a tilted, roughened disk

Abstract

An expression is derived for the cross correlation of the electric field scattered from a roughened metallic disk to two points in the far zone. Both exponential and Gaussian surface correlations are considered. In the calculation of the cross correlation, careful treatment is given to the terms involving the surface slope, and our new results are applicable to a broader range of surface roughness and observation angle than were earlier approximate methods. The cross correlation is then reduced to give the backscattering cross section of the disk as a function of the tilt or incident angle for both types of surface correlation. It is found that the cross section for the Gaussian surface falls off rapidly with increasing tilt angle. A particularly interesting new finding is that the cross section for the exponential surface actually increases under certain roughness conditions as the tilt angle is increased. While the effect of shadowing is not included in the analysis, we derive an expression showing the limiting value of the tilt angle below which shadowing effects are negligible. In illustration of these basic results, experiments are presented for the backscattering from roughened surfaces prepared by bead blasting and by ion-beam etching.