A Study of Surface Roughness and Its Effect on the Backscattering Cross Section of Spheres

The effect on the scattering cross section of a perfectly conducting object produced by surface roughaess whose scale is only a small fraction of a wavelength is discussed. The object itself is assumed large compared with the wavelength. The roughness is assumed to be statistically random in nature and it is shown that this can be treated by means of an impedance boundary condition. This permits the use of known results to determine the resulting modification to the cross section of the unperturbed object. Experimental data obtained by measuring the backscattering cross section of a large rough sphere at three frequencies, S, X and K band, are presented. It is found that even for a sphere whose depth of roughness is as large as 10-2,λ the measured change in cross section is no nore than about 0.1 db. This is in good agreement with the theoretical prediction.