Backscattering cross section of a roughened sphere

Abstract

The backscattering cross section of a perfectly conducting, roughened sphere is presented. It is derived from the calculation of the electric-field cross correlation at two temporal frequencies and at two points in the backscatter direction. Careful treatment has been given to the calculation of the ensemble average of the surface height and slope terms, particularly in the backscatter from the off-axis regions of the sphere where the angles of illumination become large. At these large angles significant portions of the surface are in shadow and fail to contribute to the backscatter. The effect of shadowing is treated as a multiplying factor of the percentage of the surface that is illuminated. The cross correlation of the field is reduced to give the backscattering cross section. Both Gaussian and exponential surface correlations are considered, representing extremes in surface structure. The cross sections of both surfaces are shown to increase for certain ranges of rms roughness and correlation length. This increase is due to the backscatter from the annular regions of the sphere, which, when viewed as an image, would appear as a bright ring or halo. These results are supported by experimental measurements taken from roughened disks as a function of the illumination angle.