New results on coherent scattering from randomly rough conducting surfaces

An approximate solution for the average field scattered by a perfectly conducting randomly rough surface having a correlation length much smaller than the electromagnetic wavelength is presented. The analysis is based on the use of a substitute surface which gives rise to the same describing equations as the true surface relative to the average scattered field. The substitute surface comprises large nonoverlapping fiat areas having random elevations with respect to the mean planar surface and arbitrary correlation between adjacent areas. The average scattered field is shown to depend upon the number of interacting areas and the surface roughness. For a given range of surface roughness there is a specific number of interacting areas which dominate the average scattered field. It is demonstrated how this number can be computed and how a continuous curve of average scattered field as a function of surface roughness is obtained. Of particular importance is the quantitative correspondence established in this paper between the surface roughness and the degree of multiple interaction on the rough surface.