The Numerical Evaluation of a Physical Optics Normalized Cross Section for a Rough Surface

: One major topic in this report is the explanation of the numerical evaluation of the physical optics normalized cross section (sigma) of a one- dimensional rough surface. A second topic involves the comparison of the numerical evaluation of sigma with two other approximate evaluations of the physical optics integral representation for sigma. Some comparisons of these three representations for sigma are made as function of surface roughness and mean surface slope. A general integral expression for sigma for a one- dimensional rough surface is analyzed and its is shown how it may be evaluated numerically. The single integral approximation is shown to require small surface slopes for good agreement whereas the geometric optics solution requires both small slopes and large Rayleigh parameter.