Unacceptable height correlation coefficients and the quasi-specular component in rough surface scattering

The purpose of this note is to put to rest once and for all the use of an erroneous result derived from the linear (or exponential) height correlation coefficient in the physical optics formulation of rough surface scatter. The form of the correlation coefficient near the origin must be quadratic so that the physical optics integral can be evaluated asymptotically. Hence, the theoretical shape of the quasi-specular component for backscatter is not due to the nature of the correlation coefficient but to the form and behavior of the probability density function for the surface slopes evaluated for tilts near their mean values, the horizontal.