Spatial densities for specular points on a gaussian surface

Specular point densities for several models of randomly rough surfaces with a Gaussian height distribution are derived. Both area densities and volume densities conditioned by the surface height variate and surface curvatures are obtained. Several shadowing functions are compared with digital computer simulation results, and the application of the slope conditional shadowing function as a modifying factor for specular point densities is described. These densities, as modified by the shadowing function, are required in determining the statistics of fields reflected from random surfaces inducing deep-phase modulation whenever discrete scatterer models are employed in the analysis.