Effect of correlation between shadowing and shadowed points in rough surface scattering

The effect of correlation between shadowing and shadowed points upon various shadowing functions is studied. The backscatter (monostatic) shadowing function for a two-dimensional perfect electric conducting surface is calculated by modifying an infinite series representation developed by Ricciardi and Sato (1983, 1986). It is shown that when correlation between all shadowing and shadowed points is neglected in the series the result reduces to one of the shadowing functions purposed by Wagner (1967). This is useful since it explains from a physical point of view one of the assumptions made by Wagner, which was necessary to obtain the closed form result. We further calculate the shadowing function with correlation included by considering the first three terms in the modified Ricciardi-Sato series. These terms provide an upper and lower bound to the exact shadowing function. We show the effect of neglecting the higher order terms by relating them to the number of intersections of the surface with the incoming rays. Finally, we present results that show that the shadowing function purposed by Smith (1967) overestimates the effect of shadowing due to the neglect of correlation between the shadowing and shadowed point and a normalization term. We also show that the shadowing function derived by Wagner, which attempts to include the effect of this correlation, does not produce an improved result