Shadowing of Randomly Rough Surfaces

The first-order probability densities of height and slope on the portions of a rough surface illuminated jointly by rays in two arbitrary directions have been evaluated for a surface generated by a stationary normal random process. The dependence of the statistical properties of the apparent surface on the angles of incidence and observation is illustrated. For the case of backscatter, a simple calculation of the “shadowing functions,” valid at very small grazing angles, and a more detailed approximation, valid at the larger angles, are shown to be in excellent agreement with the computer-simulation results of Brockelman and Hagfors.