Scattering from a perfectly conducting rough interface is developed in terms of a generalized angular spectrum of plane waves which includes both upward and downward traveling waves. This spectral formulation is used to examine the interrelationships between three classical approximate techniques in rough surface scattering, i.e., physical optics, boundary perturbation, and extinction theorem. These methods are also traced to conventional deterministic scattering analysis techniques. In particular, physical optics is related to the Magnetic Field Integral Equation, boundary perturbation is shown to result from the Electric Field Integral Equation subsequent to invoking the Rayleigh Hypothesis, and the extinction theorem is equivalent to the Extended Boundary Condition Method. The capabilities and limitations of these rough surface approximate techniques are developed using the angular spectrum approach, and they are discussed in detail. © 1985.
Brown, G. S. (1985). A comparison of approximate theories for scattering from rough surfaces. Wave Motion, 7(2), 195–205. https://doi.org/10.1016/0165-2125(85)90046-0