Scattering from a randomly rough half-plane

The scattering and diffraction of a plane wave by a randomly rough half-plane are investigated. Such a nonplane boundary problem is related to the degradation of an antenna due to the random distortion of the reflector and the scattering and diffraction by rough walls. The present formulation is a combination of three techniques: the small perturbation, the Wiener-Hopf method, and a group-theoretic consideration for determining the form of the scattered wave. Using the shift invariant property of the homogeneous random plane, the D/sup a/-Fourier transform which converts the scattered wave into a homogeneous random function of x with a complex variable is defined. Assuming a slightly rough case, such a homogeneous random function is expanded into a perturbation series. The first-order wave field is then obtained by the Wiener-Hopf technique.<>