Scattering of waves from a random cylindrical surface

The present paper deals with the scattering of waves in two-dimensional space by the random surface of a circular object, which is meant to be a preliminary study for treating three-dimensional scattering by a random sphere. The theory is formulated using a stochastic functional method and a group-theoretic consideration related to the rotation of the circle, in a manner analogous to the authors’ previous treatment of the scattering by a planar random surface [Radio Sci. 15, 1049 (1980); J. Math. Phys. 22, 471 (1981); Radio Sci. 16, 831, 847 (1981); J. Opt. Soc. Am. A 2, 2208 (1985)]. First, the randomly scattered wave for cylindrical wave injection is given in terms of the Wiener–Hermite functional of the random field on the circle, and then the scattered field for plane-wave injection is synthesized by superposing cylindrical waves. The differential cross sections for the coherent and incoherent scattering are obtained, and a statistical version of the optical theorem is shown to hold. Some numerical calculations are made for the Mie scattering by the random circular surface with Dirichlet and Neumann conditions.