Scattering matrix of a nearly circular cylinder

The acoustic scattering matrix for a cylinder whose cross sectional boundary deviates from a circle is determined by using a boundary perturbation method. It is shown how to obtain the scattering matrix approximation up to a desired order, for a scatterer with a given impedance. The limits of hard and soft scatterers are included as special cases. In addition, the first-order scattering matrix is used to solve an optimization problem, i.e., that of finding the shape of the scatterer which yields a reflected field closest to a given field in a least-squares sense. (C) 1999 Elsevier Science B.V. All rights reserved.