SHAPE RECONSTRUCTION USING DIFFRACTED WAVES AND CANONICAL SOLUTIONS

This work deals with the determination of the shape of a generally-non -circular impenetrable cylinder from the way it scatters incident soun d. A complete family (of generally non-orthogonal functions) represent ation of the scattered field is employed to match the total measured f ield. The resolution of the direct problem during the inversion is byp assed by assuming a priori that the coefficients in the field represen tation are locally those of an impenetrable circular cylinder. These c oefficients are known explicitly to within a single parameter which is determined by resolution of a nonlinear equation. This parameter is n one other than the length of the position vector joining the origin to the given point on the boundary of the cylinder, so that by varying t he locations of the field measurement point and boundary point one gen erates a discrete form of the polar coordinate parametric equation of the boundary. Numerical examples of the results of the inversion schem e are given for cylinders with both convex (circular, elliptical) and non-convex boundaries.