Approximating the scattering coefficients for a non-Rayleigh obstacle by boundary defect minimization

The coefficients which appear in the representation of the far-field scattered by a twodimensional, perfectly electrically conducting obstacle, depend on the normal derivative of the scattered field on the obstacle boundary, $\partial_N v |_{\Gamma}$. A family of functions, W, deduced from the minimization of a boundary defect, is shown to be linearly independent and complete. As a consequence the approximation of @Nv|gamma results from a well posed algebraic problem. The approximation error is estimated from an a priori bound on the equation error in terms of the eigenvalues of a boundary integral operator. Rayleigh's hypothesis is nowhere required of the obstacle. These results justify some obstacle inversion methods which originated from heuristic arguments