Inverse scattering from an open arc

A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound‐soft or perfectly conducting arc from a knowledge of the far‐field pattern for the scattering of time‐harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far‐field operator, which for a fixed incident wave maps the boundary arc onto the far‐field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.