Uniqueness to inverse acoustic scattering from coated polygonal obstacles with a single incoming wave

Abstract

It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. As a by-product, we prove that the wave field cannot be real-analytic on each corner point lying on the convex hull of the scatterer. Our arguments are based on the Schwarz reflection principle for the Helmholtz equation satisfying the impedance boundary condition on a flat boundary.