Shape identification in inverse medium scattering problems with a single far-field pattern

Abstract

Consider time-harmonic acoustic scattering from a bounded penetrable obstacle D ⊂ R N embedded in a homogeneous background medium. The index of refraction characterizing the material inside D is supposed to be Hölder continuous near the corners. If D ⊂ R 2 is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions N ≥ 3, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering wavenumbers in domains with corners. As a byproduct, we show that the smoothness conditions in previous corner scattering results are only required near the corners.