Uniqueness theorems for the inverse problem of acoustic scattering. (English) Zbl 0539.76086
Summary: Uniqueness theorems are obtained for the problem of determining the shape of a sound-soft or sound-hard obstacle from a knowledge of (1) the far- field pattern at a fixed value of the wave number and a finite number of distinct incident fields, or (2) the total scattering cross section for an interval of wave numbers and the incident field propagating in an arbitrary direction.