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Description:
In this paper, we prove uniqueness in determining a sound-soft ball or polyhedral scatterer in the inverse acoustic scattering problem with a single incident point source wave in \R^N (N=2,3). Our proofs rely on the reflection principle for the Helmholtz equation with respect to a Dirichlet hyperplane or sphere, which is essentially a 'point-to-point' extension formula. The method has been adapted to proving uniqueness in inverse scattering from sound-soft cavities with interior measurement data incited by a single point source. The corresponding uniqueness for sound-hard balls or polyhedral scatterers has also been discussed.