Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers

This paper addresses the uniqueness for an inverse acoustic obstacle scattering problem. It is proved that a general sound-hard polyhedral scatterer in R-N(N >= 2), possibly consisting of finitely many solid polyhedra and subsets of (N - 1)-dimensional hyperplanes, is uniquely determined by N far-field measurements corresponding to N incident plane waves given by a fixed wave number and N linearly independent incident directions. A simple proof, which is quite different from that in Alessandrini and Rondi (2005 Proc. Am. Math. Soc. 6 1685-91), is also provided for the unique determination of a general sound-soft polyhedral scatterer by a single incoming wave.