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.

We consider reshaping an obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification are particularly studied. Stability estimates are derived for scattering amplitude in terms of the diameter of a small obstacle, which implies that the limiting case for minification corresponds to a perfect cloaking, i.e., the obstacle is invisible to detection.

Abstract. This paper concerns thermoacoustic tomography and photoacoustic tomography, two couple-physics imaging modalities that attempt to combine the high resolution of ultrasound and the high contrast capabilities of electromagnetic waves. We give sufficient conditions to recover both the sound speed of the medium being probed and the source.

We study resonance for the Helmholz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasistatic approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of a inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann-Poincaré operator associated with the inclusion.

We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schrödinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first established. Three uniqueness results are then obtained for the corresponding inverse problems in determining the variance of the source, the potential and the expectation of the source, respectively, by the associated far-field measurements. First, a single realization of the passive scattering measurement can uniquely recover the variance of the source without the a priori knowledge of the other unknowns. Second, if active scattering measurement can be further obtained, a single realization can uniquely recover the potential function without knowing the source. Finally, both the potential and the first two statistic moments of the random source can be uniquely recovered with full measurement data. The major novelty of our study is that on the one hand, both the random source and the potential are unknown, and on the other hand, both passive and active scattering measurements are used for the recovery in different scenarios.