Uniqueness in inverse scattering with phaseless near-field data generated by superpositions of two incident plane waves

This paper is concerned with the uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency. It can be proved that the unknown scatterer can be uniquely determined by the phaseless near-field data. The proof is based on the analysis of the phase information and the application of Rellich's lemma together with the Green's formula for the radiating solutions to the Helmholtz equation or the Stratton--Chu formula for the radiating solutions to the Maxwell equations

Simultaneous recovery of a locally rough interface and the embedded obstacle with the reverse time migration

Consider the inverse acoustic scattering of time-harmonic point sources by an unbounded locally rough interface with bounded obstacles embedded in the lower half-space. A novel version of reverse time migration is proposed to reconstruct both the locally rough interface and the embedded obstacle. By a modified Helmholtz-Kirchhoff identity associated with a planar interface, we obtain a modified imaging functional which has been shown that it always peaks on the local perturbation of the interface and on the embedded obstacle. Numerical examples are presented to demonstrate the effectiveness of the method.Comment: 21 pages, 19 figure

Reverse time migration for inverse acoustic scattering by locally rough surfaces

Consider the inverse scattering of time-harmonic point sources by an infinite rough surface which is supposed to be a local perturbation of a plane. A novel version of reverse time migration is proposed to reconstruct the shape and location of the rough surface. The method is based on a modified Helmholtz-Kirchhoff identity associated with a special rough surface, leading to a modified imaging functional which always reaches a peak on the boundary of the rough surface for sound-soft case and penetrable case, and hits a nadir on the boundary of the rough surface for sound-hard case. Numerical experiments are presented to show the powerful imaging quality, especially for multi-frequency data.Comment: 29 pages,26 figure