Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data

Abstract

This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed frequency in two dimensions. We consider the case where a Dirichlet boundary condition is imposed on the locally rough surface. This problem models inverse scattering of plane acoustic waves by a one-dimensional sound-soft, locally rough surface; it also models inverse scattering of plane electromagnetic waves by a locally perturbed, perfectly reflecting, infinite plane in the transverse electric polarization case. We prove that the locally rough surface is uniquely determined by the phaseless near-field data generated by a countably infinite number of plane waves and measured on an open domain above the locally rough surface. Further, a direct imaging method is proposed to reconstruct the locally rough surface from the phaseless near-field data generated by plane waves ...