Recovery of the shape of an obstacle and the boundary impedance from the far-field pattern

Abstract

In this paper, we consider an inverse scattering problem for an obstacle $D \subset \mathcal{R}^{3}$ with Robin boundary condition. A reconstruction procedure for identifying both the shape of the obstacle and the boundary impedance from the far-field pattern is proposed. Our method is to transform the far-field patterns into the near-field patterns, then construct an indicator function from which we can determine the boundary shape. Having known the shape of $D$, the boundary impedance is recovered by moment method for the known boundary.