The inverse scattering problem for a partially coated cavity with interior measurements

Abstract

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.

Keywords:

• inverse scattering
• mixed boundary value problem
• boundary impedance
• interior measurements
• linear sampling method

AMS Subject Classifications:

• 35R30
• 65F22
• 65R20
• 65R32

Acknowledgments

The research of Y.Q.Hu and J.J.Liu are supported by NSFC No.11161130002, No.11071039 and the Fundamental Research Funds for the Central Universities No. 3207011102. The research of F. Cakoni is supported in part by the Air Force Office of Scientific Research Grant FA9550-11-1-0189 and NSF Grant DMS-1106972.