On the reconstruction of surface impedance from the far-field data in inverse scattering problems

Abstract

Consider the reconstruction of the surface impedance from the far-field data for all incident directions arising in the inverse scattering problems. We derive an important identity involving the unknown impedance, from which a numerical scheme for determining the surface impedance is proposed in the framework of the probe method. In this scheme, we firstly recover the scattered wave corresponding to the point sources from the far-field data of the scattered wave for incident plane waves, and then reconstruct the surface impedance from the information about the scattered wave related to the point sources by the integral equation method. We prove the solvability of this integral equation of the first kind for the surface impedance and analyse this reconstruction scheme. The numerical examples are also presented, showing the validity of our method, especially for the smooth surface impedance.

Keywords:

• inverse scattering
• integral equations
• surface impedance
• potential method
• uniqueness
• numerics

AMS Subject Classifications::

• 35P25
• 35R30
• 78A45

Acknowledgements

This work is supported by NSFC (Nos 11071039, 11161130002). The authors thank the anonymous referees for their careful reading and valuable suggestions which greatly improved this article.