The identification of a penetrable obstacle with mixed transmission conditions from far field measurements

Abstract

We consider the two-dimensional electromagnetic inverse scattering problem for a dielectric medium partially coated with a thin layer of highly conductive material. Using the linear sampling method, we show that the approximate solution of the far field equation can be used to reconstruct the support of the coating in addition to the shape of the scattering obstacle. We also deduce formulaes providing point-wise reconstruction of the surface conductivity on the coated portion and the real index of refraction on the uncoated portion of the boundary. Numerical examples are given for the case with constant surface conductivity and index of refraction showing the viability of our reconstruction procedure.

Keywords:

• linear sampling
• mixed transmission conditions
• inhomogeneous medium
• inverse scattering

AMS Subject Classifications::

• 35R30
• 35Q60
• 35J40
• 78A25

Acknowledgements

F. Cakoni gratefully acknowledges the support of the U.S. Air Force Office of Scientific Research under Grant FA9550-08-1-0138. M. Sini gratefully acknowledges the support of the FWF under the SFB 013 project.