Methods and Applications of Analysis

The Determination of Anisotropic Surface Impedance in Electromagnetic Scattering

Fioralba Cakoni and Peter Monk

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Abstract

We consider the inverse scattering problem of determining the anisotropic surface impedance of a bounded obstacle from far field measurements of the electromagnetic scattered field due to incident plane waves. Such an anisotropic boundary condition can arise from surfaces covered with patterns of conducting and insulating patches. We show that the anisotropic impedance is uniquely determined if sufficient data is available, and characterize the non-uniqueness present if a single incoming wave is used. We derive an integral equation for the surface impedance in terms of solutions of a certain interior impedance boundary value problem. These solutions can be reconstructed from far field data using the Herglotz theory underlying the Linear Sampling Method. We complete the paper with preliminary numerical results.

Article information

Source
Methods Appl. Anal., Volume 17, Number 4 (2010), 379-394.

Dates
First available in Project Euclid: 24 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.maa/1306249558

Mathematical Reviews number (MathSciNet)
MR2800558

Zentralblatt MATH identifier
1230.78016

Subjects
Primary: 65M32: Inverse problems 35J25: Boundary value problems for second-order elliptic equations 78A46: Inverse scattering problems

Keywords
Anisotropic coatings electromagnetic inverse scattering mixed boundary conditions determination of boundary coefficients

Citation

Cakoni, Fioralba; Monk, Peter. The Determination of Anisotropic Surface Impedance in Electromagnetic Scattering. Methods Appl. Anal. 17 (2010), no. 4, 379--394. https://projecteuclid.org/euclid.maa/1306249558


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