Methods and Applications of Analysis

Volume 17 (2010)

Number 4

The Determination of Anisotropic Surface Impedance in Electromagnetic Scattering

Pages: 379 – 394



Fioralba Cakoni

Peter Monk


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.


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

2010 Mathematics Subject Classification

35J25, 65M32, 78A46

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