Identification of generalized impedance boundary conditions in inverse scattering problems

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February 2010, 4(1): 19-38. doi: 10.3934/ipi.2010.4.19

Identification of generalized impedance boundary conditions in inverse scattering problems

Laurent Bourgeois ^1, and Houssem Haddar ^2,

1.	Laboratoire POEMS, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France
2.	INRIA Saclay Ile de France / CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex

Received March 2009 Revised November 2009 Published February 2010

Abstract
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In the context of scattering problems in the harmonic regime, we consider the problem of identification of some Generalized Impedance Boundary Conditions (GIBC) at the boundary of an object (which is supposed to be known) from far field measurements associated with a single incident plane wave at a fixed frequency. The GIBCs can be seen as approximate models for thin coatings, corrugated surfaces or highly absorbing media. After pointing out that uniqueness does not hold in the general case, we propose some additional assumptions for which uniqueness can be restored. We also consider the question of stability when uniqueness holds. We prove in particular Lipschitz stability when the impedance parameters belong to a compact subset of a finite dimensional space.

Keywords: uniqueness, generalized impedance boundary conditions, Inverse scattering problems in electromagnetism and acoustics, stability..

Mathematics Subject Classification: 35J05, 35Q60, 35R30, 45A05, 45P0.

Citation: Laurent Bourgeois, Houssem Haddar. Identification of generalized impedance boundary conditions in inverse scattering problems. Inverse Problems & Imaging, 2010, 4 (1) : 19-38. doi: 10.3934/ipi.2010.4.19

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