Inverse Problems and Imaging (IPI)

Identification of generalized impedance boundary conditions in inverse scattering problems

Pages: 19 - 38, Volume 4, Issue 1, February 2010      doi:10.3934/ipi.2010.4.19

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Laurent Bourgeois - Laboratoire POEMS, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France (email)
Houssem Haddar - INRIA Saclay Ile de France / CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France (email)

Abstract: 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:  Inverse scattering problems in electromagnetism and acoustics, generalized impedance boundary conditions, uniqueness, stability.
Mathematics Subject Classification:  35J05, 35Q60, 35R30, 45A05, 45P05.

Received: March 2009;      Revised: November 2009;      Available Online: February 2010.