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Identification électromagnétique de petites inclusions enfouies

Souhir Gdoura 1 
1 DRE - Département de Recherche en Electromagnétisme ; EMG - Département Electromagnétisme - L2S
L2S - Laboratoire des signaux et systèmes : 1289, SUPELEC-Campus Gif
Abstract : The aim of this work is the electromagnetic non-iterative detection of small buried objects. The direct scattering problem is dealt with by means of an asymptotic formula of the field scattered by inclusions the size of which is much smaller than the wavelength of the illumination in the embedding medium. Taking into account the multiple scattering in the case of two spherical inclusions is made through a specific polarization tensor which is computed in an appropriate bispherical co-ordinate system. The Foldy-Lax model is also used so as to take into account the coupling between several inclusions. The numerical simulations show that this coupling effect is only felt within the near neighborhood. A half-space configuration is also focused onto. The Green dyads are calculated exactly by numerical brute-force first. Then three methods of approximation to compute the Sommerfeld integrals involved in their calculation are investigated, the simulations showing that they save quite some time in the calculation of these dyads while being accurate enough in most cases. The coupling between a sphere and the interface is also investigated via the introduction of an adequate polarization tensor again computed in bispherical co-ordinates (now, one of the two spheres is degenerating into the planar interface). Each time, the scattered fields simulated by the asymptotic method are compared to fields obtained by the so-called Coupled Dipole Method (CDM). The asymptotic method yields satisfactory values of the scattered field when the size of inclusions is indeed small enough vs. the wavelength of the illumination. Then, the imaging algorithm MUSIC is used to detect these inclusions from their Multi-Static Response (MSR) matrix as collected by a planar array of ideal transceiver dipoles. The analysis of the singular values and singular vectors of the MSR matrix shows that there is some difference between the data calculated by the asymptotic formula and those that are calculated by the CDM method. But this difference does not persist whenever one considers noisy data, even at relatively low noise level. In both cases, the MUSIC algorithm allows us to estimate the position of the inclusions, the notion of "super-localization" being discussed in particular. A method is also proposed to estimate the orientation of a buried, inclined ellipsoid.
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Submitted on : Tuesday, December 13, 2011 - 11:18:07 AM
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  • HAL Id : tel-00651167, version 2

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Souhir Gdoura. Identification électromagnétique de petites inclusions enfouies. Electromagnétisme. Université Paris Sud - Paris XI, 2008. Français. ⟨NNT : ⟩. ⟨tel-00651167v2⟩

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