Backpropagation imaging in nonlinear harmonic holography in the presence of measurement and medium noises

Habib Ammari 1 Josselin Garnier 2, 3 Pierre Millien 1
1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LJLL - Laboratoire Jacques-Louis Lions
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Abstract : In this paper, the detection of a small reflector in a randomly heterogeneous medium using secondharmonic generation is investigated. The medium is illuminated by a time-harmonic plane wave at frequency ω. It is assumed that the reflector has a nonzero second-order nonlinear susceptibility, and thus emits a wave at frequency 2ω in addition to the fundamental frequency linear scattering. It is shown how the fundamental frequency signal and the second-harmonic signal propagate in the medium. A statistical study of the images obtained by migrating the boundary data is performed. It is proved that the second-harmonic image is more stable with respect to medium noise than the one obtained with the fundamental signal. Moreover, the signal-to-noise ratio for the second-harmonic image does not depend either on the second-order susceptibility tensor or on the volume of the particle.
Keywords : waves in random media imaging in complex media
Type de document :
Article dans une revue
SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2014, 7 (1), pp.239-276. 〈10.1137/130926717〉
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https://hal.archives-ouvertes.fr/hal-01017778
Contributeur : Serena Benassù <>
Soumis le : jeudi 3 juillet 2014 - 10:40:14
Dernière modification le : jeudi 29 mars 2018 - 17:08:04

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Habib Ammari, Josselin Garnier, Pierre Millien. Backpropagation imaging in nonlinear harmonic holography in the presence of measurement and medium noises. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2014, 7 (1), pp.239-276. 〈10.1137/130926717〉. 〈hal-01017778〉

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