Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors

We investigate the acoustic selective focusing properties of time reversal in a two-dimensional acoustic waveguide. A far-field model of the problem is proposed in the time-harmonic case. In order to tackle the question of selective focusing, we derive an asymptotic model for small scatterers. We sh...

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Bibliographic Details
Published in:Inverse problems 2007-02, Vol.23 (1), p.1-25
Main Authors: Pinçon, B, Ramdani, K
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
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Summary:We investigate the acoustic selective focusing properties of time reversal in a two-dimensional acoustic waveguide. A far-field model of the problem is proposed in the time-harmonic case. In order to tackle the question of selective focusing, we derive an asymptotic model for small scatterers. We show that in the framework of this limit problem, approximate eigenvectors of the time reversal operator can be obtained when the number of propagating modes of the waveguide is large enough. This result provides, in particular, a mathematical justification of the selective focusing properties observed experimentally. Some numerical experiments on selective focusing are presented.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/23/1/001