Décomposition de l'Opérateur de Retournement Temporel appliquée à l'imagerie et à la caractérisation ultrasonore

Abstract : Acoustic scattering analysis is an important tool in acoustic imaging and characterization with applications among non-destructive testing, medical imaging or underwater acoustics. The method employed in the manuscript is the Decomposition of the Time Reversal Operator or DORT method. It consists in the study of the Time Reversal invariants. For a given transducers array, the invariants correspond to the singular vectors obtained by singular value decomposition of the array response matrix K. Each vector is associated with a singular value. The DORT method is here used to characterize different elastic object such as cylinder, tube, sphere and two cylinders. The formalism of decomposition of the scattered pressure in normal modes of vibrations or harmonics allows to determine the theoretical Time Reversal invariants. The N dimension problem, where N is the number of transducers, is reduced to a problem which dimension is about 2k0a+1, where a is the characteristic object dimension and k0 the wave number in the surrounding fluid. This approach gives analytical expressions of the singular values and vectors in the small object limit (k0a < 0,5) and in the Rayleigh limit (2a less than the focal spot). Theses results are experimentally verified and in agreement with the previous point of view : for a small cylinder, it exists a main singular value associated with the singular vector which focuses isotropicly on the scatterer. Furthermore, analogies with the two dimensional electromagnetism are also shown. [A corrected and updated version of the manuscript is available as a book (EUE September 2010). The fluid scattering case (cylinder and sphere) has been corrected. The hollow elastic sphere scattering has been added. The cylindrical projected mode formalism has been adapted to the spherical case. The reference list has been updated.]
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Contributor : Jean-Gabriel Minonzio <>
Submitted on : Monday, September 5, 2011 - 3:38:37 PM
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  • HAL Id : tel-00128772, version 2


Jean-Gabriel Minonzio. Décomposition de l'Opérateur de Retournement Temporel appliquée à l'imagerie et à la caractérisation ultrasonore. Acoustique [physics.class-ph]. Université Paris-Diderot - Paris VII, 2006. Français. ⟨tel-00128772v2⟩



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