Multiple scattering between two elastic cylinders and invariants of the time-reversal operator : Theory and experiment

The decomposition-of-the-time-reversal-operator method is an ultrasonic method based on the analysis of the array response matrix used for detection and characterization. The eigenvalues and the eigenvectors of the time-reversal operator (equivalent to the singular values and the singular vectors of the array response matrix) provide information on the localization and nature of scatterers in the insonified medium. Here, the eigenmodes of the time-reversal operator are studied for two elastic cylinders: The effects of multiple scattering and anisotropic scattering are considered. Analytical expressions for the singular values are established within the isotropic scattering approximation. Then, the comparison with a complete model is presented, putting in evidence the importance of the anisotropy of the scattering. Experiments, carried out at central frequency 1.5MHz on 0.25mm diameter nylon and copper cylinders embedded in water, confirm the theory. In particular, the small cylinder limit and the effect o...

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