Selective focusing in multiple-target media: the transfer matrix method

The iterative time reversal mirror provides an elegant way of focusing in a multiple-target media on the most reflective one. This paper presents a method to focus on the other targets. This method is derived from the theoretical study of the iterative time reversal process. It relies on both the definition of transfer matrix K of the system (array of transducers+medium of interest) and the introduction of the time reversal operator K*K. It is shown that, in the case of well-resolved targets of different reflectivities, each target corresponds to one eigenvector of K*K. This eigenvector provides the optimum delay law to focus on the associated target. The principle is to measure K, to calculate the eigenvectors of K*K and to transmit one eigenvector in order to focus on the corresponding target. An experimental validation of the method is given