EIGENMODES OF THE TIME-REVERSAL OPERATOR - A SOLUTION TO SELECTIVE FOCUSING IN MULTIPLE-TARGET MEDIA

The iterative time reversal mirror provides an elegant way of focusing in multiple target media oh the most reflective one. This paper presents a method to focus on the other targets. It is derived from a theoretical Study of the iterative time reversal process. The iterative process can be described at each frequency by a time reversal operator which can be diagonalized. The eigenvectors of this operator are eigenmodes of the time reversal process. In the case of well resolved targets of different ''brightness'', the rank of the time reversal operator is equal to the number of targets and each eigenvector of non zero eigenvalue provides the optimal phase and amplitude law focus on the corresponding target. An experimental validation of these results is given.