THE ITERATIVE TIME-REVERSAL PROCESS - ANALYSIS OF THE CONVERGENCE

The efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated. In a multitarget media, the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown [C. Prada, F. Wu, and M. Fink, J. Acoust. Soc. Am. 90, 1119 (1991)]. The theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of L transducers in a given medium as a linear system of L inputs/L outputs. The system is characterized at each frequency by its transfer matrix K and the time reversal iterative process is then described by a time reversal operator KK. Because of the reciprocity principle, this operator is Hermitian. The following result is shown: If the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator KK with nonzero eigenvalue corresponds to one of the targets in the set and provides the optimum phase law to focus on it. Furthermore, the eigenvalue is proportional to the reflectivity of the target. In particular, the “brightest” target is associated to the eigenvector of greatest eigenvalue so that the iterative time reversal process leads to a wave focusing on this target. This analysis is illustrated by numerical and experimental results. © 1995, Acoustical Society of America. All rights reserved.