DECOMPOSITION OF THE TIME-REVERSAL OPERATOR - DETECTION AND SELECTIVEFOCUSING ON 2 SCATTERERS

The decomposition of the time reversal operator (DORT) method is a sel ective detection and focusing technique using an array of transmit-rec eive transducers. It relies on the theory of iterative time reversal m irrors which was presented by Prada ed al. [C. Prada, J. L. Thomas, an d M. Fink, J. Acoust. Sec. Am. 97, 62-71 (1995)]. The time reversal op erator was defined as K(omega)K(omega), where omega is the frequency, means complex conjugate, and K(omega) is the transfer matrix of the array of L transducers insonifying a time invariant scattering medium . It was shown that this time reversal operator can be diagonalized an d that for ideally resolved scatterers of different reflectivities, ea ch of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatter ers. The DORT method consists in determining these eigenvectors and us ing them for the selective focusing. This paper presents a complete an alysis of this method in the case of two scatterers. The mathematical expressions of the eigenvectors are given and several experimental res ults are described. In particular, the effectiveness of the method to focus selectively through an inhomogeneous medium is established. (C) 1996 Acoustical Society of America.