C. Prada et al., DECOMPOSITION OF THE TIME-REVERSAL OPERATOR - DETECTION AND SELECTIVEFOCUSING ON 2 SCATTERERS, The Journal of the Acoustical Society of America, 99(4), 1996, pp. 2067-2076
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.