Multiple eigenvalues of the time reversal operator for a small spherical scatterer

Abstract

Time reverse mirrors have been used to discriminate and focus energy on individual scatterers embedded in difficult media. A time reverse mirror consists of an array of transceivers, each of which records the incident pressure field then re-emits a time reversed image of it. Prada [J. Acoust. Soc. Am. 97(1) (1995)] described this operation in terms of a time reverse operator whose eigenvalues are associated with individual scatterers in the medium. In particular, it was shown that there was a one-to-one correspondence between the eigenvalues and scatterers for the case of well separated scatterers whose density is identical to the medium. In this talk, Prada’s approached is generalized to scatterers of arbitrary densities where the scattered wave is no longer spherical. It is shown that the one-to-one correspondence between scatterers and eigenvalues of the time reversal operator is broken. For the specific case of a small spherical scatterer, there are three eigenvalues. Physical interpretations of the three eigenvalues and the implications for applications of the time reverse method will be discussed. [Work performed under the auspices of the Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.]