Time reversal mirrors and invariants of the time reversal operator: Application to detection and imaging in biological media

Abstract

Acoustic time reversal mirrors have been developed in the Laboratoire Ondes et Acoustique for several years. In inhomogeneous media and especially in the presence of multiple scattering, these systems provide outstanding focusing properties. While used in pulse echo mode, the time reversal process can be iterated, leading to selective focusing on the most reflective point among a set of scatterers. This iteration is also used to enhance the echo from a defect like a kidney stone or a microcalcification in the breast. The iterative time reversal process is described by a matrix call the Time Reversal Operator (TRO). The eigenvectors of this matrix provide the invariants of the iterative time reversal process, their analysis is the base of the D.O.R.T. method. It allows the separation of the echoes from several scatterers in an inhomogeneous medium and the selective focusing on any of them. Furthermore, when an estimate of the medium’s Green function is available, high‐resolution and low‐noise images can be achieved using the backpropagation of the dominant eigenvectors. The principle of acoustic time reversal mirrors and the D.O.R.T. method will be described through several examples.