Didier Cassereau
Mathias Fink
Lab. Ondes et Acoust., E.S.P.C.I., Univ. Paris VII, 10 rue Vauquelin, 75231 Paris Cedex 05, France
For several years, time-reversal methods were developed in this laboratory, theoretically and experimentally, to optimize focusing of an ultrasonic pressure field on a target in homogeneous and heterogeneous media. In this work, the problem is analyzed in the case of focusing through a plane interface separating two media with different sound speeds and densities. The principle consists in considering the target as an active source of an acoustic field measured by a mirror. Then, the mirror time-reverses this field, and an acoustic wave back propagates and is focused on the initial target position. A theoretical approach and numerical simulations are presented using one or two plane infinite time-reversal mirrors working on the reflected and/or transmitted components of the field generated by the source. It is shown that it can be more efficient to time reverse the reflected or transmitted field, depending on the velocity contrast between the two media. The problem of mirrors of finite size is also discussed, resulting in a broader focusing peak. Finally, the time-reversal method is compared to the standard Fermat's surface technique, that reduces to a time-delay computation according to Snell's law. It will be shown how the time-reversal method, that takes into account the whole information coming from the medium, improves the focalization on the initial target position.