Real time inverse filter focusing by iterative time reversal

Abstract

In order to achieve an optimal focusing through heterogeneous media, we need to build an inverse filter of the propagation operator. Time-reversal achieves such an inverse filter in nondissipative media. However, as soon as losses appear in the medium, time-reversal is no more equivalent to an inverse filter. Consequently, it does no more produce the optimal focusing and beam degradations may appear. In such cases, previous works have shown that the optimal focusing can be recovered by using a spatiotemporal inverse filter technique. This process requires the presence of a set of receivers inside the medium but allows us to reach the optimal focusing even in extreme situations such as ultrasonic focusing through a human skull. To date, it remained time consuming and implied fastidious numerical calculations. We propose here a new way to process this inverse filtering in real time and without any calculation. The new process is based on iterative time-reversal processing. Contrary to the classical inversion, this iteration does not require any computation as it achieves the inverse filter experimentally using waves propagation instead of computational power. The feasibility of this iterative technique is theoretically and experimentally demonstrated for ultrasound applications and its potential for telecommunications is discussed.