Focusing in transmit–receive mode through inhomogeneous media: The time reversal matched filter approach

For a few years, adaptive time delay focusing techniques have been extensively studied in order to focus through inhomogeneous media. However, these techniques can only correct the effects of a thin aberrator located near the array. Time reversal of ultrasonic fields allows another approach to focus in the transmit mode through inhomogeneous media. Compared to the adaptive time delay focusing technique, time reversal requires the transmission of different waveforms from each individual element of an array. Focusing via time reversal is shown to be optimal in comparison with time delay focusing since it realizes the spatio-temporally matched filter to the inhomogeneous propagation transfer function between the array and the focal point. In previous papers Fink et al., Proc. IEEE Ultrasonics Symposium, Montreal (1989), focusing by time reversal has been described in the transmit mode only. A complete focusing in inhomogeneous medium requires the extension of this technique in the receive mode. This paper describes the extension of the matched filter approach in the receive mode and it is shown that optimal focusing in this mode can be achieved using adaptive convolution beamforming techniques instead of simple time delay lines. Theoretical and experimental results are presented to show the efficiency of this technique compared to adaptive delay line focusing.