Comparison between time reversal focusing in absorbing medium and inverse filtering

To focus ultrasonic waves in inhomogeneous media using a phased array, one has to calculate the optimal set of signals (for monochromatic waves, amplitude and phase (D.R. Jackson and D.R. Dowling, 1991)) to be applied on the transducers of the array. The solution obtained by Time Reversal Processing (TRP) corresponds to the spatial and temporal filter matched to an initial source available in the medium. However, this process doesn't ensure that the field amplitude at other locations is as small as possible. The authors have illustrated this problem previously using the example of focusing through the human skull, which is an absorbing medium. The authors found that in order to obtain good focusing, it is necessary to add to the time reversal process an amplitude compensation that takes into account absorption. Another approach consists in using an entire array of transducers on both sides of the skull. The authors measure and compare the focal quality obtained in the different cases: matched filter, inverse filter and amplitude compensation combined with time reversal.