Optimal Spatiotemporal Focusing Through Multiple Scattering Media

Overview & Synopsis

In the context of echographic imaging, focusing of ultrasound in the human body can be achieved with a transducer array and electronic delay lines. However, that principle is not practicable any more as soon as the thickness of the medium of interest exceeds the mean free path. In such multiple scattering media, it was shown that spatiotemporal focusing can be achieved using time-reversal: a training pulse is sent from a source located at the intended focal point, travels through the scattering medium and is captured at a transducer array, the time reversal mirror (TRM). The waveforms received on the TRM are flipped in time and sent back, resulting in a wave converging at the desired focus location. Time reversal focusing is optimal in the sense that it achieves a spatiotemporal matched filter. Here we propose an approach for optimal focusing that does not require a direct measurement of the impulse response between the transducer array and the intended focal point. The key idea is to use a nonlinear feedback intensity signal to shape the incident pulsed wave front. We show that the limit of a true spatiotemporal matched filter can be achieved contrary to analogous methods recently proposed in optics.