Time-reversal is the process whereby a signal is emitted by a source and propagates in a medium with scatterers in it. The waves are recorded at a receiver over a time much larger than the original pulse duration so as to capture the multiple scattering. The receiver then reverses the waveform in time and re-emits it into the same channel. The waves back-propagate through the medium retracing the multiple scattering paths taken on the way to the receiver and ultimately refocus at the original source location in space and time. Time-reversal in an enclosure with a single detector achieves spatial focusing of the acoustic energy to within one half of a wavelength of the initial sound signal.
A two-dimensional finite-difference time-domain code was calibrated to study the phenomena of time compression and spatial focusing of time-reversed acoustic signals in closed environments with strong reverberations. By varying several factors such as reflectivity of the walls and the addition of randomly-placed detectors and scatterers in the enclosure, the quality of spatial focusing is investigated.
One of our main results is that time-reversal in enclosures with a keyhole aperture of size comparable to the width of the initial wave front achieves tight spatial focusing of the acoustic field at the source. Despite the limitation that the keyhole is perceived as "the source'' by the detector, the relative magnitude and temporal-delay information of the reverberant wave fields in the source chamber and in the detector chamber indicate the actual source location.
Time-reversal in complex indoor environments is tested. Regardless of whether the transmission or the reception of the signal are done from an area cluttered with nearby scatterers, the acoustic field distribution after time-reversal is higher in the area close to where the time-reversed waveform is transmitted. Due to its characteristic spatial focusing of signals, time-reversal can deliver trains of pulses to desired locations. However, our results show that the temporal compression obtained is not sufficient to eliminate inter- symbol interference (ISI) in the transmitted message.