Time Reversal Matched Field Processing: An Analytical Justification

The paper develops an analytical model to explain the phenomena of super resolution focusing achieved with time-reversal, matched field processing (TR/MFP). Our analytical model is based on multipaths introduced due to total internal reflections of the transmitted signal within a random medium. Under minor constraints, we show that the transfer function [unk] for the field observed at the location[unk] of the scatterer contains a squared sinc term. Since multiplication of two similar sinc functions in the frequency domain is equivalent to the convolution of two rectangular functions with equal widths in the time domain, the result of convolution is a triangular function with a distinct peak at [unk]. In comparison, the transfer function [unk] for the field observed at an arbitrary site[unk] includes multiplication of two sinc functions with different lobe widths, which leads to a trapezoidal function with no distinct peak in the time domain. In addition, the transfer function [unk] at any arbitrary site[unk] contains a third sinc function, which peaks to its maximum value of (2P + 1) at the location of the scatterer[unk]. This factor further amplifies super resolution focusing at the scatterer.