Time Reversal in Changing Environments

This paper analyzes the refocusing properties of time-reversed acoustic waves that propagate in different media during the forward and backward propagation phases. We show how the refocused signal is modified as the medium during backward propagation departs from the medium during forward propagation. The derivation is based on the analysis of the correlation of two fields propagating in different backgrounds. The correlation is described by the Wigner transform of the two fields, which satisfies in the limit of high frequencies a generalized radiative transfer equation. The theory is presented in two and three space dimensions in the transport and diffusive regimes. Numerical experiments show a remarkable agreement with theory.

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