Spatial, temporal, and thermal contributions to focusing contrast by time reversal in a cavity

The accuracy of wave focusing by time reversal depends on a quantity termed ‘contrast ratio’ that measures the amplitude of a localized peak of velocity relatively to background noise. A comprehensive expression for the contrast ratio in a lossy cavity is derived by modal decomposition of the wave field. This expression accounts for the effects of the mechanical and the dimensional properties of the cavity, the bandwidth of the excitation signal, the number of sources, and the duration of time reversal window. The expression can predict the characteristics of a given process such as the long-time saturation and the single-channel time reversal limit. The expression also models the effect of temperature variations on focusing accuracy and shows that thermal drift exhibits two regimes. In the first regime, small temperature variations have little effect on contrast. The second regime is characterized by a rapid deterioration of contrast. Experimental measurements show close agreement with the theory.