Time-reversal super-resolution and stability in a weak scattering medium

Abstract

The properties of super-resolution and stability in time-reversal focusing of an acoustic wave are investigated using perturbation theory in a finite scattering medium with weak sound-speed fluctuations. Although super-resolution is obscured by weak scattering of the coherent field, the incoherent field still shows time-reversal enhanced focusing and the analytically tractable results may provide physical insight into time-reversal in stronger scattering media. Using first-order perturbation theory, the correlation scales of focused time-reversed field are defined by the scales of the fluctuations in the medium, the scale of effective aperture of the time-reversal array due to scattering and boundary conditions, the bandwidth of the system, and the array geometry. In this weak scattering example analytic expressions for the first and second moments of the time-reversal Green’s function operator are found and provide physical insight into the mechanism of time-reversal focusing and the role of bandwidth in super-resolution and stability. Numerical simulation using discrete point scatterers are performed to compare with the analytic results and to investigate the transitional behavior of time-reversal focusing from weak to stronger scattering.