Theory and applications of time reversal and interferometric imaging

In time reversal, an array of transducers receives the signal emitted by a localized source, time reverses it and re-emits it into the medium. The emitted waves back-propagate to the source and tend to focus near it. In a homogeneous medium, the cross-range resolution of the refocused field at the source location is λ₀L/a, where λ₀ is the carrier wavelength, L is the range and a is the array aperture. The refocusing spot size in a homogeneous medium is independent of the bandwidth of the pulse, but broad-band can help in reducing spurious Fresnel zones. In a noisy (random) medium, the cross-range resolution is improved beyond the homogeneous diffraction limit because the array can capture waves that move away from it at the source, but get scattered onto it by the inhomogeneities. We refer to this phenomenon as super-resolution of the time reversal process in random media. Super-resolution implies in particular that, because of multipathing, the array appears to have an effective aperture a_e that is greater than a. Since a_e depends on the scattering medium, it is not known. In this paper we present a brief review of time reversal theory in a remote sensing regime and a robust procedure for estimating a_e from the signals received at the array. Knowing a_e permits assessing quantitatively super-resolution in time reversal for applications in spatially localized communications with reduced interference. We also review interferometric imaging and its relation to time reversal and to matched field imaging. We show that a_e quantifies in an explicit way the loss of resolution in interferometric array imaging.