Theory and applications of time reversal and interferometric imaging

Abstract

In time reversal, an array of transducers receives the signal emitted by a localizedsource, time reverses it and re-emits it into the medium. The emitted wavesback-propagate to the source and tend to focus near it. In a homogeneousmedium, the cross-range resolution of the refocused field at the source location isλ0L/a, whereλ0 is the carrierwavelength, L isthe range and a is the array aperture. The refocusing spot size in a homogeneous medium is independent ofthe bandwidth of the pulse, but broad-band can help in reducing spurious Fresnel zones. Ina noisy (random) medium, the cross-range resolution is improved beyond the homogeneousdiffraction 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 inparticular that, because of multipathing, the array appears to have an effectiveaperture ae that isgreater than a.Since ae depends on the scattering medium, it is not known. In this paper we present a brief reviewof time reversal theory in a remote sensing regime and a robust procedure for estimatingae from the signals received at the array. Knowingae permits assessing quantitatively super-resolution in time reversal for applications in spatiallylocalized communications with reduced interference. We also review interferometric imagingand its relation to time reversal and to matched field imaging. We show thatae quantifies in an explicit way the loss of resolution in interferometric array imaging.