Characterization of scattering object with the decomposition of the time-reversal operator: Theory and experiment

Abstract

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers, J. Acoust. Soc. Am. 109, (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by a cylinder measured by a linear array of transducers is considered. Experimental results are obtained for wires of different diameters and different materials. It is shown how the singular-value distribution and the singular vectors depend on the elastic wave speeds cL, cT, the density and the radius of each wire. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.