Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: theory and experiment

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (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 an elastic cylinder, imbedded in water, measured by a linear array of transducers is considered. In this case, the array response matrix has three nonzero singular values. Experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength. It is shown how the singular value distribution and the singular vectors depend on the elastic velocities cL, cT, the density rho of each wire, and on the density rho0 and velocity c0 of the surrounding fluid. 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.