Decomposition of the time reversal operator applied to subwavelength localization of scatterers

Abstract

The decomposition of the time reversal operator (DORT method in French) is an ultrasonic detection method based the analysis of the whole pulse echo responses of an array. The eigenvalues and the eigenvectors of the time reversal operator (i.e., singular values and singular vectors of the array response matrix) provides information on localization of scatterers in the insonified medium. Recent experiments shows how DORT can also be used as a characterization method of subwavelength scatterers as cylinders [Minonzio et al., J. Acoust. Soc. Am. accepted May (2004)]. It has been shown that multiple singular values are associated with a single scatterer and that the singular vectors are combinations of the normal modes (monopole, dipole) of vibrations. In this study, interactions between two subwavelength cylinders less than a wavelength apart are described. Multiple scattering affects the singular value distribution. Experiments and calculations have been carried out on nylon and metal cylinders with diameters ranging from 0.07 to 0.2 mm. The central frequency is 1.5 MHz, and the scatterers are 5 cm away from the array. The estimator multiple signal characterization (MUSIC) is used for subwavelength localization of scatterers [Prada et al., J. Acoust. Soc. Am. 114, 235–243 (2003)].