Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process?

This is the second article in a series of two dealing with the statistical moments of ultrasonic waves transmitted through a disordered medium with resonant multiple scattering. Second-order moments in time and space are considered here. An ultrasonic pulsed wave is transmitted from a point source to a 128-element receiving array through two-dimensional samples with various thicknesses. The samples consist of random collections of parallel steel rods immersed in water. The scattered waves are recorded, time reversed, and sent back into the medium. The time-reversed waves are converging back to their source and the quality of spatial and temporal focusing on the source is related to the second-order moments of the scattered wave (correlation) in time and in space. Experimental results show that it is possible to obtain a robust estimation on a single realization of disorder, taking advantage of the wide frequency bandwidth. The spatial resolution of the system is only limited by the correlation length of the scattered field, and no longer by the array aperture. As the sample thickness is increased, the quality of focusing saturates, which we believe is linked to the Thouless factor g. In the thickest sample, $g\sim 30,$ which is still well above the localization threshold.