Conventional ultrasound imaging generally relies on a single scattering assumption. Assuming a homogeneous speed of sound, a one-to-one correspondence is actually found between each scatterer position and the time-of-flight of the associated echoes. However, in strongly scattering media such as granular media, multiple scattering (MS) cannot be neglected beyond a few scattering mean free paths ls, the typical distance between two scattering events. A conventional image is then no longer a satisfying estimator of the medium reflectivity. Here, we propose an original solution relying on a matrix formalism to cope with MS and image deeper than the conventional MS limit. As a proof-of-concept, our experiment consists in the acquisition of a reflection matrix associated with a 2D ultrasound probe (1024 elements −3 MHz central frequency) of a steel sphere sinking in fluidized glass beads immersed in water (ls ≈ Ø600 μm). As expected, we show that the target echo vanishes into the MS background when it goes deeper than a few ls. Interestingly, an iterative time-reversal analysis of the reflection matrix is proposed to compensate for the phase distortions induced by the gap between the effective medium properties and our beamforming model. The target can then be tracked at larger penetration depths than the usual MS limit.

Conventional ultrasound imaging generally relies on a single scattering assumption and a constant sound hypothesis. However, in dense granular sediments where the glass beads diameter is comparable to the wavelength (typically 500 μm), both hypothesizes are no longer valid, resulting in a loss of resolution and contrast, up to the situation where a target to image could totally vanish in the fog. To better characterize this strongly scattering medium, we have conducted several ultrasonic experiments in reflection and in transmission, either on the diffused wave or on the coherent one. Both the transport and scattering mean free paths are estimated in the imaging bandwidth (1–5 MHz), alongside with the phase velocity and extinction length of the coherent wave. These results are compared with an analytical model, i.e. Generalized Coherent Potential Approximation*, which considers a coated sphere buried in an effective medium. Finally, we show a dispersive beamformer which takes into account the measured phase and group velocity. This allows us to obtain a more resolved and contrasted image in such a scattering medium. * Jing X, Sheng P, Zhou M. Phys Rev Lett. 1991