Reflection matrix approach in a multiple scattering regime: Application to the tracking of a sinking sphere in quicksand

• Published in: The Journal of the Acoustical Society of America 2021-10, Vol.150 (4), p.A195-A195
• Main Authors: Le Ber, Arthur, Bureau, Flavien, Jia, Xiaoping, Tourin, Arnaud, Fink, Mathias, Aubry, Alexandre
• Format: Article
• Language: English
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/10.0008102

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.