Reflection matrix approach for quantitative imaging of complex media

We present a physically intuitive matrix approach for quantitative imaging of complex media. While standard reflection imaging methods generally rely on confocal focusing operations, matrix imaging consists of decoupling the location of the incident and received focal spots [1]. Following this principle, a self-portrait of the focusing process can be obtained around each point of the medium. The Gouy phase shift exhibited by each focal spot can be leveraged to finely monitor the wave velocity distribution inside the medium [2]. A local multiple scattering rate can also be evaluated and its depth evolution can lead to a local measurement of the scattering mean free path, independently from absorption losses [3]. The approach is here demonstrated with ultrasound for a controllable phantom system before being applied in vivo to liver. The wave velocity and the scattering mean free path are quantitative markers for biomedical diagnosis but they are also important monitoring parameters for nondestructive testing and geophysical applications. This work thus opens important perspectives for quantitative imaging of heterogeneous media in all fields of acoustics. [1] W. Lambert etal., Phys. Rev. X 10, 021048 (2020). [2] F. Bureau et al., arXiv:2409.13901 (2024). [3] A. Goicoechea et al., Phys. Rev. Lett. 133, 176301 (2024).