Wave propagation in disordered media is an interdisciplinary research topic with particular importance in condensed matter and cold atom physics, optics, acoustics, and seismology. The effect of disorder on wave propagation is generally quantified by a scattering length ℓ equal to a typical distance between two scatters. For a medium of size L << ℓ scattering only slightly disturbs propagation while for L >> ℓ one enters the regime of multiple scattering.

It is in this regime that one deals with mesoscopic phenomena: these phenomena take place at spatial scales longer than the wavelength and scattering length ℓ but shorter than the coherence length of the wave Lcoh. Mesoscopic phenomena were first demonstrated for low-temperature electrical transport in metals and semiconductors where they give rise to a plethora of fascinating effects: permanent currents, Aharonov-Bohm oscillations, weak localization, universal conductance fluctuations, etc. It was later realized that many of these phenomena can also be observed for "classical" waves such as light in suspensions or powders of small particles, microwaves, acoustic or seismic waves.

In another field of human activity - aquaculture - acoustic waves have been used for decades to detect and count fish both in the open sea (sonar) and in aquatic farms. A fish is a strong diffuser of sound, mainly due to its swim bladder - a pocket of air necessary for its buoyancy - which strongly diffuses the sound. Insonified by an acoustic wave, an isolated fish produces an acoustic echo that is easily detectable, and a sparse group of fish produces a number of echoes equal to the number of fish, thus allowing to count the fish and to estimate their biomass. However, this approach is naturally limited to low densities of fish and fails in dense schools that are the reality of modern aquatic farms and where multiple acoustic scattering prevents distinguishing echoes from individual fish. There is therefore a need to develop acoustic methods that would allow the non-invasive probing of dense schools of fish in the multiple acoustic wave scattering regime.