Reflection matrix approach for quantitative imaging of scattering media

We present a physically intuitive matrix approach for wave imaging and characterization in scattering media. The experimental proof-of-concept is performed with ultrasonic waves, but this approach can be applied to any field of wave physics for which multi-element technology is available. The concept is that focused beamforming enables the synthesis, in transmit and receive, of an array of virtual transducers which map the entire medium to be imaged. The inter-element responses of this virtual array form a focused reflection matrix from which spatial maps of various characteristics of the propagating wave can be retrieved. Here we demonstrate: (i) a local focusing criterion that enables the imaging quality to be evaluated everywhere inside the medium, including in random speckle; (ii) a tomographic measurement of wave velocity, which allows for aberration corrections in the original image; (iii) an highly resolved spatial mapping of the prevalence of multiple scattering, which constitutes a new and unique contrast for ultrasonic imaging. More generally, this matrix approach opens an original and powerful route for quantitative imaging in wave physics.