When imaging with classical waves, multiple scattering (MS) is often seen as an unavoidable obstacle. The diffraction-limited resolution obtainable with methods such as microscopy requires that single-scattering (SS) dominates; for depths where MS processes become important, such methods result in an image without any connection to the reflectivity of the medium. Conversely, techniques such as diffuse optical tomography take advantage of the diffuse nature of light, but their resolution power is limited. To do better, methods such as wavefront shaping and adaptive optics have been developed. Focussing through a thick diffusive layer was demonstrated using a transmission matrix approach consisting of the measurement of Green’s functions between each pixel of a spatial light modulator (SLM) and of a charge-coupled device (CCD) camera across the medium. To image inside a multiple-scattering medium, we present a matrix approach based on the experimental measurement of a reflection matrix from the medium. An analysis based on the geometric and statistical properties of this reflection matrix can enhance the SS contribution which would otherwise be swamped by MS at large depths, and correct the resulting image for aberration effects induced by the turbid medium itself. The correction does not require the presence of bright scatterers, does not rely on any feedback loop and works even at depths where the field-of-view contains several isoplanatic patches. Here we present the application of our reflection matrix approach to optical imaging in biological tissues. Compared to OCT and related methods, we demonstrate an extension of the current imaging-depth limit.
Our approach first consists in measuring a time-gated reflection matrix associated to a scattering medium using a spatial light modulator at the input and a CCD camera at the output. An interferometric arm allows to discriminate the scattered photons as a function of their time of flight. Inspired by previous works in acoustics, a random matrix approach then allows to get rid of multiple scattering. This improves by far the detection and imaging of targets embedded in or hidden behind a highly scattering medium. As proof of concept, we tackle with the issue of imaging ZnO micrometric beads across a highly scattering paper sheet whose optical thickness is of 12.5 ls, with ls the scattering mean free path. This experimental situation is particularly extreme, even almost desperate for imaging. The ballistic wave has to go through 25 ls back and forth, thus undergoing an attenuation of 10^-11 in intensity. For an incident plane wave, 1 scattered photon over 1000 billions is associated to the target beads. In optical coherence tomography, the single-to-multiple scattering ratio is of 5×10^-4 which prevents from any target detection and imaging. On the contrary, our approach allows to get rid of most of the multiple scattering contribution in this extreme situation. By means of the time-reversal operator, the ballistic echoes associated to each bead are extracted and allow to reconstruct a satisfying image of the targets. The perspective of this work is to apply this promising approach to in-depth imaging of biological tissues.
We recently showed how the correlations of a broadband and incoherent wave-field can directly yield the time-dependent Green's functions between scatterers of a complex medium [Badon et al., Phys. Rev. Lett., 2015]. In this study, we apply this approach to the imaging of optical transport properties in complex media. A parallel measurement of millions of Green's functions at the surface of several strongly scattering samples (ZnO, TiO2, Teflon tape) is performed. A statistical analysis of this Green’s matrix allows to investigate locally the spatio-temporal evolution of the diffusive halo within the scattering sample. An image of diffusion tensor is then obtained. It allows to map quantitatively the local concentration of scatterers and their anisotropy within the scattering medium. The next step of this work is to test this approach on biological tissues and illustrate how it can provide an elegant and powerful alternative to diffuse optical imaging techniques.
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