Spatio-temporal imaging of light transport in highly scattering media under white light illumination

Abstract

Imaging the propagation of light in time and space is crucial in optics, notably for the study of complex media. We here demonstrate the passive measurement of time-dependent Green's functions between every point at the surface of a strongly scattering medium by means of low coherence interferometry. The experimental access to this Green's matrix is essential since it contains all the information about the complex trajectories of light within the medium. In particular, the spatio-temporal spreading of the diffusive halo and the coherent backscattering effect can be locally investigated in the vicinity of each point acting as a virtual source. On the one hand, this approach allows a quantitative imaging of the diffusion constant in the scattering medium with a spatial resolution of the order of a few transport mean free paths. On the other hand, our approach is able to reveal and quantify the anisotropy of light diffusion, which can be of great interest for optical characterization purposes. This study opens important perspectives both in optical diffuse tomography with potential applications to biomedical imaging and in fundamental physics for the experimental investigation of Anderson localization. INTRODUCTIONLight is the most common probe for investigating complex media at the mesoscopic scale as it offers both an excellent resolution and is non invasive at moderate energies. Nonetheless, due to the inhomogeneous distribution of refractive index, light suffers multiple scattering while propagating in or through the medium. Unveiling the complexity of light scattering is then necessary to retrieve the features of an object of interest or of the surrounding environment. In an inhomogeneous medium, it is a classical approach to consider a scattering sample as one realization of a random process, and study statistical physical quantities such as the mean intensity [1][2][3]. Under this approach, several physical parameters are relevant to characterize wave propagation in scattering media: the scattering mean-free path l s , the transport mean-free path l t , the diffusion constant D, the absorption length l a . Classical back scattering imaging techniques, such as optical coherence tomography, fail when multiple scattering predominates [4]. However, one can still measure the long-scale spatial variations of the diffusive parameters. The resulting image is not an image of the refractive index n(r) but e.g., of the diffusion constant D(r) with a resolution of the order of the transport mean free path l t , at best. In the literature, diffuse optical tomography is the gold standard technique to reconstruct the spatial distribution of transport parameters at each point of a volume from intensity measurements at the surface [5]. Unfortunately, this inverse problem is intrinsically nonlinear with respect to the optical properties of the medium. This method is thus computationally intensive and limited in terms of spatial resolution [6][7][8] (e.g. 5 mm in human soft tissues).In this paper, we propose a simple and effic...

Diffusion in Translucent Media

“…Measurements of optical 11,15,18,19,42 and ultrasound 16 pulsed transmission through random slabs show that on average photons arrive earlier than predicted by diffusion theory even in samples with L > 5ℓ. The average delay time t D can also be determined from the transmission eigenvalues and energy density profiles of the transmission eigenchannels 37 (Supplementary Note 4).…”

Reflection Matrix Approach for Quantitative Imaging of Scattering Media

“…The perspective of this work is to extract from ρðrÞ quantitative maps of scattering parameters, such as the elastic mean free path or the absorption length [24,40], and transport parameters, such as the transport mean free path [62,68,69] or the diffusion coefficient [62,63,70]. While diffuse tomography in transmission provides only a macroscopic measurement of such parameters, preliminary studies demonstrate how a reflection matrix recorded at the surface can provide transverse measurements of transport parameters [31,32,65,71]. The focused reflection matrix we introduce here connects each point inside the medium to all other points.…”

Distortion matrix concept for deep optical imaging in scattering media

“…An alternative is to switch from a scanning to a full-field illumination scheme. A measurement of the coherent reflection matrix R can be performed under a spatially incoherent illumination ( 49 , 50 ). This full-field configuration would allow to record the reflection matrix over millimetric volumes in a moderate acquisition time.…”