Time-domain reflectance diffuse optical tomography with Mellin-Laplace transform for experimental detection and depth localization of a single absorbing inclusion

Abstract

We show how to apply the Mellin-Laplace transform to process time-resolved reflectance measurements for diffuse optical tomography. We illustrate this method on simulated signals incorporating the main sources of experimental noise and suggest how to fine-tune the method in order to detect the deepest absorbing inclusions and optimize their localization in depth, depending on the dynamic range of the measurement. To finish, we apply this method to measurements acquired with a setup including a femtosecond laser, photomultipliers and a time-correlated single photon counting board. Simulations and experiments are illustrated for a probe featuring the interfiber distance of 1.5 cm and show the potential of time-resolved techniques for imaging absorption contrast in depth with this geometry.

Time-resolved diffuse optical tomography using fast-gated single-photon avalanche diodes

“…For SD = 15 mm, the depth is underestimated when the inclusion is deeper than 25 mm. Such behavior has already been observed on simulations [28]. For SD = 5 mm, the depth of the most superficial inclusions is overestimated.…”

“…The reconstruction method is fully described in [18,28]. The image reconstruction is done in 2D within the plane (x, z) of Fig.…”

“…Whereas the inverse problem to solve is non-linear, we consider it linear at each iteration of the algorithm, and express it in the matrix form Y = WX by using the perturbation approach of the diffusion equation. In our case, we link changes in absorption in the medium (matrix X) to a combination of MLT of the measurements performed in the studied medium and in the reference (matrix Y) with a sensitivity matrix W. This matrix is obtained by a combination between MLT of Green's functions estimated in the medium and the reference measurement [28]. To take into account the noise present on high orders of MLT, we added a left preconditioner L consisting of a diagonal matrix whose diagonal elements estimate the inverse of the standard deviation of each order of the MLT of Y.…”

“…We consider the stabilization of the depth of the reconstructed absorbing inclusion as convergence, which is reached in less than 10 iterations for all tested cases. All the details of the reconstruction method are documented in [18] for theoretical material on the MLT and in [28] for using this algorithm to process experimental signals.…”

“…Our reconstruction algorithm requires the use of a reference measurement in a known medium in order to take into account the Instrument Response Function (IRF), but no direct measurement of this IRF [28]. In this work, we used the measurement in the phantom without the inclusion as a reference (homogeneous measurement).…”