Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination

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Abstract
Simple analytical expressions for the point spread function (PSF) at different depths can save computation time and improve the performance of inverse algorithms for optical imaging. In particular, application of such formulas simplifies quantification of the optical characteristics of tissue abnormalities inside highly scattering media. Earlier it was shown within the random walk theory framework that the PSF for time-resolved transillumination imaging through a highly scattering slab is well represented by a Gaussian. We have experimentally validated a simple formula of the random walk model for the effective width of this Gaussian, as a function of time delay, at different depths of the target. Presented analysis of published experimental data, concerning effective width of the PSF, for a slab of considerably smaller thickness also demonstrates good agreement between the data and predictions of our model. This PSF width determines spatial resolution of the time-resolved imaging and is widely discussed in the literature.