Quantitative estimation of optical properties in bilayer media within the subdiffusive regime using a tilted fiber-optic probe in diffuse reflectance spectroscopy, part 1: a theoretical framework for designing probe geometry.

As biological tissues are highly heterogeneous, there is a great interest in developing non-invasive optical approaches capable of characterizing them in a very localized manner. Obtaining accurate absolute values of the local optical properties from the measured reflectance requires finding a probe geometry, which allows us to solve this inverse problem robustly and reliably despite neglecting the higher-order moments of the scattering phase function. Our goal is to develop a theoretical framework for designing tilted-fiber diffuse reflectance probes that allow quantitative estimation of the optical properties corresponding to limited tissue volume (typically a few cubic millimeters). Relationships among probe geometry, sampled tissue volume, and robustness of the inverse solver to calculate optical properties from reflectance are studied using Monte Carlo simulations. The analysis of the number of scattering events of the collected photons leads to the establishment of relationships among the probe geometry, the sampled tissue volume, and the validity of a subdiffusive regime for the reflectance. A methodology is proposed for the design of new compact probes with tilted fiber geometry that can quantitatively estimate the values of the optical coefficients in a localized manner within living biological tissues by recording diffuse reflectance spectra.

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