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.

Significance: 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. Aim: 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). Approach: 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. Results: 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. Conclusions: 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.