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Single-fiber reflectance spectroscopy of isotropic-scattering medium: An analytic perspective to the ratio-of-remission in steady-state measurements

Piao, Daqing
Slaton, Joel W.
Recent focused Monte Carlo and experimental studies on steady-state single-fiber reflectance spectroscopy (SfRS) from a biologically relevant scattering medium have revealed that, as the dimensionless reduced scattering of the medium increases, the SfRS intensity increases monotonically until reaching a plateau. The SfRS signal is semi-empirically decomposed to the product of three contributing factors, including a ratio-of-remission (RoR) term that refers to the ratio of photons remitting from the medium and crossing the fiber-medium interface over the total number of photons launched into the medium. The RoR is expressed with respect to the dimensionless reduced scattering parameter μ's dfib, where μ's is the reduced scattering coefficient of the medium and dfib is the diameter of the probing fiber. We develop in this work, under the assumption of an isotropic-scattering medium, a method of analytical treatment that will indicate the pattern of RoR as a function of the dimensionless reduced scattering of the medium. The RoR is derived in four cases, corresponding to in-medium (applied to interstitial probing of biological tissue) or surface-based (applied to contact-probing of biological tissue) SfRS measurements using straight-polished or angle-polished fiber. The analytically arrived surface-probing RoR corresponding to single-fiber probing using a 15° angle-polished fiber over the range of μ's dfib = (10-2 103) agrees with previously reported similarly configured experimental measurement from a scattering medium that has a Henyey-Greenstein scattering phase function with an anisotropy factor of 0.8. In cases of a medium scattering lightanisotropically, we propose how the treatment may be furthered to account for the scattering anisotropy using the result of a study of light scattering close to the point-of-entry by Vitkin et al.