Single-Fiber Reflectance Spectroscopy of Isotropic-Scattering Medium: An Analytic Perspective to the Ratio-of-Remission in Steady-State Measurements

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 s μ fib d  , where s μ is the reduced scattering coefficient of the medium and fib d 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   2 3 s μ 10 10 fib d    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 light OPEN ACCESS Photonics 2014, 1 566 anisotropically, 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. (Nat. Commun. 2011, doi:10.1038/ncomms1599).