How to improve a primary-secondary dual-source model of diffuse reflectance near the point of entry

Sensing or imaging using diffuse reflectance requires a model of the light-medium interaction to assess the scattering and absorption of the medium. For source-detector separation (SDS) much smaller than a reduced scattering pathlength, it is challenging to implement a model of diffuse reflectance that is both simple and robust. A simple primary-secondary dual-source model [Piao & Patel, 2017] is shown applicable to SDS of ~1/10th of the reduced scattering pathlength. The secondary model-source, which is a derivative of the primary model-source, was placed very near the medium-air interface to help increase the modeled diffuse reflectance that is generally inadequately handled by incorporating model-source within the medium. The primary-secondary dual-source approach has been useful experimentally [Yariv et al, 2019, ACS Omega]; however, the model strongly overestimates near the point-of-entry. A simple improvement is to add a scaling factor in the form of first-order exponential relaxation with respect to the SDS, to suppress the overestimation near the point-of-entry without affecting elsewhere. Monte Carlo (MC) simulations of a large range of tissue properties have been used to settle a single length constant of relaxation needed in the simple scaling approach, to make the model’s applicability near the point-of-entry passing below <i>&mu;'_s&rho;</i> = 10⁻³. The spirit of the correction approach to the radially resolved diffuse reflectance is also extendable to modeling area-integrated diffuse reflectance corresponding to a center-illuminated-area-detection geometry containing the point-of-entry. The model improvement was shown applicable to measurements from an aqueous medium of scattering and absorption varied over 2 orders of magnitude.