A refined analytical model for reconstruction problems in diffuse reflectance spectroscopy

A refined analytical model of spatially resolved diffuse reflectance with small source-detector separations (SDSs) for the in vivo skin studies is proposed. Compared to the conventional model developed by Farrell et al., it accounts for the limited acceptance angle of the detector fiber. The refined model is validated in the wide range of optical parameters by Monte Carlo simulations of skin diffuse reflectance at SDSs of units of mm. Cases of uniform dermis and two-layered epidermis-dermis structures are studied. Higher accuracy of the refined model compared to the conventional one is demonstrated in the separate, constraint-free reconstruction of absorption and reduced scattering spectra of uniform dermis from the Monte Carlo simulated data. In the case of epidermis-dermis geometry, the recovered values of reduced scattering in dermis are overestimated and the recovered values of absorption are underestimated for both analytical models. Presumably, in the presence of a thin mismatched topical layer, only the effective attenuation coefficient of the bottom layer can be accurately recovered using a diffusion theory-based analytical model while separate reconstruction of absorption and reduced scattering fails due to the inapplicability of the method of images. These findings require implementation of more sophisticated models of light transfer in inhomogeneous media in the recovery algorithms.