Simple empirical master–slave dual-source configuration within the diffusion approximation enhances modeling of spatially resolved diffuse reflectance at short-path and with low scattering from a semi-infinite homogeneous medium

We present an empirical master-slave dual-source configuration within the diffusion approximation that enhances modeling of spatially resolved diffuse reflectance at short-path and with low scattering from a semi-infinite homogeneous medium when irradiated by a pencil beam. An isotropic virtual source positioned at a depth of 1/(reduced scattering coefficient) is used as the master source. A second isotropic virtual source whose depth and intensity depend upon those of the master source and tissue property according to a set of simple empirical formulas is added as the slave source. When tested for a semi-infinite homogeneous medium, this master-slave dual-source model consistently produces the aggressive peaking of the diffuse reflectance toward the point of entry, which is significantly underestimated by the model prediction that involves only the master source. Monte Carlo simulations have shown the effectiveness of this empirical model at a short source-detector separation of 1/100 of 1/(reduced scattering coefficient) and an absorption to reduced scattering ratio as strong as 1, with an error within 20% in the near field (1/10 of 1/(reduced scattering coefficient)).