研究了Delta-P1近似模型的双点源近似空间分辨漫反射解。推导了在散射相函数中引入Dirac delta函数项后的辐射输运方程以及有效光源项的表达式;推导了有效光源项双点源近似下基于Delta-P1近似模型的漫反射率RDelta-P1,2(ρ)表达式;与漫射近似下漫反射率RSDA(ρ)的比较结果表明,双点源Delta-P1近似模型的空间分辨漫反射解RDelta-P1,2(ρ)能够应用于中、高反照率的散射介质,并能较好地描述光源附近(ρ约为1.5 mm)的辐射强度分布,误差均小于15%。此外,Delta-P1近似下的空间分辨漫反射的解析表达式中含有散射相函数的二阶参量γ,这对于在近光源区域由空间分辨漫反射测量数据来反演生物组织的光学参量具有重要的意义。

The analytic solution for spatially-resolved diffuse reflectance based on the Delta-P1 approximation for the two-point-source approximation is investigated. We have derived the radiative transport equation and the expression of the effective source by using scattering phase function which contains Dirac delta function. The analytic solution RDelta-P1,2(ρ) considering two-point-source approximation to the Delta-P1 model is presented. By comparing RDelta-P1,2(ρ) with the diffusion approximation RSDA(ρ),it is demonstrated that the Delta-P1 approximation RDelta-P1,2(ρ) models the radiance in moderate albedo media or close to source (ρ about 1.5 mm) more accurately than diffusion theory with the relative errors within 15%. Furthermore,the analytic solution RDelta-P1,2(ρ) provides the prediction of the second-order parameter γ of phase function,which is important for developing the inversion algorithm to recover optical parameters from the spatially-resolved diffuse reflectance measurements with small source-detector separations.