We propose the $\delta {\text -} S{P_N}$ approximation for the frequency domain coupled radiative transfer equations modeling fluorescence with collimated incident beams and present its numerical implementation using the finite element method. The performance of the proposed model is investigated with respect to Monte Carlo simulations and the standard $S{P_N}$ approximation over sub-centimeter domains for various optical properties. We find that the $\delta {\text -} S{P_N}$ approximation is more accurate than the $S{P_N}$ in the near-source region, and provides improved estimates of phase and partial currents, at both excitation and emission wavelengths, over a wider range of optical properties. The accuracy of the $\delta {\text -} S{P_N}$ model improves with increase in approximation order for normally incident beams.

中文翻译：

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用于定向源和散射数值建模的 δ-SPN 近似

我们提出了$\delta {\text -} S{P_N}$近似值用于模拟具有准直入射光束的荧光的频域耦合辐射传递方程，并使用有限元方法介绍其数值实现。针对各种光学特性，针对蒙特卡罗模拟和亚厘米域上的标准$S{P_N}$近似来研究所提出模型的性能。我们发现$\delta {\text -} S{P_N}$近似值比近源区中的$S{P_N}$更准确，并且在激励和发射波长，具有更广泛的光学特性。的准确性$\delta {\text -} S{P_N}$模型随着正常入射光束近似阶数的增加而改进。