δ-SP_N approximation for numerical modeling of directional sources and scattering

We propose the δ-SP_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 SP_N approximation over sub-centimeter domains for various optical properties. We find that the δ-SP_N approximation is more accurate than the SP_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 δ-SP_N model improves with increase in approximation order for normally incident beams.