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

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Abstract

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.

© 2021 Optical Society of America

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Supplementary Material (1)

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Supplement 1       Supplementary plots for emission wavelength and tabulated error metrics.

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