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

Area of Science:

• Biomedical Optics
• Computational Physics
• Radiative Transfer Theory

Background:

• Accurate modeling of radiative transfer is crucial for understanding light propagation in scattering media, particularly in fluorescence imaging.
• Existing approximations like the standard SPN method have limitations in accurately capturing complex light-matter interactions, especially near sources.

Purpose of the Study:

• To introduce and numerically implement the delta-SPN approximation for frequency-domain radiative transfer equations in fluorescence modeling.
• To evaluate the performance and accuracy of the delta-SPN approximation against Monte Carlo simulations and the standard SPN method.

Main Methods:

• Developed the delta-SPN approximation for coupled radiative transfer equations under collimated incident beams.
• Implemented the model using the finite element method for numerical solutions.
• Validated the model's performance using Monte Carlo simulations over sub-centimeter domains with varying optical properties.

Main Results:

• The delta-SPN approximation demonstrated superior accuracy over the standard SPN method, particularly in the near-source region.
• Improved estimates for phase and partial currents were observed at both excitation and emission wavelengths.
• Accuracy increased with higher approximation orders for normally incident beams.

Conclusions:

• The delta-SPN approximation offers a more accurate and robust approach for modeling fluorescence in scattering media compared to traditional methods.
• This improved model enhances the prediction of light transport phenomena, benefiting applications in biomedical optics and photonics.