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Analytical Green's function for the fluorescence simplified spherical harmonics equations in turbid medium
Limin Zhang1, Xi Yi2, Jiao Li1
1Tianjin University, College of Precision Instrument and Optoeletronics Engineering, Tianjin 300072, ChinabTianjin Key Laboratory of Biomedical Detecting Techniques and Instrument, Tianjin 300072, China.
We present an analytical solution for fluorescence simplified spherical harmonics (SPN) equations in turbid media. This method offers advantages over diffusion approximation, especially for small source-detector separations and high absorption scenarios.
Area of Science:
- Biomedical Optics
- Photonic Applications
- Mathematical Modeling
Background:
- Analytical solutions for fluorescence simplified spherical harmonics (SPN) equations in turbid media are complex due to coupled excitation/emission light processes and fluence rate moments.
- Diffusion approximation (DA) is a common method, but it has limitations, particularly in certain optical conditions.
Purpose of the Study:
- To derive analytical solutions for fluorescence SPN equations in regular geometries.
- To demonstrate the effectiveness and advantages of the SPN method compared to DA and Monte Carlo simulations.
Main Methods:
- Utilized an eigen-decomposition strategy combined with Green's function approach.
- Applied well-developed analytical methods from diffusion approximation (DA).
Main Results:
- Successfully derived analytical solutions for fluorescence SPN equations.
- Demonstrated the effectiveness of the proposed method through comparisons.
- Highlighted the advantages of SPN equations for small source-detector separations and high absorption.
Conclusions:
- The Green's function approach with eigen-decomposition provides an effective method for solving fluorescence SPN equations.
- The SPN method shows promise for applications in turbid media, outperforming DA in specific scenarios.
