Application of the modified spherical harmonics method to some problems in biomedical optics

Area of Science:

• Physics
• Applied Mathematics
• Optical Engineering

Background:

• The radiative transport equation (RTE) is crucial for modeling light propagation in scattering media.
• Existing methods like the diffusion approximation have limitations, especially in accurately determining optical properties.
• Accurate solutions are needed for applications in medical imaging, material science, and astrophysics.

Purpose of the Study:

• To present the modified spherical harmonics (MSH) method as an efficient and accurate solution for the RTE.
• To demonstrate the MSH method's capability in an inverse scheme for determining medium optical properties.
• To show the MSH method's applicability for solving fluorescence fluence in infinite media.

Main Methods:

• A semi-analytical method, modified spherical harmonics (MSH), was employed.
• The MSH method was applied to solve the RTE in an infinite medium with an isotropic source.
• An inverse scheme utilizing fluence data was developed to retrieve optical properties.

Main Results:

• The MSH method proved to be a fast and rigorous solution for the RTE.
• The inverse scheme successfully determined optical properties without the drawbacks of the diffusion approximation.
• The MSH method was validated for solving fluorescence fluence from a point source.

Conclusions:

• The MSH method is a powerful tool for solving the radiative transport equation.
• It offers a robust alternative to the diffusion approximation for optical property determination.
• The MSH method has broad applicability in modeling light transport and fluorescence phenomena.