Analytical Green's function for the fluorescence simplified spherical harmonics equations in turbid medium

It is more complicated to write the analytical expression for the fluorescence simplified spherical harmonics ( SPN) equations in a turbid medium, since both the processes of the excitation and emission light and the composite moments of the fluence rate are described by coupled equations. Based on an eigen-decomposition strategy and the well-developed analytical methods of diffusion approximation (DA), we derive the analytical solutions to the fluorescence SPN equations for regular geometries using the Green's function approach. By means of comparisons with the results of fluorescence DA and Monte Carlo simulations, we have shown the effectiveness of our proposed method and the expected advantages of the SPN equations in the case of small source-detector separation and high absorption.