Analytical solutions of the simplified spherical harmonics equations.
We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source.
Institut für Lasertechnologien in der Medizin und Messtechnik, Helmholtzstrasse 12, D-89081 Ulm, Germany.
Andre
A
Liemert
Alwin
A
Kienle
D000465:Algorithms; D003198:Computer Simulation; D008027:Light; D009010:Monte Carlo Method; D012542:Scattering, Radiation