Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.
This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.
Tianjin University, State Key Laboratory of Precision Measuring Technology and Instrument, Tianjin 300072, China.
Zhenzhi
Z
Shi
Huijuan
H
Zhao
Kexin
K
Xu
D004058:Diffusion; D005583:Fourier Analysis; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009391:Nephelometry and Turbidimetry / Q000706:statistics & numerical data*; D055620:Optical Phenomena; D012542:Scattering, Radiation