P3 approximation equation of light transport in a slab medium: steady-state and time domains

P3 equations in a slab medium in the steady state and the time domain are proposed in this study. The spatially resolved diffuse reflectance and transmittance of the steady-state P3 equation are presented. Two time-domain equations in a slab medium, the optical parameter method and the double diffusion coefficient method, are established. The Monte Carlo simulation acted as an experimental result for comparison, and the results from the diffusion equation and P3 were compared against the Monte Carlo results. The results showed that the detection distance was less than twice the thickness of the medium, and the P3 equation results were in good agreement with the Monte Carlo simulation results. For the steady state, the P3 equation was more accurate than the diffusion equation when the distance was greater than 0.6 mm and less than 2 mm. However, when the absorption coefficient increased, the P3 steady-state equation was more accurate than the diffusion equation. In the time domain, the optical parameter method was more accurate than the double diffusion coefficient method and the diffusion equation. Therefore, the P3 approximation model can replace the diffusion model, and it can be applied to study tissue optics.