P3 equation steady-state model of light transport in semi-infinite thick rectangular medium

The P3 approximation equation is more accurate when studying the light transport in biological media, but it is difficult to establish a mathematical model, so the diffusion model is adopted. Although someone have established the approximate solution of P3 equation, the numerical solution of P3 equation is still a common method. On the basis of P3 equation for light transmission in semi-infinite thick media, the author establishes the steady-state solution of P3 equation for light transport in rectangular semi-infinite thick media. The equation is assumed to be a rectangle laterally and a semi-infinite thick medium vertically. A mathematical model of spatially-resolved diffuse reflection is listed, of which the mathematical model is continuation of a diffusion model and is verified with Monte Carlo simulation. The results show that the rectangular semi-infinite thick P3 equation of light is completely correct. Calculations and Monte Carlo simulations show that the P3 equation is more accurate when the absorption coefficient is large. Therefore, our P3 model can replace the diffusion approximation model and play an important role in biomedical optics.