Vector radiation transport in scattering media is a research hotspot. The exact analytical solution to the vector radiative transfer equation cannot be obtained without the simplified treatment, and it needs to be calculated by numerical calculation methods. The polarized Monte Carlo program simulates the transmission of mass photons. As it does not lead to computational errors due to finite dispersion, the program is usually employed as a standard to verify the computational accuracy of other methods. At present, this method can obtain the outgoing polarization state of each light wave after the solution is obtained, but it is difficult to know the photon transmission situation. This limits the analysis of the polarization state retention of scattering light. However, photons with good retention characteristics of the polarization state usually have a small information loss and a long transmission distance. The study and analysis of these photons can be potentially applied to extract good transmission signals.

This paper proposes a method to count the photon polarization states during forward transmission into scattering media on the basis of the polarization meridian Monte Carlo program. The original algorithm and improved algorithm are shown in Fig. 1. The white part is required for calculating both the original algorithm and the improved algorithm, and the blue part is the additional flow for calculating the improved algorithm. One hundred thousand parallelly polarized photons or right-handed circularly polarized photons are sent into a slab represented by one particular particle distribution for each environment, and photons are transmitted at a given distance. Then, the aggregated polarization is calculated from the photons that arrive in a given area, and photons on the front face of the slab are considered the transmitted photons. This process continues for all the launched photons, and the result is calculated. For the original algorithm, a photon completes forward transmission when it passes through a specific forward distance. The improved algorithm adds a link to output the polarization state of each photon. Moreover, the improved algorithm can count the total number of received photons and the number of photons similar to the polarization state of the initial photon.

This paper uses an example to compare the original algorithm and the improved algorithm. The following simulations are performed in the polystyrene suspension with a mass concentration of 2.08 μg/μm³. The wavelength of incident light is 532 nm, and polystyrene's refractive index is 1.597. The particle diameter of the polystyrene suspension is 1 μm in simulation, and the transmission distance is 10 cm. One hundred thousand parallelly polarized photons or right-handed circularly polarized photons are launched for simulations of the original algorithm and the improved algorithm separately. There are 66358 received photons after the transmission of parallelly polarized photons and 66367 after the transmission of right-handed circularly polarized photons. After that, the first 100 received photons are selected as samples (Figs. 3 and 4). Calculations show that for the sample data of parallelly polarized photons, the N_RoPS is 0.13, and for the sample data of right-handed circularly polarized photons, the N_RoPS is 0.53. The calculation results are both similar to the overall situation. The simulated calculation of polarized light transmission in the polystyrene suspension demonstrates that the optimized method can not only reflect the change in the photon polarization state but also count the percentage of photons with good retention characteristics of the polarization state. The comparison between the original results and the optimization results shows that the results of the optimized algorithm are less than the polarization degree value. This is because the optimized algorithm not only avoids the error introduced in the calculation of the intensity difference in the orthogonal component but also excludes photons that are not similar to the polarization state of the initial photon.

Compared with the polarized Monte Carlo program, the improved method can not only reflect the change in the photon polarization state but also count the percentage of photons with good retention characteristics of the polarization state. It reflects the change in the polarization state of the transmitted photons in multiple dimensions. This study can provide technical support for research on the extraction of excellent transmission signals.