An equivalent incident light model for multiple scattering and polarization neutral point of skylight

The symmetry breaking in the skylight polarization pattern is caused by the shape of the atmosphere and multi-scattering. We analyzed the physical processes of multi-scattering and found out that when neutral points split from two into four there should be an altitude shift of the center of polarization pattern. The altitude shift could be positively related to the split angle of the neutral point, which would reduce the accuracy of polarization navigation based on the single scattering model. To quantify the positive relationship which is useful for error correction in navigation, the Monte-Carlo method was used to simulate the multiple scattering processes of sunlight. The simulation results show that the split angle of the neutral point is in direct proportion to the altitude shift angle. Experimental data from Horvath also show the proportional relation. According to the simulation results and experimental data, an equivalent incident light model was established to explain the proportional relation which could be used in sunlight navigation.