Optimal Orientation Angle Configuration of Polarizers Exists in a 3 x 3 Mueller Matrix Polarimeter

A 3 x 3 Mueller matrix polarimeter, as one of the primary polarization measurement tools, has attracted intensive interest in various fields of polarization optics. In this paper, from a novel viewpoint with more mathematical analysis of the basic configuration and the working performance of a 3 x 3 Mueller matrix polarimeter, we systematically study the relationship between Mueller matrix measurement errors with the configuration and characteristics of polarizers in the polarimeter. We figure out that, mathematically, there is an optimal orientation angle configuration (0 degrees, 60 degrees, and 120 degrees) of polarizers, which inherently ensures a minimal relative measurement error in general. Moreover, we interpret the internal source of such a robust error resistance under this optimized configuration mathematically for the first time. Simulation and practical experiments show the effectiveness of our mathematical analyses, and compared to the frequently used orientation angle configuration, the average relative error is reduced by up to 32% under such an optimized configuration.