Error modeling and analysis of dual-mode high-precision solar polarimetry using a three-waveplate system based on particle swarm optimization

Solar spectral polarization information is currently the primary technique for analyzing high spatial-resolution full-vector solar magnetic field maps of the photosphere and chromosphere, with its core relying on high-precision polarization measurement technology. In polarization modulation components, three main error sources exist: azimuth angle error, axial thickness error, and oblique incidence error. These errors collectively act on the waveplate Mueller matrix, affecting measurement accuracy. This paper addresses the challenge posed by the significant impact of axial thickness error, which arises during the fabrication of stepped rotating three-waveplate modulation systems that are focused solely on circular polarization measurement, by deriving a mathematical model for waveplate phase matching, substantially reducing manufacturing difficulty. Additionally, a multi-dimensional error propagation model is established for both full Stokes vector measurement and circular polarization-only measurement modes. Using the particle swarm optimization algorithm, we comprehensively analyze the influence of the three error sources on both modes and determine the required error thresholds to achieve an absolute polarization measurement accuracy of 2 × 10^-4.