Optical modeling of systematic uncertainties in detector polarization angles for the Atacama Cosmology Telescope

We present an estimate of the Atacama Cosmology Telescope (ACT) detector polarization angle systematic uncertainty from optics perturbation analysis using polarization-sensitive ray tracing in CODE V optical design software. Uncertainties in polarization angle calibration in CMB measurements can limit constraints on cosmic birefringence and other cosmological parameters sensitive to polarization leakage. Our framework estimates the angle calibration systematic uncertainties from possible displacements in lens positions and orientations, and anti-reflection coating (ARC) thicknesses and refractive indices. With millimeter displacements in lens positions and percent-level perturbations in ARC thicknesses and indices from design, we find the total systematic uncertainty for three ACT detector arrays operating between 90--220 GHz to be at the tenth of degree scale. Reduced lens position and orientation uncertainties from physical measurements could lead to a reduction in the systematic uncertainty estimated with the framework presented here. This optical modeling may inform polarization angle systematic uncertainties for current and future microwave polarimeters, such as the CCAT Observatory, Simons Observatory, and CMB-S4.