The Simons Observatory: Detector Polarization Angle Calibration using Sparse Wire Grid with Initial Data Sets of the Small Aperture Telescope

Improved measurements of $B$-modes in the cosmic microwave background can be obtained through accurate calibration of the orientation of detector antennas as projected onto the sky. Miscalibration of the detector polarization angle leads to a leakage of $E$-modes into $B$-modes, which can bias the detection of the latter. To achieve a $\sigma(r)$ of 0.003, the Simons Observatory Small Aperture Telescopes are required to calibrate the global polarization angle on the sky with an accuracy ${\lesssim}0.1^\circ$. We demonstrate a fully remote-controllable calibration system using a ``sparse wire grid," which injects a rotatable linear polarized signal across the telescope's focal plane. This calibration system is installed and operational on a Small Aperture Telescope at its observing site at the Parque Astron\'omico in the Atacama desert in Chile. We developed a pipeline for the detector polarization angle calibration, and demonstrate it using initial data for 93~GHz and 145~GHz frequency bands. The observed distribution of detector polarization angles is in agreement with the instrument design. Statistical uncertainties for the relatively calibrated polarization angles are $0.02^\circ$ and $0.03^\circ$ at 93~GHz and 145~GHz, respectively. Systematic uncertainty was evaluated to be $0.08^\circ$ at the hardware development and fabrication stage. Their sum in quadrature is less than $0.1^\circ$.