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

TL;DR

This work addresses the need for precise polarization-angle calibration to prevent $E$-to-$B$ leakage in CMB B-mode searches, aiming for $\sigma(r)=0.003$. It introduces a fully remote sparse wire grid (SWG) calibration system on a Simons Observatory SAT, leveraging HWP demodulation and 16-angle SWG rotations to recover detector polarization angles from $Q$-$U$ measurements. The analysis yields per-detector uncertainties of $0.02^\circ$ at 93 GHz and $0.03^\circ$ at 145 GHz, with a hardware systematic of $0.08^\circ$, combining to a total calibration error below $0.1^\circ$. The method shows 12 discrete detector orientations consistent with design, validates the SWG approach, and plans to extend to all SAT modules with absolute orientation later anchored by a tilt-sensor gravity reference and cross-checks against Tau A.

Abstract

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 $σ(r)$ 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 Astronómico 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 $0.1^\circ$.

Figures (9)

• Figure 1: A cross-section of a small aperture telescope (SAT) and the sparse wire grid (SWG) calibration system. A photo of the SWG is also shown. The big yellow arrow from the top indicates the incident light from the sky. The position of the SWG is remotely set at "calibration position" or "stored position" by using two linear actuators. Detectors on the focal plane receive signals passed through the optical elements, and the SWG is the first element viewed from the sky side.
• Figure 2: An illustration of the SWG calibration. The positive direction of the SWG rotation, $\theta_\mathrm{SWG}$, is defined as counterclockwise viewed from above the telescope. The operation of the SWG is described in the text. A single detector pixel on the focal plane has two orthogonal antenna orientations. We use $\theta_\mathrm{det}$ as the calibrated polarization sensitive direction of the detector, and $\theta_\mathrm{det,\,CAD}$ as the design angle specified in the computer aided design (CAD) of the detector module. The simulated response of a single detector is also shown. The response in stokes parameters is obtained after the demodulation (see Section \ref{['subsec:demodulation']}).
• Figure 3: An online status monitor of the SWG. The raw data encoding wire direction is shown with the green line in the upper panel, tracking the stepwise rotation of the SWG. The spatial intervals between the measurement angles are approximately 22.5 degrees. The operation range is defined by four limit switches (LS) highlighted as solid lines in the bottom panel.
• Figure 4: (Top panel) The modulated signal response of a single detector (in arbitrary units, a.u.) as a function of the HWP angle. The solid line and the dashed line are the response at the 16th and 15th measurement angles of the SWG rotation, respectively. Their phase difference represents the difference of the SWG direction, $22.5^\circ$. (Bottom panel) The power spectral density (PSD) of the modulated signal. The peaks at around 2, 4 and 8 Hz correspond to the $1f$, $2f$, and $4f$ harmonics of the HWP rotation. The shaded range is defined as the signal range to be demodulated with a band-pass filter. Details are described in the text.
• Figure 5: (Top panel) The direction of the SWG, $\theta_\mathrm{SWG}$, as a function of time during a single calibration run. (Bottom panel) The demodulated response of a single detector. We use the $Q$ and $U$ response only when the SWG is kept at each measurement angle for 10 seconds.