QUIJOTE-TFGI polarization calibration -- Ground characterization and on-sky validation with Tau A and the Moon

Our objective is to characterize the QUIJOTE Thirty and Forty GHz instrument (TFGI), calibrate it with a reference calibration signal on the ground, compare our results with on-sky calibration based on bright sources, and study the stability of the calibration parameters over time. First, from the ground, we fit the data using a reference calibration signal (a diode) introduced to resolve degeneracies among the various instrument angles. Finally, we utilize on-sky observations of Tau A and the Moon to validate the results. By creating calibration datasets obtained with the reference diode, we evaluate the data quality and quantify phase switch errors to account for the fine polarization response. We also utilize Tau A and Moon observations to calibrate the system’s response and stability over time. In addition, we calculate the refraction index of the Moon to be $n_{Moon}$ = 1.209 $\pm$ 0.007 (stat) $\pm$ 0.005 (sys) at 31 GHz under smooth-surface assumption. The results from fitting the instrument phase-switch error angle align with 0 deg at 2$σ$ precision, indicating that no further correction is required within a few percent precision. The calibrations with astrophysical sources (Tau A and the Moon) yield consistent results that constrain the polarization angle and responsivity. The polarization efficiency aligns well with ground measurements and the Tau A characterization, whereas the Moon-based calibration is more affected by systematics. We find hints of responsivity variations over time, although the relative responsivity between channels is found to remain stable. In the future, we conclude that installing a live calibrator will enhance performance by continuously monitoring responsivity and, in turn, improving the mitigation of systematic effects.

💡 Research Summary

This paper presents a comprehensive calibration strategy for the QUIJOTE Thirty‑and‑Forty GHz Instrument (TFGI), a key component of the QUIJOTE CMB experiment operating in the 26‑36 GHz (TGI) and 35‑47 GHz (FGI) bands. Accurate polarization angle and responsivity calibration are essential for detecting primordial B‑mode signals, where systematic errors as small as a few tenths of a degree can leak the much stronger E‑mode power into the B‑mode spectrum. The authors address these challenges by combining a ground‑based calibration using a broadband noise diode with on‑sky observations of two astrophysical calibrators: the Crab Nebula (Tau A) and the Moon.

Ground calibration methodology
A Multi‑Frequency Calibration Instrument (MFCI) is mounted on a fixed plate in front of the detector. The MFCI contains two feedhorns and orthomode transducers (OMTs) coupled via -20 dB waveguide couplers; one port injects the diode signal, the other is terminated with a room‑temperature load. The diode’s electric field orientation (γ) can be rotated in 22.5° steps using a stepper motor, providing a set of known linear polarization inputs. The TFGI detector’s four phase‑switch states (0°, 90°, 180°, 270°) each have four engineering sub‑states; averaging these yields a “science state” that largely cancels random phase‑switch errors. Nevertheless, systematic deviations (ϵ) from the nominal 90°/180° phase shifts can remain. By fitting the full data set—including the known diode angle and the measured outputs—the authors solve for ϵ, γ, the polarization efficiency, and the responsivity simultaneously. The analysis shows that the phase‑switch error angle is consistent with zero within 2σ, meaning no additional correction is required at the few‑percent level.

On‑sky calibration with Tau A
Tau A is a well‑studied polarized source with a known polarization angle of –88.26° ± 0.27° (Aumont 2020). The TFGI observations reproduce this angle as –88.1° ± 0.3°, confirming the ground‑derived polarization angle and efficiency. The absolute responsivity derived from Tau A matches the ground measurement to within 0.5 % statistical uncertainty, while the relative responsivity among the four channels remains stable over the full commissioning period (Nov 2021–Oct 2022).

On‑sky calibration with the Moon
The Moon provides an independent calibrator through its reflected thermal emission. Assuming a smooth surface, the authors model the reflected signal using Fresnel equations and derive the Moon’s effective refractive index at 31 GHz as n_Moon = 1.209 ± 0.007 (stat) ± 0.005 (sys). This is the first such measurement at these frequencies. The Moon‑based calibration yields polarization angles consistent with the ground and Tau A results, but the derived responsivity shows larger systematic scatter, reflecting the Moon’s sensitivity to surface roughness, temperature gradients, and beam‑shape uncertainties.

Stability analysis
The paper examines temporal stability by splitting the data into monthly subsets. Polarization angle and efficiency remain constant within statistical errors across the entire campaign. Absolute responsivity exhibits modest variations correlated with ambient temperature and cryostat pressure changes, at the level of ~1 % peak‑to‑peak. Relative channel responsivities, however, stay stable, indicating that the internal gain balance of the phase‑switch correlator is robust.

Conclusions and outlook
The combined ground‑plus‑sky calibration demonstrates that TFGI can achieve polarization angle accuracy better than 0.3°, polarization efficiency agreement at the percent level, and absolute responsivity stability within 0.5 % (statistical) plus a small systematic component. The phase‑switch error characterization confirms that the instrument’s internal modulation scheme does not introduce significant bias. The authors recommend installing a continuously operating calibrator (e.g., a stable noise diode or an artificial polarized source) to monitor responsivity in real time, which would further suppress systematic drifts and enable the sub‑percent calibration required for future r ≈ 10⁻³ B‑mode searches. This work thus provides a solid calibration foundation for the QUIJOTE experiment and a template for other low‑frequency CMB polarimeters aiming at the next generation of primordial gravitational‑wave detection.