🔭 astrophysics

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

This paper characterizes and validates the polarization calibration of the QUIJOTE Thirty and Forty GHz instrument by comparing ground-based reference diode measurements with on-sky observations of Tau A and the Moon, confirming the stability of relative responsivity and polarization efficiency while identifying the need for a live calibrator to mitigate systematic effects.

Original authors: Alessandro Fasano, Mateo Fernández-Torreiro, Guillermo Pascual-Cisneros, Roger John Hoyland, Francisco Javier Casas-Reinares, Ricardo Tanausú Génova-Santos, Michael William Peel, Rafael Rebolo-López

Published 2026-04-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alessandro Fasano, Mateo Fernández-Torreiro, Guillermo Pascual-Cisneros, Roger John Hoyland, Francisco Javier Casas-Reinares, Ricardo Tanausú Génova-Santos, Michael William Peel, Rafael Rebolo-López, José Alberto Rubiño-Martín

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, ancient ocean. For decades, astronomers have been mapping the "waves" of this ocean—the Cosmic Microwave Background (CMB)—to understand how the universe began. But recently, they've realized that to see the most subtle, ripples in the water (called "B-modes," which could prove the universe expanded instantly after the Big Bang), they need to measure the direction of the waves with extreme precision.

This is where the QUIJOTE telescope comes in. Located in the Canary Islands, it's a high-tech "wave detector" designed to listen to the faint whispers of the early universe. However, before it can listen to the universe, it has to make sure its own ears aren't "deaf" or "twisted."

This paper is essentially the quality control report for one specific sensor (called "Pixel 23") on the QUIJOTE telescope. The team had to answer three big questions:

Is the sensor sensitive enough? (Responsivity)
Is it good at detecting the direction of the waves? (Polarization Efficiency)
Is it pointing in the right direction? (Polarization Angle)

Here is how they tested it, explained with everyday analogies:

1. The "Sound Check" (Ground Calibration)

Before the telescope looks at the sky, the team performed a "sound check" right on the ground.

The Analogy: Imagine you are tuning a guitar. You don't just play a song; you pluck a specific string with a known pitch to see if the guitar is in tune.
The Experiment: They used a special device (a "diode") that acts like a perfect, artificial star. They injected a known signal directly into the sensor.
The Twist: To make sure the sensor wasn't just "guessing" the direction, they put a rotating filter (a polarizer) in front of the signal, changing the angle 22.5 degrees at a time. It's like spinning a pair of sunglasses in front of a light bulb to see if the sensor correctly identifies the light's orientation from every angle.
The Result: The sensor passed with flying colors. It correctly identified the angles, and the "twist" in its internal gears (phase errors) was so small it was practically zero.

2. The "Celestial Test Drive" (On-Sky Calibration)

Ground tests are great, but the real world is messy. The telescope needs to be tested while actually looking at space. They used two famous "celestial test drivers":

A. The Crab Nebula (Tau A)

The Analogy: Think of the Crab Nebula as a lighthouse. It's incredibly bright, steady, and its "flash" (polarization) is well-known and trusted by astronomers worldwide.
The Test: They pointed the telescope at this lighthouse. Since they knew exactly how bright and how polarized the lighthouse should be, they could compare it to what the telescope saw.
The Result: The telescope's view matched the lighthouse's reputation almost perfectly. This confirmed that the sensor was measuring the "direction" of the waves correctly.

B. The Moon

The Analogy: If the Crab Nebula is a lighthouse, the Moon is a giant, glowing billiard ball. It doesn't have a fixed "flash" like the lighthouse; instead, it glows with heat. Because of how light bends when it hits the Moon's surface, it creates a very specific, predictable pattern of polarization (like a four-leaf clover pattern).
The Test: They scanned the Moon to see if the telescope could detect this specific clover pattern.
The Surprise: The telescope saw the pattern, but it was a bit "fuzzier" than expected. However, by using the Moon, they were able to calculate a new, precise value for the refractive index of the Moon (how much the Moon bends light). It's like using a telescope to measure the density of a rock you've been looking at for centuries.

3. The "Drifting Clock" Problem (Stability)

One of the most interesting findings was about time.

The Analogy: Imagine you have a stopwatch. If you check it in the morning, it says 10 seconds. If you check it again in the afternoon, it says 15 seconds. The stopwatch isn't broken, but it's drifting.
The Finding: The team noticed that the telescope's sensitivity (how "loud" it hears the universe) changed by about 15% over a few months. It wasn't broken; it was just reacting to the environment (like temperature changes).
The Solution: They realized that to get perfect science, they need a "live clock" inside the telescope. They plan to install a small, internal signal generator that checks the telescope's sensitivity every 30 seconds, just like a pilot checking their instruments mid-flight.

The Bottom Line

This paper is a success story. The QUIJOTE telescope's sensor is calibrated, stable, and ready.

It knows exactly where it is pointing (within 1 degree).
It knows how sensitive it is.
It has passed tests using both a "perfect artificial star" and real cosmic objects.

The team has identified a few small quirks (like the sensitivity drifting over time), but they have a clear plan to fix them. Now that the instrument is "tuned," it can start its real job: hunting for the faintest whispers of the Big Bang, helping us understand the very birth of our universe.

1. Problem Statement

The Cosmic Microwave Background (CMB) polarization, particularly the search for primordial B-modes, requires instrumentation with unprecedented precision. Two critical challenges for ground-based experiments like QUIJOTE (Q-U-I JOint TEnerife) are:

Polarization Angle Calibration: Any unaccounted systematic error in the polarization angle can convert strong E-modes into spurious B-modes, contaminating the cosmological signal. The target precision is better than 0.1–0.2 degrees.
Detector Responsivity: Uncertainties in detector responsivity introduce multiplicative biases in Stokes parameters and cause leakage between temperature (T) and polarization (E/B) modes. Calibration must be at the sub-percent level.
Systematic Effects: Instrumental imperfections, such as phase-switch errors and non-linearities, must be characterized and mitigated to ensure data reliability.

The QUIJOTE Thirty and Forty GHz Instrument (TFGI) needed rigorous calibration to validate its performance before full scientific operations. This study focuses on Pixel 23 (the central detector at 31 GHz) as a benchmark for the entire focal plane.

2. Methodology

The authors employed a multi-faceted calibration strategy combining ground-based tests with on-sky observations of astrophysical sources.

A. Ground Characterization (MFCI)

Setup: A Multi-Frequency Calibration Instrument (MFCI) was mounted on the telescope focal plane. It utilized a noise diode (Keysight 346CK011) and a rotating polarizer to inject known signals.
Degeneracy Breaking: To resolve degeneracies between instrument angles and phase-switch errors, the polarizer was rotated to six specific angles ( $\gamma$ : -45.0° to 67.5° in 22.5° steps).
Mathematical Framework: The team fitted the detector output voltages to a set of equations relating Stokes parameters ( $I, Q, U$ ) to the input polarization angle, gain, polarization efficiency ( $\eta$ ), and phase-switch error angles ( $\epsilon$ ).
Data Assessment: They analyzed time-stream data for saturation (noting signals reaching 10V) and stability (drift < 2 mV/min), confirming the system was stable enough for calibration despite minor drifts.

B. On-Sky Validation

Tau A (Crab Nebula): Used as a bright, stable, and well-characterized polarized source.
- Efficiency & Responsivity: Derived by comparing measured flux/polarization fraction against the known model of Tau A.
- Polarization Angle: Calculated by comparing the measured angle against the known rotation-measure-corrected angle of Tau A ( $\gamma_{TauA} \approx -88.3^\circ$ ).
The Moon: Used as a secondary calibrator with a different emission mechanism (thermal emission with weak polarization due to surface refraction).
- Modeling: The team modeled the Moon's thermal emission and polarization using Fresnel equations, treating the Moon's refractive index ( $n_{Moon}$ ) as a free parameter.
- Fitting: They fitted the observed Stokes $Q$ and $U$ maps (which exhibit a quadrupolar pattern) to the model to derive the polarization angle and responsivity.

3. Key Contributions

Phase-Switch Error Characterization: The study successfully isolated and quantified the phase-switch error angles ( $\epsilon$ ).
Moon Refractive Index: By inverting the calibration problem (fixing efficiency based on Tau A), the authors derived a new, precise value for the Moon's refractive index at 31 GHz.
Methodology Benchmarking: The paper establishes a robust calibration workflow for TFGI, comparing ground-based diode calibration against two distinct astrophysical sources to validate consistency.
Identification of Systematics: The work identified temporal variations in responsivity and highlighted the limitations of current ground testing (lack of full optical path) versus on-sky performance.

4. Key Results

Polarization Efficiency ( $\eta$ )

Ground (MFCI): $\eta = 95 \pm 2\%$ .
Tau A: $\eta = 95 \pm 3\%$ .
Moon: $\eta = 89 \pm 16\%$ (higher uncertainty due to modeling complexities).
Conclusion: Ground and Tau A results are consistent within $1\sigma$ , validating the instrument's high polarization efficiency.

Responsivity ( $R$ )

Variability: Significant temporal variations were observed. Responsivity values derived from Tau A and the Moon differed by $\sim 15\%$ , and values fluctuated by a factor of $\sim 1.5$ over a three-month period.
Stability: While absolute responsivity varied, the relative responsivity between channels remained stable, suggesting a common system component (e.g., backend temperature) drives the drift.
Ground vs. Sky: Ground measurements (using a direct diode injection) yielded different absolute values than on-sky measurements, likely due to non-linearities from the high-power diode and the absence of telescope optics in the ground test.

Polarization Angle ( $\phi_c$ )

Phase Errors: The fitted phase-switch error angles were consistent with 0 degrees at the $2\sigma$ level (mean error $\approx 1.3^\circ$ with $\sigma \approx 0.65^\circ$ ). No correction is required for scientific data at the $\sim 1^\circ$ precision level.
Consistency:
- Ground: $\sim 131.5^\circ$ (CH1).
- Tau A: $\sim 132.0^\circ$ (CH1).
- Moon: $\sim 127.2^\circ$ (CH1).
Conclusion: Tau A provides the most reliable reference due to its stable emission and lack of geometric modeling uncertainties. The Moon results show a $\sim 3^\circ$ deviation, attributed to systematic modeling errors, but still offer a robust check.

Moon Refractive Index

By fixing the polarization efficiency to the Tau A value, the authors calculated the Moon's refractive index at 31 GHz:
$n_{Moon} = 1.209 \pm 0.007 \text{ (stat)} \pm 0.009 \text{ (sys)}$
This is consistent with previous measurements (e.g., Losovskii 1967) and supports the use of the Moon as a polarization calibrator.

5. Significance and Future Outlook

Validation of TFGI: The results confirm that the QUIJOTE-TFGI instrument meets the scientific requirements for polarization angle accuracy ( $\sim 1^\circ$ ) and efficiency ( $\sim 95\%$ ).
Systematic Mitigation: The identification of temporal responsivity drifts underscores the need for continuous monitoring. The authors conclude that installing a live internal calibrator (a diode sampling every 30 seconds) is essential to track these variations in real-time.
Scientific Impact: Achieving these calibration standards is critical for the QUIJOTE experiment's goal of constraining the tensor-to-scalar ratio ( $r$ ) and characterizing Galactic foregrounds. The methodology developed here serves as a blueprint for future ground-based CMB experiments aiming for sub-degree polarization angle precision.

In summary, this paper successfully characterizes the QUIJOTE-TFGI instrument, demonstrating that while ground calibration is effective for efficiency and angle, on-sky sources (specifically Tau A) are necessary for validating absolute responsivity and stability. The work paves the way for high-precision CMB polarization science by identifying and quantifying key systematic effects.