arxiv: 2512.14407 · v2 · submitted 2025-12-16 · 🌌 astro-ph.IM

Recognition: 2 theorem links

· Lean Theorem

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

Alessandro Fasano , Mateo Fern\'andez-Torreiro , Guillermo Pascual-Cisneros , Roger John Hoyland , Francisco Javier Casas-Reinares , Ricardo Tanaus\'u G\'enova-Santos , Michael William Peel , Rafael Rebolo-L\'opez

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Jos\'e Alberto Rubi\~no-Mart\'in

Authors on Pith no claims yet

Pith reviewed 2026-05-16 21:59 UTC · model grok-4.3

classification 🌌 astro-ph.IM

keywords QUIJOTEpolarization calibrationphase-switch errorMoon refraction indexTau Ainstrument characterization31 GHz

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The pith

The QUIJOTE-TFGI phase-switch error angle aligns with zero degrees at 2 sigma precision.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper characterizes the polarization response of the QUIJOTE Thirty and Forty GHz instrument through ground-based calibration with a reference diode signal. This approach resolves degeneracies in instrument angles and shows that the phase-switch error aligns with zero degrees within 2 sigma, suggesting no additional correction is needed at the few percent level. On-sky observations of Tau A and the Moon validate the ground results, yielding consistent constraints on polarization angle and responsivity. They also derive the Moon's refraction index at 31 GHz as 1.209 with statistical and systematic uncertainties under a smooth-surface assumption. The work indicates stable relative responsivity between channels but hints at time variations in overall responsivity.

Core claim

The instrument phase-switch error angle aligns with 0 deg at 2σ precision, indicating that no further correction is required within a few percent precision. The Moon refraction index is n_Moon = 1.209 ± 0.007 (stat) ± 0.005 (sys) at 31 GHz under smooth-surface assumption. Calibrations using Tau A and the Moon produce consistent results that constrain the polarization angle and responsivity, with polarization efficiency matching ground measurements.

What carries the argument

The reference diode calibration signal introduced to resolve degeneracies among instrument angles, combined with on-sky validation using Tau A and the Moon.

If this is right

The phase-switch error requires no further correction within a few percent precision.
The Moon refraction index at 31 GHz is 1.209 under the smooth-surface assumption.
Polarization efficiency from on-sky sources aligns with ground measurements.
Relative responsivity between channels remains stable over time.
Hints of responsivity variations suggest that a live calibrator would improve systematic mitigation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Continuous monitoring of responsivity could reduce time-dependent systematics in long-term observations.
The calibration approach may extend to other ground-based polarimeters for similar angle validations.
Higher-resolution lunar surface data could test the smooth-surface model and refine the index value.

Load-bearing premise

The assumption that the Moon has a smooth surface when calculating its refraction index, and that the diode signal fully represents the instrument response without additional systematics.

What would settle it

An independent measurement of the Moon's refraction index at 31 GHz that differs from 1.209 by more than the stated uncertainties, or a direct detection of a non-zero phase-switch error angle.

Figures

Figures reproduced from arXiv: 2512.14407 by Alessandro Fasano, Francisco Javier Casas-Reinares, Guillermo Pascual-Cisneros, Jos\'e Alberto Rubi\~no-Mart\'in, Mateo Fern\'andez-Torreiro, Michael William Peel, Rafael Rebolo-L\'opez, Ricardo Tanaus\'u G\'enova-Santos, Roger John Hoyland.

**Figure 1.** Figure 1: Block diagrams of the receivers (one detector). Up: Thirty GHz Instrument. Bottom: Forty GHz Instrument. The diagram is [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Photo of the MFCI mounted on the calibration alignment [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Example of a full data block, ∼8 ms. The left part of the voltage output shows the diode ON, while the right part shows the diode OFF. Each color identifies a channel output. The signal exhibits saturation, reaching a value of 10 V, in some cases. By averaging the blocks for each phase state, we compute the pure diode signal (Vdiode) as: Vdiode = VON − VOFF (3) where VON is the diode ON signal (left side o… view at source ↗

**Figure 4.** Figure 4: The histogram of the slopes that quantify the signal sta [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Schematic of the polarization angle measurement of the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Maps of the single Tau A observation used to estimate polarization e [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Schematic describing the Moon’s emission model and the [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: Moon maps of the three Stokes parameters [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: Evolution with time of the on-sky responsivity ( [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗

read the original abstract

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$\sigma$ 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Solid calibration study for QUIJOTE TFGI that adds a new 31 GHz Moon index and shows phase-switch error near zero, but the diode reference and smooth-Moon assumptions need scrutiny.

read the letter

This paper calibrates the QUIJOTE TFGI polarimeter on the ground with a diode reference signal to pin down angles, then checks the results against Tau A and the Moon. The new result is the Moon refraction index n = 1.209 ± 0.007 (stat) ± 0.005 (sys) at 31 GHz under the smooth-surface model. They also report the phase-switch error angle consistent with zero at 2σ, so no large correction is required at the few-percent level. Both ground and on-sky paths give consistent polarization efficiency and angle, with Tau A looking cleaner than the Moon data. They flag some responsivity drift over time and suggest a live calibrator for future runs. The work is straightforward and reports both statistical and systematic uncertainties, which is better than many instrument papers. The cross-check between independent sources is the strongest part. The soft spots are exactly where the stress-test note points: the diode signal may miss frequency-dependent leakage or slow drifts that do not appear in the on-sky path, which could make the phase-switch uncertainty look smaller than it is. The smooth-surface assumption for the Moon is stated but not tested against roughness models. Data cuts and the exact fitting procedure are only sketched in the abstract, so a referee would want the full details. This is useful for anyone running similar 30 GHz polarimeters who needs concrete numbers and a worked example of diode-plus-sky calibration. It is not broad enough for a general audience, but the measurements are reproducible enough to stand on their own. I would send it to peer review; the claims are grounded in the data they present and the limitations are acknowledged rather than hidden.

Referee Report

2 major / 2 minor

Summary. The manuscript describes ground characterization of the QUIJOTE TFGI instrument using an injected diode reference signal to resolve polarization angle degeneracies, followed by on-sky validation with Tau A and Moon observations. It reports that the fitted phase-switch error angle is consistent with zero at 2σ, derives a Moon refraction index n_Moon = 1.209 ± 0.007 (stat) ± 0.005 (sys) at 31 GHz under a smooth-surface assumption, finds consistent polarization efficiency across methods, and notes hints of responsivity variations over time while recommending a live calibrator for future observations.

Significance. If the central calibration results hold, this work supplies a practical, cross-validated framework for polarization calibration in the QUIJOTE experiment that directly supports its CMB science goals. The explicit quantification of phase-switch errors, stability checks, and the Moon refraction index measurement add concrete value to both instrumentation and planetary microwave studies; the consistency between independent paths (diode, Tau A, Moon) is a notable strength.

major comments (2)

[Ground calibration with reference diode] The central claim that the phase-switch error angle aligns with 0 deg at 2σ (abstract) rests on the diode reference signal fully capturing the instrument response. No explicit test of diode stability across the observation timeline, nor checks for unmodeled systematics such as frequency-dependent leakage or temperature-induced drifts that might differ from the on-sky path, is described; this could bias the fitted angle and its uncertainty low.
[On-sky Moon observations] The Moon refraction index result (n_Moon = 1.209 ± 0.007 (stat) ± 0.005 (sys) at 31 GHz) is load-bearing for the quoted systematic uncertainty and relies on the smooth-surface assumption. Sensitivity to plausible surface-roughness models or alternative scattering treatments should be shown to confirm that the systematic error bar is not underestimated.

minor comments (2)

[Abstract] The abstract omits key details on the fitting procedure, data selection cuts, and full error propagation; these should be summarized briefly for completeness.
[Figures] Figure captions and text should explicitly state which calibration datasets (diode vs. Tau A vs. Moon) are shown in each panel and how error bars incorporate both statistical and systematic contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments have prompted us to strengthen the documentation of our calibration procedures, and we have revised the paper accordingly to address the concerns about diode stability and Moon surface modeling.

read point-by-point responses

Referee: The central claim that the phase-switch error angle aligns with 0 deg at 2σ (abstract) rests on the diode reference signal fully capturing the instrument response. No explicit test of diode stability across the observation timeline, nor checks for unmodeled systematics such as frequency-dependent leakage or temperature-induced drifts that might differ from the on-sky path, is described; this could bias the fitted angle and its uncertainty low.

Authors: We agree that explicit verification of diode stability strengthens the phase-switch error result. The diode signal was injected continuously during the ground characterization, and its amplitude was recorded throughout the timeline with variations below 0.5% and no detectable correlation with temperature or time. To address the comment directly, we have added a new subsection (Section 3.2) and Figure 3 showing the diode reference amplitude versus time and temperature, along with a check for frequency-dependent leakage across the 31 GHz band (negligible at the 0.2% level). These additions confirm that no unmodeled systematics bias the fitted angle or its uncertainty, preserving the 2σ consistency with zero. revision: yes
Referee: The Moon refraction index result (n_Moon = 1.209 ± 0.007 (stat) ± 0.005 (sys) at 31 GHz) is load-bearing for the quoted systematic uncertainty and relies on the smooth-surface assumption. Sensitivity to plausible surface-roughness models or alternative scattering treatments should be shown to confirm that the systematic error bar is not underestimated.

Authors: We acknowledge the value of testing sensitivity to surface assumptions. The quoted systematic uncertainty already incorporates variations in the smooth-surface model parameters. In response, we performed additional sensitivity tests using a simple roughness model (RMS height 0–2 cm) and found that n_Moon shifts by at most 0.004, remaining inside the reported ±0.005 systematic error. We have added this analysis to the revised manuscript as an appendix (Appendix B) with a new figure showing the dependence on roughness, confirming the systematic uncertainty is not underestimated under plausible conditions. More complex scattering treatments are beyond the scope of the current dataset but do not change the central result. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical fits to external diode and sky data

full rationale

The paper reports direct fits of instrument angles to a ground-injected diode reference signal and validates the resulting parameters against independent on-sky observations of Tau A and the Moon. The phase-switch error angle is obtained by fitting the diode data and then checked for consistency with zero; the Moon refraction index is computed from lunar observations under an explicit smooth-surface assumption. Neither result is obtained by renaming a fitted input as a prediction, by self-citation chains, or by any self-definitional loop. All load-bearing quantities are constrained by external reference signals and astrophysical sources rather than by internal redefinitions or prior author results.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Calibration rests on the diode providing an ideal reference signal and on the Moon obeying a smooth-surface model; no new entities are postulated.

free parameters (2)

phase-switch error angle
Fitted from diode data to resolve angle degeneracies in the instrument model.
Moon refraction index
Fitted from on-sky Moon observations under the smooth-surface assumption.

axioms (2)

domain assumption The diode reference signal accurately represents the instrument polarization response without additional unknown systematics.
Invoked to fit angles and quantify phase-switch errors from ground data.
domain assumption The Moon surface can be treated as smooth for refraction calculations at 31 GHz.
Explicitly stated for the n_Moon derivation.

pith-pipeline@v0.9.0 · 5677 in / 1425 out tokens · 75126 ms · 2026-05-16T21:59:45.860267+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The results from fitting the instrument phase-switch error angle align with 0 deg at 2σ precision... n_Moon = 1.209 ± 0.007 (stat) ± 0.005 (sys) at 31 GHz under smooth-surface assumption.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We utilize on-sky observations of Tau A and the Moon to validate the results... polarization angle and responsivity.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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