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arxiv: 2606.31720 · v1 · pith:7FA4XEWGnew · submitted 2026-06-30 · 🌌 astro-ph.IM · astro-ph.CO

Robust CMB polarisation mapmaking with a rotating half-wave plate

Wuhyun Sohn , Simon Biquard , Josquin Errard , Radek Stompor This is my paper

Pith reviewed 2026-07-01 02:59 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.CO
keywords CMB polarizationmapmakinghalf-wave platemarginalizationatmospheric contaminationpolarization leakageground-based surveys
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The pith

A mapmaking method marginalizes signals varying slower than a quarter half-wave plate rotation to recover unbiased CMB polarization maps amid strong unpolarized contaminants.

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

The paper introduces a mapmaking technique for CMB polarization data taken with a rotating half-wave plate that explicitly accounts for intense unpolarized signals from the atmosphere and ground pickup. It works by marginalizing over any signals that change slowly relative to the rotation timescale, leaving the sky polarization intact. A reader would care because these contaminants routinely exceed the target signal by orders of magnitude, and the approach claims to deliver maps whose noise approaches the theoretical minimum while keeping contamination low. The same procedure also reduces intensity-to-polarization leakage provided the plate spins fast enough compared with the time for the beam to cross a sky feature.

Core claim

The central claim is that marginalizing over all signals varying slowly compared to the polarimeter's angle rotation on the sky produces unbiased estimates of CMB polarization, with nearly optimal noise levels and minimal contamination when the unpolarized signals vary on timescales longer than a quarter of the half-wave plate rotation period; the same procedure additionally mitigates intensity-to-polarisation leakage whenever the rotation period is short relative to the beam-scale crossing time.

What carries the argument

Marginalization over signals varying on timescales longer than roughly one-quarter of the half-wave plate rotation period, which isolates the polarization sky signal from the dominant unpolarized contaminants.

If this is right

  • Maps reach nearly optimal noise performance when the variability condition holds.
  • Contamination from atmosphere and ground pickup remains minimal.
  • Intensity-to-polarisation leakage is efficiently suppressed if the rotation period is short relative to beam crossing time.
  • The estimator is ready for use on upcoming ground-based CMB surveys.

Where Pith is reading between the lines

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

  • Faster half-wave plate rotation could extend the range of atmospheric fluctuation speeds the method can tolerate.
  • The separation principle might apply to other modulated polarization observations where slow systematics dominate.
  • Scan strategies that spend more time per sky pixel could benefit from tighter control on the rotation-to-variability ratio.
  • Tests with injected fast-varying contaminants would directly probe the boundary stated in the performance condition.

Load-bearing premise

Unpolarized contaminant signals vary on timescales longer than roughly one quarter of the half-wave plate rotation period.

What would settle it

A controlled simulation or observation in which unpolarized signals are made to vary faster than one quarter of the rotation period, then checking whether the resulting polarization maps show clear bias or excess noise above the expected level.

Figures

Figures reproduced from arXiv: 2606.31720 by Josquin Errard, Radek Stompor, Simon Biquard, Wuhyun Sohn.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of the POMME deprojection operator [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The power spectra of the deprojected noise, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A pictorial summary of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Map estimates obtained from TOD simulations with [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Noise levels on the polarisation power spectrum evaluated from atmospheric simulations. The pseudo- [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The average value of residual [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Noise levels on the polarisation power spectra analogous to Figure 5, but applied to TODs generated only with CMB [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Response to random sinusoidal input for various [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
read the original abstract

We present a novel mapmaking method for obtaining unbiased estimates of CMB polarisation, tailored to modern CMB experiments with a rotating half-wave plate. These experiments are exposed to strong unpolarised contaminant sources, such as atmospheric emission and ground pickup, which can be several orders of magnitude stronger than the sky signal. Our mapmaker mitigates these systematic effects by marginalising over all signals that vary slowly compared to the timescale of a polarimeter's angle rotation on the sky, while recovering high-fidelity polarisation maps. When the variability timescales of the unpolarised signals exceed a quarter of the half-wave plate rotation period, the method can produce maps with nearly optimal noise levels and minimal contamination. Furthermore, if the half-wave plate rotation period is sufficiently short relative to the beam-scale crossing time, the method efficiently mitigates the sky intensity-to-polarisation leakage. This mapmaker, named the Polarisation-Optimised Map-Making Estimator (POMME), is implemented within the open-source FURAX package and is ready for application to upcoming ground-based CMB surveys.

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.

Referee Report

2 major / 2 minor

Summary. The paper introduces the Polarisation-Optimised Map-Making Estimator (POMME) for CMB polarization mapmaking with a rotating half-wave plate (HWP). It marginalizes over unpolarized contaminants (atmosphere, ground pickup) that vary slowly relative to the HWP rotation timescale, claiming to recover unbiased polarization maps with nearly optimal noise and minimal contamination when contaminant variability timescales exceed one-quarter of the HWP period. It further claims efficient mitigation of intensity-to-polarization leakage when the HWP period is short compared to the beam crossing time. The method is implemented in the open-source FURAX package.

Significance. If the central claims hold, the method addresses a practical challenge for ground-based CMB experiments where unpolarized signals can dominate the polarized sky by orders of magnitude. The open-source implementation in FURAX is a strength that facilitates adoption. The approach could improve map fidelity for upcoming surveys without requiring additional hardware or aggressive filtering.

major comments (2)
  1. [§3.2, Eq. (12)] §3.2, Eq. (12): The marginalization operator is constructed by projecting out modes varying slower than the HWP rotation, but no explicit demonstration is given that this operator is orthogonal to the 4f-modulated polarization templates; without this, the claim of unbiased recovery and 'minimal contamination' when timescales exceed 1/4 period rests on an unproven assumption.
  2. [§5.1, Figure 5] §5.1, Figure 5: The noise performance is shown to approach optimal only for variability timescales several times longer than the 1/4-period threshold; no quantitative analysis or simulation explores the transition region near the cutoff, leaving the boundary condition stated in the abstract without direct support.
minor comments (2)
  1. [§2] The notation for the HWP rotation frequency f_HWP is introduced inconsistently between §2 and §4; a single definition in a notation table would improve clarity.
  2. [Figure 3] Figure 3 caption does not specify the exact cutoff frequency used in the marginalization for the displayed maps.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for identifying areas where additional clarity and analysis would strengthen the manuscript. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [§3.2, Eq. (12)] The marginalization operator is constructed by projecting out modes varying slower than the HWP rotation, but no explicit demonstration is given that this operator is orthogonal to the 4f-modulated polarization templates; without this, the claim of unbiased recovery and 'minimal contamination' when timescales exceed 1/4 period rests on an unproven assumption.

    Authors: We agree that an explicit demonstration of orthogonality would remove any ambiguity. The marginalization operator in Eq. (12) is a projection onto the subspace of signals whose Fourier content lies below the chosen cutoff frequency (one-quarter of the HWP rotation frequency). Because the polarization templates are modulated at exactly 4f, their time-domain representation is orthogonal to all modes below that cutoff by construction of the Fourier basis. Nevertheless, we did not include a short algebraic proof of this inner-product vanishing. In the revised manuscript we will add a brief appendix (or subsection in §3.2) that writes the inner product explicitly and shows it is identically zero when the variability timescale exceeds the cutoff, thereby confirming that the polarization templates remain unaffected. revision: yes

  2. Referee: [§5.1, Figure 5] The noise performance is shown to approach optimal only for variability timescales several times longer than the 1/4-period threshold; no quantitative analysis or simulation explores the transition region near the cutoff, leaving the boundary condition stated in the abstract without direct support.

    Authors: The referee is correct that Figure 5 presents results only for timescales comfortably longer than the nominal threshold. The abstract statement follows directly from the frequency-domain cutoff used to define the marginalization operator, but we acknowledge that the transition region itself was not sampled. We will add a new panel (or supplementary figure) that scans variability timescales from 0.2 to 2 times the HWP period, reporting both bias and noise degradation as continuous functions of that ratio. This will provide quantitative support for the precise boundary quoted in the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity: method is a direct statistical construction

full rationale

The paper defines POMME as a marginalization procedure over signals varying slowly relative to HWP rotation, with performance claims explicitly conditioned on contaminant timescales exceeding one-quarter of the rotation period. No equations or steps are presented that reduce the claimed unbiased maps or noise optimality to fitted parameters, self-citations, or definitional tautologies; the construction is presented as a self-contained statistical estimator whose validity rests on the stated timescale assumption rather than on any internal redefinition or imported uniqueness result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that contaminant signals vary slowly relative to HWP rotation; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Unpolarised contaminant signals vary on timescales longer than approximately one-quarter of the HWP rotation period.
    This timescale separation is required for the marginalization to produce near-optimal noise and minimal contamination.

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discussion (0)

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Reference graph

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