Systematic effect induced by misalignment in a Reflective Polarization Modulator for CMB, and application to the LiteBIRD case

[Abridged] The LiteBIRD mission aims to measure the Cosmic Microwave Background (CMB) polarization with unprecedented precision, targeting the detection of primordial B modes and a precise determination of the tensor-to-scalar ratio r. A central component of LiteBIRD are the polarization modulators based on Half-Wave Plates (HWP). In this work, we investigate systematic effects caused by a small, constant misalignment between the reflective HWP’s rotation axis and optical axis, which mimics a wedge-like effect. This effect can introduce HWP-synchronous pointing errors, biasing polarization measurements and generating spurious B modes. Using the LiteBIRD simulation framework, we implement this wedge-like misalignment in time-ordered data and evaluate its impact on reconstructed maps and angular power spectra. Our results show that the contamination predominantly mimics lensing B modes rather than primordial tensor modes, and its impact is reduced when increasing the number of detectors. By estimating the resulting error on the tensor-to-scalar ratio, we set constraints on the maximum allowable wedge angle to ensure systematic effects remain below mission requirements. This study emphasizes the critical importance of precise optical alignment in CMB polarization experiments. Future work will address the additional effects of time-dependent HWP wobbling and more realistic scenarios with non-ideal detector pairs.

💡 Research Summary

The paper investigates a subtle but potentially critical systematic effect for the LiteBIRD satellite – a small, constant misalignment between the rotation axis of its reflective half‑wave plate (HWP) and the instrument’s optical axis, quantified as a “wedge angle” (α_wedge). Although the HWP is assumed to be perfectly plane‑parallel, an offset of even a few arcminutes causes the reflected beam to trace a circular pattern on the sky as the plate rotates, producing an HWP‑synchronous pointing error. This error propagates from the time‑ordered data (TOD) through map‑making to the final B‑mode power spectrum.

Using the LiteBIRD simulation framework (LBS), the authors inject the wedge effect into CMB‑only simulations (no noise, no foregrounds) for a range of detector configurations (2, 4, and 6 detectors) and a set of wedge angles from 0 to ~30 arcmin. The scanning strategy (precession angle 45°, spin angle 50°, precession period 3.2058 h, spin rate 0.05 rpm, HWP rotation 0.5 rpm) is kept identical to the mission baseline. The misalignment is implemented as a common boresight offset that rotates with the HWP, reproducing the geometric consequences of the wedge without altering the rest of the optical chain.

The key findings are:

1. Spectral Signature – The spurious B‑mode power generated by the wedge peaks at multipoles ℓ≈100–300 and closely mimics the shape of the lensing B‑mode spectrum. Consequently, even in a universe with r = 0, the analysis would infer a non‑zero B‑mode signal if the wedge is not corrected.

2. Dependence on Detector Count – Increasing the number of detectors reduces the amplitude of the systematic bias roughly proportionally. With six detectors the induced Δr (the bias on the tensor‑to‑scalar ratio) is about 30 % smaller than with two detectors, illustrating the benefit of detector redundancy in averaging out pointing distortions.

3. Tolerance Levels – By comparing the systematic bias Δr_wedge to the mission requirement on the total error δr < 10⁻³, the authors derive a maximum allowable static wedge angle of α_max ≈ 22.7 arcmin. However, they note that for α_wedge > 4 arcmin the pointing and beam‑reconstruction errors become the dominant source of contamination, exceeding the allocated systematic budget.

4. Implications for Design – The study emphasizes that precise alignment of the HWP rotation axis is essential. Achieving an alignment better than ~4 arcmin would keep pointing‑related systematics well below the error budget, while a looser tolerance up to ~22 arcmin would still satisfy the overall r‑bias requirement but would leave less margin for other systematics.

5. Future Work – The current analysis assumes a static wedge angle. In practice, a reflective HWP may exhibit “wobble” – a time‑dependent variation of the wedge angle due to mechanical imperfections. Such dynamics would introduce additional harmonics at the HWP rotation frequency and could exacerbate the bias. The authors plan to extend the simulation pipeline to include time‑varying wedge angles, realistic detector pair mismatches, instrumental noise, and astrophysical foregrounds, and to develop mitigation strategies (e.g., in‑flight calibration, data‑driven de‑projection).

Overall, the paper provides a clear quantitative framework for assessing HWP‑induced pointing systematics, establishes concrete alignment tolerances for the LiteBIRD mission, and demonstrates that detector redundancy can partially alleviate the effect. These results are directly relevant to the design and calibration of not only LiteBIRD but also other upcoming CMB polarization experiments that rely on rotating HWPs for systematic control.