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

TL;DR

This study analyzes a wedge-like systematic arising from a small misalignment between the reflective HWP rotation axis and the optical axis in LiteBIRD, which induces HWP-synchronous pointing errors and spurious $B$-modes. Using end-to-end TOD simulations within the LiteBIRD framework, the authors quantify how the wedge imprint propagates to maps and $C_\ell^{BB}$, finding that the contamination resembles lensing $B$-modes rather than primordial tensors and grows with the wedge angle while decreasing with more detectors. They define a maximum allowable wedge angle $\alpha_{\max}$ to keep the induced bias $\Delta r_{\text{wedge}}$ below mission requirements and demonstrate that a two-parameter model separating tensor and lensing-like wedge signals improves the fit, though the wedge cannot be fully absorbed by a single $r$ parameter. The results highlight the critical importance of precise optical alignment and provide concrete tolerances (and their scaling with detector count) to control wedge-related systematics, while noting the limitations of a constant-angle assumption and outlining future work on time-dependent wobble and detector non-idealities.

Abstract

[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.

Figures (15)

• Figure 1: Schematic of the observational parameters. The telescope boresight is at an angle $\beta=50^{\circ}$ to the spin axis and rotates at a rate of 0.05 rpm. The spin axis is rotated around the anti-Sun direction through precession with an angle $\gamma=45^{\circ}$ in 3.2058 h. The anti-Sun axis rotates around the Sun in one year. With a combination of the three motions, the boresight can cover the entire sky in half a year litebird2023probing. This figure is taken from Figure 37 of litebird2023probing and is distributed under the Creative Commons Attribution License.
• Figure 2: Schematic of the optical configuration, highlighting the reflective HWP and the systematic effects introduced by the wedge angle $\alpha_\text{wedge}$. The diagram illustrates the light propagation through the telescope and how the wedge angle modifies the optical path, introducing systematics. The inset zoom provides a closer view of the reflective HWP. The reflective HWP is assumed ideal; this misalignment mimics the effect of a physical wedge in a transmissive HWP.
• Figure 3: Comparison between hit maps (mission duration: 4 hours) for different wedge angles: $\alpha = 0$ arcmin (left) and $\alpha = 60$ arcmin (right). Each case includes a full-sky view (top) and a zoomed-in view (bottom). The presence of a wedge angle introduces a spreading effect in the hit distribution, resulting in a broader and less concentrated scanning pattern, as evident in the right panels.
• Figure 4: Comparison between hit maps in zoomed-in view (mission duration: 1 year) for different wedge angles: $\alpha = 0$ arcmin (left) and $\alpha = 10$ arcmin (right). The maps focus on one of the most observed regions, the North Ecliptic Pole, centered at $(\mathrm{lon}, \mathrm{lat}) = (0^{\circ}, 90^{\circ})$, covering a sky patch of approximately $20^{\circ} \times 20^{\circ}$. To facilitate a direct comparison, the same colour scale has been applied to both maps.
• Figure 5: Periodograms of the simulated timeline for different wedge angles $\alpha$. The three rows correspond to $\alpha = 1$ arcmin (first), $\alpha = 10$ arcmin (second), and $\alpha = 60$ arcmin (third), compared to the ideal case $\alpha = 0$ arcmin (in gray). The right columns provide a zoomed-in view around $4\,\nu_{\text{HWP}}$, highlighting the growth of additional power for increasing $\alpha$ values. The dashed lines indicate the range $3-5\,\nu_\text{HWP}$. As $\alpha$ increases, additional harmonics of the HWP rotation frequency (orange solid line) become apparent due to the periodic nature of the effect. All frequencies are expressed in units of the HWP rotation frequency $\nu/\nu_\text{HWP}$.