QuickPol: Fast calculation of effective beam matrices for CMB polarization

Abstract

Current and planned observations of the cosmic microwave background (CMB) polarization anisotropies, with their ever increasing number of detectors, have reached a potential accuracy that requires a very demanding control of systematic effects. While some of these systematics can be reduced in the design of the instruments, others will have to be modeled and hopefully accounted for or corrected a posteriori. We propose QuickPol, a quick and accurate calculation of the full effective beam transfer function and of temperature to polarization leakage at the power spectra level, as induced by beam imperfections and mismatches between detector optical and electronic responses. All the observation details such as exact scanning strategy, imperfect polarization measurements, and flagged samples are accounted for. Our results are validated on Planck high frequency instrument (HFI) simulations. We show how the pipeline can be used to propagate instrumental uncertainties up to the final science products, and could be applied to experiments with rotating half-wave plates.

Planck2018 results

“…The small excess of 0.1% around = 500 is associated with the effective cut-off of the LFI-dominated low-frequency signal component employed by Commander. These general trends are due to small mismatches between the full asymmetric beams, as implemented through pixel-space FEBeCoP (Mitra et al 2011) convolutions, and the azimuthally symmetric effective beam transfer functions, as implemented with QuickBeam (Hivon et al 2017). For instance, a fall-off of 0.3 % at ≈ 2000 corresponds to a mismatch of about 0.05 FWHM in the two models.…”

Full-sky beam convolution for cosmic microwave background applications

“…This is ultimately due to the incomplete description of spinweighted fields on the sphere. 19 A workaround for this issue is obtained by first calculating the spin-0 spherical harmonic coefficients of the P L (a well-defined operation at the pole) field and use an analytic expression for the spin-±2 spherical harmonic coefficients of the transformation factor e ∓2iφ (see (Hivon et al 2017)). By doing so, we may rewrite the above relation for P in the harmonic domain:…”

“…However, the 1/ scaling of the factor in front of the 3 j symbols suppresses any large deviations of from , which in practise means that b P L m and ±2 b P m share band-limits. As explained in Hivon et al (2017), for a sufficiently localised beam, the kernel K m may be approximated as diagonal per azimuthal mode m, i.e. K m ≈ δ ∀m.…”

“…8 In more practical terms, the real and imaginary parts of b I 2 correspond to the components of the unpolarized beam with azimuthal parts proportional to cos 2φ and sin 2φ respectively. Only in this limit (perfect uniform coverage in θ, φ and ψ), the leakage may be described independently per mode; leakage from to and m to m will occur in more general cases (Hu et al 2003;Hanson et al 2010;Hivon et al 2017). In the case of azimuthally symmetric beams (Eq.…”

TE correlation coefficient of PlancLouis1, Li2, Tristram3 2019Phys. Rev. D9080View full textAdd to dashboardCite

“…We note however that R T E will be impacted by systematics leading to additive biases, one example is the uncorrected temperature to polarisation leakage in Planck polarisation maps [4,20].…”