BeyondPlanck VIII. Efficient Sidelobe Convolution and Correction through Spin Harmonics

TL;DR

This paper presents a new spin harmonics-based convolution algorithm for efficient sidelobe correction in CMB analysis, achieving significant speed-ups and simplifying implementation within the BeyondPlanck Bayesian framework.

Contribution

The authors introduce a novel spin harmonics formulation of the Conviqt convolution algorithm, improving efficiency and ease of implementation for sidelobe correction in CMB data analysis.

Findings

Speed-up of 3-10 times over previous methods

Good agreement with Planck LevelS in sidelobe estimates

Novel sidelobe rms maps for uncertainty quantification

Abstract

We introduce a new formulation of the Conviqt convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for BeyondPlanck, the first end-to-end Bayesian Gibbs sampling framework for CMB analysis. We compare our implementation to the previous Planck LevelS implementation, and find good agreement between the two codes in terms of accuracy, but with a speed-up reaching a factor of 3--10, depending on the frequency bandlimits, $l_{\textrm{max}}$ and $m_{\textrm{max}}$. The new algorithm is significantly simpler to implement and maintain, since all low-level calculations are handled through an external spherical harmonic transform library. We find that our mean sidelobe estimates for Planck LFI agree well with previous efforts. Additionally, we present novel sidelobe rms maps that quantify the uncertainty in the sidelobe corrections due to variations in the sky model.