BeyondPlanck VIII. Efficient Sidelobe Convolution and Correction through
  Spin Harmonics
  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.
