Application of beam deconvolution technique to power spectrum estimation for CMB measurements

TL;DR

This paper introduces two innovative methods for estimating the CMB angular power spectrum directly from time-ordered data, effectively correcting for asymmetric beam effects and incomplete sky coverage, applicable up to high multipoles.

Contribution

The paper presents two novel methods for power spectrum estimation that directly analyze time-ordered data and account for asymmetric beams, improving accuracy over previous techniques.

Findings

Successfully applied to Planck 70 GHz data simulations

Corrected beam effects up to multipole ℓ=1500

Covered the full multipole range without gaps

Abstract

We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from earlier ones in that the power spectrum is estimated directly from time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been masked out to remove foreground contamination, leaving a pure CMB signal, but incomplete sky coverage. The first method (DQML) is derived as the optimal quadratic estimator, which simultaneously yields an unbiased spectrum estimate and minimizes its variance. We successfully apply it to multipoles up to $\ell$=200. The second method is derived as a weak-signal approximation from the first one. It yields an unbiased estimate for the full multipole range, but relaxes the requirement of minimal variance. We validate the methods with simulations for the 70 GHz channel of {\tt Planck} surveyor, and demonstrate that we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$ spectra up to multipole $\ell$=1500. Together the two methods cover the complete multipole range with no gap in between.