Beam Window Functions

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Beam window functions have computed with the Febecop Pipeline (as described there), and the QuickPol pipeline (see Hivon et al, 2017[1], and the Planck 2016 Likelihood paper[2]).

The beam window functions relate, over the full sky or over a masked sky, the angular power spectrum measured (in the absence of noise) on a map produced by a set of detectors [math]C_{XX}^{map}(\ell)[/math], to the true underlying sky angular power spectrum [math]C_{XX}^{sky}(\ell)[/math] (assumed to have isotropic statistical properties, as is the case for the CMB).

QuickPol effective beam window functions[edit]

They are available in two forms:

  • The beam window functions [math]b_{T}, b_{E}, b_{B},[/math]

such that [math]C_{XX}^{map}(\ell) = b_{X}^2(\ell) w_{pix}^2(\ell) C_{XX}^{sky}(\ell)[/math] for X=T, E or B, and where [math]w_{pix}[/math] is the pixel window function, which depends on the resolution parameter Nside (=2048 for Planck HFI maps). They are provided in FITS files, in a format compatible with HEALPix tools such as synfast and smoothing, as well as with PolSpice.

  • Beam matrices:

[math]W_{XY,X'Y'}(\ell)[/math] such that [math]C_{XY}^{map}(\ell) = W_{XY,X'Y'}(\ell) w_{pix}^2(\ell) C_{X'Y'}^{sky}(\ell)[/math] for X,Y,X',Y'= T, E or B


  1. Hivon E., Mottet, S. & Ponthieu N., 2017 QuickPol: Fast calculation of effective beam matrices for CMB polarization A&A 598, A25, 2017A&A...598A..25H
  2. Planck collaboration, 2018, Planck 2016 results. V. Legacy Power Spectra and Likelihoods

Cosmic Microwave background

(Planck) High Frequency Instrument

Flexible Image Transfer Specification