Beam Window Functions

Beam window functions have computed with the Febecop Pipeline (as described there), and the QuickPol pipeline (see Hivon et al, 2017 , and the 2018 Planck Likelihood paper).

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).

1. QuickPol effective beam window functions

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 [[2]] tools such as synfast and smoothing, as well as with PolSpice.

• Beam matrix