# Difference between revisions of "Beam Window Functions"

Line 20: | Line 20: | ||

==== Beam matrices ==== | ==== Beam matrices ==== | ||

− | W_{XY,X'Y'}(\ell)</math>, | + | <math>W_{XY,X'Y'}(\ell)</math>, |

such that | such that | ||

<math>C_{XY}^{map}(\ell) = \sum_{X',Y'} W_{XY,X'Y'}(\ell) w_{pix}^2(\ell) C_{X'Y'}^{sky}(\ell)</math> | <math>C_{XY}^{map}(\ell) = \sum_{X',Y'} W_{XY,X'Y'}(\ell) w_{pix}^2(\ell) C_{X'Y'}^{sky}(\ell)</math> |

## Revision as of 09:21, 16 February 2018

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 CMB).

, to the true underlying sky angular power spectrum (assumed to have isotropic statistical properties, as is the case for the## Contents

### QuickPol effective beam window products[edit]

They are available in two forms:

#### Beam window functions[edit]

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.

such that for X=T, E or B, and where is the pixel window function, which depends on the resolution parameter Nside (=2048 for Planck#### Beam matrices[edit]

, such that for X,Y,X',Y'= T, E or B

### References[edit]

- ↑ 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 - ↑ Planck collaboration, 2018,
*Planck 2016 results. V. Legacy Power Spectra and Likelihoods*

Cosmic Microwave background

(Planck) High Frequency Instrument

Flexible Image Transfer Specification