# Difference between revisions of "Beam Window Functions"

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− | Beam window functions have computed with the Febecop Pipeline (as described [[Effective_Beams#Statistics_of_the_effective_beams_computed_using_FEBeCoP| | + | Beam window functions have computed with the Febecop Pipeline (as described [[Effective_Beams#Statistics_of_the_effective_beams_computed_using_FEBeCoP|there]]), and |

the QuickPol pipeline | the QuickPol pipeline | ||

− | (see Hivon et al, 2017 <ref>Hivon E., Mottet, S. & Ponthieu N., 2017 ''QuickPol: Fast calculation of effective beam matrices for CMB polarization'' A&A 598, A25, [[http://cdsads.u-strasbg.fr/abs/2017A&A...598A..25H|2017A&A...598A..25H]]</ref>). | + | (see Hivon et al, 2017 <ref>Hivon E., Mottet, S. & Ponthieu N., 2017 ''QuickPol: Fast calculation of effective beam matrices for CMB polarization'' A&A 598, A25, [[http://cdsads.u-strasbg.fr/abs/2017A&A...598A..25H|2017A&A...598A..25H]]</ref>, 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). | ||

# QuickPol effective beam window functions | # QuickPol effective beam window functions | ||

− | |||

− | |||

They are available in two forms: | They are available in two forms: | ||

− | * The beam window | + | * The beam window functions <math>b_{T}, b_{E}, b_{B},</math> |

− | <math>b_{T}, b_{E}, b_{B},</math> | + | such that \\ |

− | such that | + | <math>C_{XX}^{map}(\ell) = b_{X}^2(\ell) w_{pix}^2(\ell) C_{XX}^{sky}(\ell)</math> \\ |

− | <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). |

− | for X=T,E or B, in FITS files, in a format compatible with HEALPix tools such as synfast and smoothing, as well as with PolSpice | + | They are provided in FITS files, in a format compatible with [[http://healpix.sourceforge.net|HEALPix]] |

+ | tools such as synfast and smoothing, as well as with PolSpice. | ||

* Beam matrix | * Beam matrix |

## Revision as of 08:33, 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 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 CMB).

, to the true underlying sky angular power spectrum (assumed to have isotropic statistical properties, as is the case for the- QuickPol effective beam window functions

They are available in two forms:

- The beam window functions

such that \\ 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.

\\ for X=T,E or B, and where is the pixel window function, which depends on the resolution parameter Nside (=2048 for Planck- Beam matrix

### References[edit]

Cosmic Microwave background

(Planck) High Frequency Instrument

Flexible Image Transfer Specification