# 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|there]]), and | 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>, and the | + | (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 Planck 2016 Likelihood paper<ref>Planck collaboration, 2018, ''Planck 2016 results. V. Legacy Power Spectra and Likelihoods''</ref>). |

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 | 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 | ||

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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, 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 [http://healpix.sourceforge.net HEALPix] | 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. | tools such as synfast and smoothing, as well as with PolSpice. | ||

− | * Beam | + | * 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 | ||

=== References === | === References === | ||

<references /> | <references /> |

## Revision as of 08:49, 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### QuickPol effective beam window functions[edit]

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 HEALPix 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 matrices:

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