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 2018 Planck Likelihood paper).
+
(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 matrix
+
* 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 [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

References[edit]

  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