Difference between revisions of "Beam Window Functions"

From Planck Legacy Archive Wiki
Jump to: navigation, search
Line 2: Line 2:
 
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 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
 
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
Line 8: Line 8:
  
  
# QuickPol effective beam window functions
+
=== QuickPol effective beam window functions ===
  
 
They are available in two forms:
 
They are available in two forms:
Line 15: Line 15:
 
<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.
  

Revision as of 08:39, 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 [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 matrix

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

Cosmic Microwave background

(Planck) High Frequency Instrument

Flexible Image Transfer Specification