Difference between revisions of "Beam Window Functions"

From Planck Legacy Archive Wiki
Jump to: navigation, search
Line 8: Line 8:
  
  
=== QuickPol effective beam window functions ===
+
=== QuickPol effective beam window products ===
  
 
They are available in two forms:
 
They are available in two forms:
* The beam window functions <math>b_{T}, b_{E}, b_{B},</math>
+
==== Beam window functions ====
 +
<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>
Line 18: Line 19:
 
tools such as synfast and smoothing, as well as with PolSpice.
 
tools such as synfast and smoothing, as well as with PolSpice.
  
* Beam matrices <math>W_{XY,X'Y'}(\ell)</math>,  
+
==== Beam matrices ====
 +
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 09:19, 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 products[edit]

They are available in two forms:

Beam window functions[edit]

[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[edit]

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