Difference between revisions of "Beam Window Functions"
| Line 13: | Line 13: | ||
* The beam window functions <math>b_{T}, b_{E}, b_{B},</math> | * The 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> |
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 matrices | + | * Beam matrices <math>W_{XY,X'Y'}(\ell)</math>, |
| − | <math>W_{XY,X'Y'}(\ell)</math> such that | + | such that |
| − | <math>C_{XY}^{map}(\ell) = W_{XY,X'Y'}(\ell) w_{pix}^2(\ell) C_{X'Y'}^{sky}(\ell)</math> | + | <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 | for X,Y,X',Y'= T, E or B | ||
=== References === | === References === | ||
<references /> | <references /> | ||
Revision as of 08:52, 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 , to the true underlying sky angular power spectrum (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
such that
for X=T, E or B, and where 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 ,
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
