Beam Window Functions
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 products
They are available in two forms:
Beam window functions
HFI maps).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
They are provided in FITS files, in a format compatible with HEALPix tools such as synfast and smoothing, as well as with PolSpice.
, such that for X,Y,X',Y'= T, E or B.
They are provided in FITS files, containing 4 extensions each:
- first one, named 'TT', contains the 9 fields: 'TT_2_TT', 'TT_2_EE', 'TT_2_BB', 'TT_2_TE', 'TT_2_TB', 'TT_2_EB', 'TT_2_ET', 'TT_2_BT', 'TT_2_BE'\\
describing the ℓ-dependent leakage template of TT towards TT, EE, BB, ... respectively.\\ TT_2_TT is the usual W'_TT_'(l) = B'_T_'(l)'^2^'.
- second extension, named 'EE', contains the 9 fields 'EE_2_TT', 'EE_2_EE', 'EE_2_BB', ... for leakage of EE towards TT, EE, BB, ...
- 3rd extension: 'BB' with 'BB_2_TT', ...
- 4th extension: 'TE' with 'TE_2_TT', ...
- %item value=0% (there is no extension #5 nor 6, corresponding to TB and EB, since these terms are unlikely \
to be major sources of contamination for the other spectra)\\ [==]
The measured C'^*^'(l) are then related to the sky ones C(l)\\
C'^TT*^'(l) = C'^TT^'(l) TT_2_TT(l) + C'^EE^'(l) EE_2_TT(l) + C'^BB^'(l) BB_2_TT(l) + C'^TE^'(l) TE_2_TT(l) \\ C'^EE*^'(l) = C'^TT^'(l) TT_2_EE(l) + C'^EE^'(l) EE_2_EE(l) + C'^BB^'(l) BB_2_EE(l) + C'^TE^'(l) TE_2_EE(l) \\ C'^TE*^'(l) = C'^TT^'(l) TT_2_TE(l) + C'^EE^'(l) EE_2_TE(l) + C'^BB^'(l) BB_2_TE(l) + C'^TE^'(l) TE_2_TE(l) \\ C'^ET*^'(l) = C'^TT^'(l) TT_2_ET(l) + C'^EE^'(l) EE_2_ET(l) + C'^BB^'(l) BB_2_ET(l) + C'^TE^'(l) TE_2_ET(l) \\ ...
- These FITS files contain the same information as the raw npz files above, with the added value that the matrix elements \\
have been re-scaled so that B'_T_'(l=0) = 1 (a relative shift < 10'^-3^' in power).
- To read these FITS file in IDL or python, see []
- 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