Abstract: | This paper presents the characterization of the in-flight beams, the beam
window functions and the associated errors for the Planck Low Frequency
Instrument (LFI). Knowledge of the beam profiles is the key to determining
their imprint on the transfer function from the observed to the actual sky
anisotropy power spectrum. The main beam distortions affect the beam window
function, complicating the reconstruction of the anisotropy power spectrum at
high multipoles, whereas the sidelobes affect the low and intermediate
multipoles. The in-flight assessment of the LFI main beams relied on the
measurements performed during Jupiter observations. By stacking the data from
Jupiter transits, the main beam profiles are measured down to -20 dB at 30 and
44 GHz, and down to -25 dB at 70 GHz. The main beam solid angles are determined
to better than 0.2% at each LFI frequency band. To ensure a characterization of
the main beam free from the radiometer noise, a dedicated tuning on the Planck
pre-launch optical model is performed. This approach provides an optical model
whose beams fully reproduce the measurements in the main beam region, but also
allow us to describe the beams at power levels lower than can be reached by the
Jupiter measurements themselves. The agreement between the simulated beams and
the scanning beams is better than 1% at each LFI frequency band. The simulated
beams are used for the computation of the window functions for the effective
beams. The error budget in the window functions was estimated considering both
main beam and sidelobe contributions, as well as taking into account the
radiometer bandshapes. The total uncertainties in the effective beam window
functions are: (at ell = 600) 2% and 1.2% at 30 and 44 GHz, respectively; and
at ell = 1000, 0.7% at 70 GHz. |