Planck 2013 results. VII. HFI time response and beams
  This paper characterizes the effective beams,the effective beam window
functions and the associated errors for the Planck HFI detectors. The effective
beam is the angular response including the effect of the optics,detectors,data
processing and the scan strategy. The window function is the representation of
this beam in the harmonic domain which is required to recover an unbiased
measurement of the CMB angular power spectrum. The HFI is a scanning instrument
and its effective beams are the convolution of: (a) the optical response of the
telescope and feeds;(b)the processing of the time-ordered data and
deconvolution of the bolometric and electronic time response; and (c) the
merging of several surveys to produce maps. The time response functions are
measured using observations of Jupiter and Saturn and by minimizing survey
difference residuals. The scanning beam is the post-deconvolution angular
response of the instrument, and is characterized with observations of Mars. The
main beam solid angles are determined to better than 0.5% at each HFI frequency
band. Observations of Jupiter and Saturn limit near sidelobes (within 5deg) to
about 0.1% of the total solid angle. Time response residuals remain as long
tails in the scanning beams, but contribute less than 0.1% of the total. The
bias and uncertainty in the beam products are estimated using ensembles of
simulated planet observations that include the impact of instrumental noise and
known systematic effects.The correlation structure of these ensembles is
well-described by five error eigenmodes that are sub-dominant to sample
variance and instrumental noise in the harmonic domain. A suite of consistency
tests provide confidence that the error model represents a sufficient
description of the data. The total error in the effective beam window functions
is below 1% at 100GHz up to ell~1500$,and below 0.5% at 143 and 217GHz up to
~2000.
