CFHTLenS: Improving the quality of photometric redshifts with precision
  photometry
  Here we present the results of various approaches to measure accurate colours
and photometric redshifts (photo-z's) from wide-field imaging data. We use data
from the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) which have been
re- processed by the CFHT Lensing Survey (CFHTLenS) team in order to carry out
a number of weak gravitational lensing studies. An emphasis is put on the
correction of systematic effects in the photo-z's arising from the different
Point Spread Functions (PSF) in the five optical bands. Different ways of
correcting these effects are discussed and the resulting photo-z accuracies are
quantified by comparing the photo-z's to large spectroscopic redshift (spec-z)
data sets. Careful homogenisation of the PSF between bands leads to increased
overall accuracy of photo-z's. The gain is particularly pronounced at fainter
magnitudes where galaxies are smaller and flux measurements are affected more
by PSF-effects. We also study possible re- calibrations of the photometric
zeropoints (ZPs) with the help of galaxies with known spec-z's. We find that if
PSF-effects are properly taken into account, a re-calibration of the ZPs
becomes much less important suggesting that previous such re-calibrations
described in the literature could in fact be mostly corrections for PSF-effects
rather than corrections for real inaccuracies in the ZPs. The implications of
this finding for future surveys like KiDS, DES, LSST, or Euclid are mixed. On
the one hand, ZP re-calibrations with spec-z's might not be as accurate as
previously thought. On the other hand, careful PSF homogenisation might provide
a way out and yield accurate, homogeneous photometry without the need for full
spectroscopic coverage. This is the first paper in a series describing the
technical aspects of CFHTLenS. (abridged)
