We discuss the construction of a photometric redshift catalogue of Luminous
Red Galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS), emphasizing the
principal steps necessary for constructing such a catalogue -- (i)
photometrically selecting the sample, (ii) measuring photometric redshifts and
their error distributions, (iii) and estimating the true redshift distribution.
We compare two photometric redshift algorithms for these data and find that
they give comparable results. Calibrating against the SDSS and SDSS-2dF
spectroscopic surveys, we find that the photometric redshift accuracy is
$\sigma \sim 0.03$ for redshifts less than 0.55 and worsens at higher redshift
($\sim 0.06$). These errors are caused by photometric scatter, as well as
systematic errors in the templates, filter curves, and photometric zeropoints.
We also parametrize the photometric redshift error distribution with a sum of
Gaussians, and use this model to deconvolve the errors from the measured
photometric redshift distribution to estimate the true redshift distribution.
We pay special attention to the stability of this deconvolution, regularizing
the method with a prior on the smoothness of the true redshift distribution.
The methods we develop are applicable to general photometric redshift surveys.