Photometric redshifts: estimating their contamination and distribution
  using clustering information
  We present a new technique to estimate the level of contamination between
photometric redshift bins. If the true angular cross-correlation between
redshift bins can be safely assumed to be zero, any measured cross-correlation
is a result of contamination between the bins. We present the theory for an
arbitrary number of redshift bins, and discuss in detail the case of two and
three bins which can be easily solved analytically. We use mock catalogues
constructed from the Millennium Simulation to test the method, showing that
artificial contamination can be successfully recovered with our method. We find
that degeneracies in the parameter space prohibit us from determining a unique
solution for the contamination, though constraints are made which can be
improved with larger data sets. We then apply the method to an observational
galaxy survey: the deep component of the Canada-France-Hawaii Telescope Legacy
Survey. We estimate the level of contamination between photometric redshift
bins and demonstrate our ability to reconstruct both the true redshift
distribution and the true average redshift of galaxies in each photometric bin.
