The Canada-France Deep Fields III: Photometric Redshift Distribution to I(AB) ~ 24

We compute accurate redshift distributions to I(AB) = 24 and R(AB) = 24.5 using photometric redshifts estimated from six-band UBVRIZ photometry in the Canada-France Deep Fields-Photometric Redshift Survey (CFDF-PRS). Our photometric redshift algorithm is calibrated using hundreds of CFRS spectroscopic redshifts in the same fields. The dispersion in redshift is \sigma/(1+z) \la 0.04 to the CFRS depth of I(AB) = 22.5, rising to \sigma/(1+z) \la 0.06 at our nominal magnitude and redshift limits of I(AB) = 24 and z \le 1.3, respectively. We describe a new method to compute N(z) that incorporates the full redshift likelihood functions in a Bayesian iterative analysis and we demonstrate in extensive Monte Carlo simulations that it is superior to distributions calculated using simple maximum likelihood redshifts. The field-to-field differences in the redshift distributions, while not unexpected theoretically, are substantial even on 30' scales. We provide I(AB) and R(AB) redshift distributions, median redshifts, and parametrized fits of our results in various magnitude ranges, accounting for both random and systematic errors in the analysis.