The Canada-France Deep Fields Survey.: III.: Photometric redshift distribution to IAB=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)less than or similar to 0.04 to the CFRS depth of I-AB=22.5, rising to sigma/(1+z)less than or similar to 0.06 at our nominal magnitude and redshift limits of I-AB=24 and z <= 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 300 scales. We provide I-AB and R-AB redshift distributions, median redshifts, and parameterized fits of our results in various magnitude ranges, accounting for both random and systematic errors in the analysis.