TITLE: Towards More Precise Photometric Redshifts: Calibration Via CCD Photometry AUTHORS: Robert J. Brunner, Andrew J. Connolly, Alexander S. Szalay, and Matthew A. Bershady PUBLISHED: to appear in ApJ Letters ABSTRACT: We present the initial results from a deep, multi-band photometric survey of selected high Galactic latitude redshift fields. Previous work using the photographic data of Koo and Kron demonstrated that the distribution of galaxies in the multi-dimensional flux space U B R I is nearly planar. The position of a galaxy within this plane is determined by its redshift, luminosity and spectral type. Using recently acquired deep CCD photometry in existing, published redshift fields, we have redetermined the distribution of galaxies in this four-dimensional magnitude space. Furthermore, from our CCD photometry and the published redshifts, we have quantified the photometric-redshift relation within the standard AB magnitude system. This empirical relation has a measured dispersion of approximately 0.02 for z < 0.4. With this work we are reaching the asymptotic intrinsic dispersions that were predicted from simulated distributions of galaxy colors.