  Surface brightness is a fundamental observational parameter of galaxies. We
show, for the first time in detail, how it can be used to obtain photometric
redshifts for galaxies, the $\mu$-PhotoZ method.
  We demonstrate that the Tolman surface brightness relation, $\mu \propto
(1+z)^{-4}$, is a powerful tool for determining galaxy redshifts from
photometric data.
  We develop a model using $\mu$ and a color percentile (ranking) measure to
demonstrate the $\mu$-PhotoZ method. We apply our method to a set of galaxies
from the SHELS survey, and demonstrate that the photometric redshift accuracy
achieved using the surface brightness method alone is comparable with the best
color-based methods.
  We show that the $\mu$-PhotoZ method is very effective in determining the
redshift for red galaxies using only two photometric bands. We discuss the
properties of the small, skewed, non-gaussian component of the error
distribution.
  We calibrate $\mu_r, (r-i)$ from the SDSS to redshift, and tabulate the
result, providing a simple, but accurate look up table to estimate the redshift
of distant red galaxies.
