  Gravitational lensing magnifies the luminosity of galaxies behind the lens.
We use this effect to constrain the total mass in the cluster Abell 1689 by
comparing the lensed luminosities of background galaxies with the luminosity
function of an undistorted field. Since galaxies are assumed to be a random
sampling of luminosity space, this method is not limited by clustering noise.
We use photometric redshift information to estimate galaxy distance and
intrinsic luminosity. Knowing the redshift distribution of the background
population allows us to lift the mass/background degeneracy common to lensing
analysis. In this paper we use 9 filters observed over 12 hours with the Calar
Alto 3.5m telescope to determine the redshifts of 1000 galaxies in the field of
Abell 1689. Using a complete sample of 151 background galaxies we measure the
cluster mass profile. We find that the total projected mass interior to
0.25h^(-1)Mpc is (0.48 +/- 0.16) * 10^(15)h^(-1) solar masses, where our error
budget includes uncertainties from the photometric redshift determination, the
uncertainty in the off-set calibration and finite sampling. This result is in
good agreement with that found by number count and shear-based methods and
provides a new and independent method to determine cluster masses.
