  We present a new method for measuring the projected mass distributions of
galaxy clusters. The gravitational amplification is measured by comparing the
joint distribution in redshift and magnitude of galaxies behind the cluster
with that of field galaxies. We show that the total amplification is directly
related to the surface mass density in the weak field limit, and so it is
possible to map the mass distribution of the cluster. The method is shown to be
limited by discreteness noise and galaxy clustering behind the lens. Galaxy
clustering sets a lower limit to the error along the redshift direction, but a
clustering independent lensing signature may be obtained from the magnitude
distribution at fixed redshift. Statistical techniques are developed for
estimating the surface mass density of the cluster. We extend these methods to
account for any obscuration by cluster halo dust, which may be mapped
independently of the dark matter. We apply the method to a series of numerical
simulations and show the feasibility of the approach. We consider approximate
redshift information, and show how the mass estimates are degraded.
