A Lens Mapping Algorithm for Weak Lensing

We develop an algorithm for the reconstruction of the two-dimensional mass distribution of a gravitational lens from the observable distortion of background galaxies. From the measured reduced shear, the lens mapping is obtained, from which a mass distribution is derived. This is unlike other methods where the convergence ("kappa") is directly obtained. We show that this method works best for sub-critical lenses, but can be applied to a critical lens away from the critical lines. For finite fields the usual mass-sheet degeneracy is shown to exist in this method as well. We show that the algorithm reproduces the mass distribution within acceptable limits when applied to simulated noisy data.