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 subcritical 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. We show that the algorithm reproduces the mass distribution within acceptable limits when applied to simulated noisy data.