Mapping the dark matter with weak gravitational lensing

We consider the problem of reconstructing the projected mass distribution in clusters from coherent distortions of background galaxies. The ellipticity of a background galaxy provides an estimate of the trace-free components of the tidal field second partial derivative of {PHI with respect to θᵢ_, θⱼ_} where PHI (θ) is the two-dimensional potential generated by the surface density SIGMA (θ). We present a technique for inverting this problem. The resulting surface density contains a strong, but incoherent, random component arising from the random intrinsic galaxy ellipticities. This can be removed by filtering. Our method is very similar in form to that of Tyson et al. , and the latter is given a rigorous interpretation as a particular implementation of filtering. We present simulations to illustrate the application of the method.