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 θ_i_, θ_j_} 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.