IMPROVING THE ACCURACY OF MASS RECONSTRUCTIONS FROM WEAK LENSING - FROM THE SHEAR MAP TO THE MASS-DISTRIBUTION

In this paper we provide a statistical analysis of the parameter-free method often used in weak lensing mass reconstructions. It is found th at a proper assessment of the errors involved in such a non-local anal ysis requires the study of the relevant two-point correlation function s. After calculating the two-point correlation function for the reduce d shear, we determine the expected error on the inferred mass distribu tion and on other related quantities, such as the total mass, and deri ve the error power spectrum. This allows us to optimize the reconstruc tion method, with respect to the kernel used in the inversion procedur e. The optimization process can also be carried out on the basis of a variational principle. In particular, we find that curl-free kernels a re bound to lead to more accurate mass reconstructions. Our analytical results clarify the arguments and the numerical simulations by Seitz & Schneider (1996).