  The weak distortions of high-redshift galaxies caused by gravitational light
deflection near clusters of galaxies can be used to reconstruct the projected
(two-dimensional) surface mass density of intermediate redshift clusters. This
technique, pioneered by Tyson, Valdes & Wenk, and Kaiser & Squires, is
reconsidered in the present paper, where we generalize the inversion equation
found by Kaiser & Squires (KS) in several respect. Adopting a different
smoothing procedure for the discreetly sampled data (individual galaxy images),
we effectively reduce the shot noise in the KS procedure. In particular we show
that the best density reconstructions are obtained if the smoothing scale is
adopted to the `strength of the signal', which yields a better resolution near
the center of the cluster where the distortions are strongest. Furthermore, we
point out the importance of boundary effects and demonstrate their disastrous
impact on rectangular data fields (CCDs) with large side ratio. Most important,
however, is the generalization of the KS method to critical clusters, i.e., to
such clusters which are capable of producing multiple images and giant luminous
arcs. The corresponding modifications of the inversion procedure are severe; in
particular, the resulting inversion equation is much more difficult to solve.
As we pointed out in a previous paper (Schneider & Seitz), there exists a local
degeneracy if the cluster is critical. We have developed an iteration procedure
to solve the inversion equation, which we demonstrate to yield a very accurate
