  The parameter-free reconstruction of the surface-mass density of clusters of
galaxies is one of the principal applications of weak gravitational lensing.
  From the observable ellipticities of images of background galaxies, the tidal
gravitational field (shear) of the mass distribution is estimated, and the
corresponding surface mass density is constructed. The noise of the resulting
mass map is investigated here, generalizing previous work which included mainly
the noise due to the intrinsic galaxy ellipticities. Whereas this dominates the
noise budget if the lens is very weak, other sources of noise become important,
or even dominant, for the medium-strong lensing regime close to the center of
clusters. In particular, shot noise due to a Poisson distribution of galaxy
images, and increased shot noise owing to the correlation of galaxies in
angular position and redshift, can yield significantly larger levels of noise
than that from the intrinsic ellipticities only. We estimate the contributions
from these various effects for two widely used smoothing operations, showing
that one of them effectively removes the Poisson and the correlation noises
related to angular positions of galaxies. Noise sources due to the spread in
redshift of galaxies are still present in the optimized estimator and are shown
to be relevant in many cases. We show how (even approximate) redshift
information can be profitably used to reduce the noise in the mass map. The
dependence of the various noise terms on the relevant parameters (lens
redshift, strength, smoothing length, redshift distribution of background
galaxies) are explicitly calculated and simple estimates are provided.
