  The reconstruction of the density profile in clusters of galaxies from the
distortion of the images of faint background galaxies is reconsidered. The
inversion formula of Kaiser \& Squires is known to provide a quantitative way
to perform this reconstruction; however, the practical application of this
formula faces two problems of principle (besides problems related to the
analysis of the observational data): (1) the shear distribution of a lens
cannot be inferred from the distortion of images, but only a combination of
shear and surface mass density can be observed. (2) The inversion formula is
exact only if one assumes observational data on the whole lens plane, whereas
in reality, the size of the data field is limited by the size of the CCD. We
have considered a possible solution to the first problem in a previous paper.
Here we consider the second problem. It is shown that the application of the
inversion formula to a finite data field induces systemmatic boundary effects.
An alternative inversion formula is derived, based on some recently published
results by Kaiser. We demonstrate, using synthetic data, that this new
inversion formula which does not require an extrapolation of the data beyond
the observed region, yields results which are comparable with those from the
Kaiser \& Squires inversion in their `noise levels', but lack the systemmatic
boundary effects.

Astrophysics