Cluster lens reconstruction using only observed local data

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.