  We present a method to estimate the lensing potential from massive galaxy
clusters for given observational X-ray data. The concepts developed and applied
in this work can easily be combined with other techniques to infer the lensing
potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an
overall best fit model for the lensing potential. After elaborating on the
physical details and assumptions the method is based on, we explain how the
numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a
central part. Our reconstruction method is tested on simulated galaxy clusters
with a spherically symmetric NFW density profile filled with gas in hydrostatic
equilibrium. We describe in detail how these simulated observational data sets
are created and how they need to be fed into our algorithm. We test the
robustness of the algorithm against small parameter changes and estimate the
quality of the reconstructed lensing potentials. As it turns out we achieve a
very high degree of accuracy in reconstructing the lensing potential. The
statistical errors remain below 2.0% whereas the systematical error does not
exceed 1.0%.
