Cluster deprojection combining multiple observable data sets

In this paper a general, parameter-free algorithm for the deprojection of o bserved, two-dimensional cluster images is proposed. The algorithm is based on the Richardson-Lucy algorithm for the rectification of observed distrib utions, and it combines multiple sets of observable data from clusters of g alaxies - weak lensing (lensing potential psi), X-ray (X-ray surface bright ness S-x), and Sunyaev-Zel'dovich (temperature decrement DeltaT(SZ)) images - to obtain information on the structure along the line-of-sight, namely t he 3-dim. gravitational potential theta. For the derivation of this multiple-data Richardson-Lucy deprojection algor ithm we specify a geometrical model for the cluster assuming axial symmetry only. We demonstrate the quality of the reconstructions using gas-dynamica l simulations assuming an inclination angle for the cluster. The achieved d eprojections are shown to yield a stable and unique reconstruction of the 3 -dim. structure of the cluster. Strategies for determining the inclination angle and the weight factors used for the reconstruction are discussed. In the end we provide an outlook on the suitability of the algorithm for pract ical applications to true observational data.