We investigate the accuracy of an experimental reconstruction of the W
igner function of the transverse motion in an atom beam using numerica
l wave packet simulations. For the example of a superposition of two G
aussians (the outcome of a double slit, for example) we study in detai
l the influence of experimental restraints on the quality of the recon
struction. For the potential candidate, metastable helium, we demonstr
ate that an accurate reconstruction of the Wigner function, especially
of its negative parts, is well within experimental reach.