  Imperfections in dilute atomic beams propagating in the paraxial regime and
in potentials of cylindrical symmetry have been characterized experimentally
through the measurement of a parameter analogous to a beam quality factor [Riou
et al., Phys. Rev. Lett. 96, 070404 (2006)]. We propose a generalization of
this parameter, which is suitable to describe dilute matter waves propagating
beyond the paraxial regime and in fully general linear atom-optical systems.
The presented quality factor shows that the atomic beam symmetry can be traded
for a better transverse collimation.
