  A generalized description of Talbot-Lau interference with matter waves is
presented, which accounts for arbitrary grating interactions and realistic beam
characteristics. The dispersion interaction between the beam particles and the
optical elements strongly influences the interference pattern in this
near-field effect, and it is known to dominate the fringe visibility if
increasingly massive and complex particles are used. We provide a general
description of the grating interaction process by combining semiclassical
scattering theory with a phase space formulation. It serves to systematically
improve the eikonal approximation used so far, and to assess its regime of
validity.
