  We present a theoretical framework to describe the effects of decoherence on
matter waves in Talbot-Lau interferometry. Using a Wigner description of the
stationary beam the loss of interference contrast can be calculated in closed
form. The formulation includes both the decohering coupling to the environment
and the coherent interaction with the grating walls. It facilitates the
quantitative distinction of genuine quantum interference from the expectations
of classical mechanics. We provide realistic microscopic descriptions of the
experimentally relevant interactions in terms of the bulk properties of the
particles and show that the treatment is equivalent to solving the
corresponding master equation in paraxial approximation.
