We investigate the influence of a Bose-Einstein condensate on the cohe
rence properties of a traversing atomic beam. We derive a master equat
ion describing the interaction between beam atoms and the condensate i
n s-wave approximation. Scattering rates are calculated and compared w
ith the case of an ordinary Boltzmann gas. Special attention is paid t
o the decoherence of the beam, i.e., the decay of spatial coherence in
the presence of the condensate. As an application, we explicitly calc
ulate the visibility of the interference pattern in a double-slit expe
riment and indicate signs for the onset of the condensation.