  We study the loss of spatial coherence in the extended wave function of
fullerenes due to collisions with background gases. From the gradual
suppression of quantum interference with increasing gas pressure we are able to
support quantitatively both the predictions of decoherence theory and our
picture of the interaction process. We thus explore the practical limits of
matter wave interferometry at finite gas pressures and estimate the required
experimental vacuum conditions for interferometry with even larger objects.
