  We study the interference of C70 fullerenes in a Talbot-Lau interferometer
with a large separation between the diffraction gratings. This permits the
observation of recurrences of the interference contrast both as a function of
the de Broglie wavelength and in dependence of the interaction with background
gases. We observe an exponential decrease of the fringe visibility with
increasing background pressure and find good quantitative agreement with the
predictions of decoherence theory. From this we extrapolate the limits of
matter wave interferometry and conclude that the influence of collisional
decoherence may be well under control in future experiments with proteins and
even larger objects.
