  We extend the theory of matter-wave interferometry of point-like particles to
non-spherical objects by taking the orientational degrees of freedom into
account. In particular, we derive the grating transformation operator, that
maps the impinging state onto the outgoing state, for a general,
orientation-dependent interaction potential between the grating and the
molecule. The grating operator is then worked out for the diffraction of
symmetric top molecules from standing light waves, and the resulting
interference pattern is calculated in the near-field. This allows us to
identify a signature of the orientational degrees of freedom in near-field
matter-wave experiments.
