  A very interesting quantum mechanical effect is the emergence of
gravity-induced interference, which has already been detected. This effect also
shows us that gravity is at the quantum level not a purely geometric effect,
the mass of the employed particles appears explicitly in the interference
expression. In this work we will generalize some previous results. It will be
shown that the introduction of a second order approximation in the propagator
of a particle, immersed in the Earth's gravitational field, and whose
coordinates are being continuously monitored, allows us to include, in the
corresponding complex oscillator, a frequency which now depends on the geometry
of the source of the gravitational field, a fact that is absent in the case of
a homogeneous field. Using this propagator we will analyze the interference
pattern of two particle beams whose coordinates are being continuously
monitored. We will compare our results againt the case of a homogeneous field,
and also against the measurement ouputs of the Colella, Overhauser, and Werner
experiment, and find that the difference in the dependence upon the geometry of
the source of the gravitational field could render detectable differences in
their respective measurement outputs.
