  Matter-wave interferometry is a highly sensitive tool to measure small
perturbations in a quantum system. This property allows the creation of
precision sensors for dephasing mechanisms such as mechanical vibrations. They
are a challenge for phase measurements under perturbing conditions that cannot
be perfectly decoupled from the interferometer, e.g. for mobile interferometric
devices or vibrations with a broad frequency range. Here, we demonstrate a
method based on second-order correlation theory in combination with Fourier
analysis, to use an electron interferometer as a sensor that precisely
characterizes the mechanical vibration spectrum of the interferometer. Using
the high spatial and temporal single-particle resolution of a delay line
detector, the data allows to reveal the original contrast and spatial
periodicity of the interference pattern from "washed-out" matter-wave
interferograms that have been vibrationally disturbed in the frequency region
between 100 and 1000 Hz. Other than with electromagnetic dephasing, due to
excitations of higher harmonics and additional frequencies induced from the
environment, the parts in the setup oscillate with frequencies that can be
different to the applied ones. The developed numerical search algorithm is
capable to determine those unknown oscillations and corresponding amplitudes.
The technique can identify vibrational dephasing and decrease damping and
shielding requirements in electron, ion, neutron, atom and molecule
interferometers that generate a spatial fringe pattern on the detector plane.
