  Interferometers with single particles are susceptible for dephasing
perturbations from the environment, such as electromagnetic oscillations or
mechanical vibrations. On the one hand, this limits sensitive quantum phase
measurements as it reduces the interference contrast. On the other hand, it
enables single-particle interferometers to be used as sensitive sensors for
electromagnetic and mechanical perturbations. Recently, it was demonstrated
experimentally, that a second-order correlation analysis can decrease the
shielding and damping requirements significantly. Thereby, the relevant
matter-wave characteristics and perturbation parameters could be extracted from
the correlation analysis of a "washed-out" interference pattern and the
undisturbed interferogram could be reconstructed. This method can be applied to
all interferometers, that produce a spatial fringe pattern on a detector with
high spatial and temporal single-particle resolution. In this article, we
present and discuss in detail the used two-dimensional second-order correlation
theory for multifrequency perturbations. The derivations of an explicit and
approximate solution of the correlation function and corresponding amplitude
spectra are provided. It is explained, how the numerical correlation function
is extracted from the measurement data. Thereby, the influence of the temporal
and spatial discretization step size on the extracted parameters is analyzed.
The influence of noise on the correlation function and amplitude spectrum is
calculated and numerically cross-checked by a comparison of our theory with
numerical single-particle simulations. Our method can also be applied for the
analysis of broad-band frequency noise, dephasing the interference pattern.
Using Gaussian distributed noise in the simulations, we demonstrate that the
relevant matter-wave parameters and the applied perturbation spectrum can be
revealed.
