We discuss methods of interferometric data reduction using coherent integration of fringe visibility. Unlike incoherent estimation techniques which discard the phase of interference, coherent integration retains as a complex quantity the contribution from each frame (or scan). In order to integrate these coherently, one must apply an OPD correction (or "phase reference") to compensate for random atmospheric pathlength fluctuations.
In an instrument with substantial bandwidth, it is also necessary to correct for fixed and random dispersion. The integrity of phase functions obtained is dependent on correct modelling of fixed optical phase functions (obtained from a calibrator observation), dispersion from air filled delay-lines (calibratable in principle), and averaging over time to reduce the effect of random atmospheric water vapor dispersion.
To achieve the best performance, it is necessary to include a dispersion tracker as well as tracking achromatic OPD, applying each as a phase correction as a function of time and of optical frequency.
Using MIDI, the N band instrument of the VLTI, which has a wide bandwidth, it is often possible to uninterruptedly track random dispersion fluctuations over an observation. Plots of dispersion fluctuations due to water vapor above the VLTI are shown, which are used (along with OPD tracking) to coherently integrate raw frames from that instrument.
The resulting complex visibility includes a unique phase delay signature reflecting the source structure. A residual "water-vapor-like" phase may be present due to unmonitored humidity in the delay line paths, and to incomplete averaging of (nominally zero-mean) atmospheric water vapor fluctuations. Nevertheless, the use of visibility phase results corrupted by random dispersion is possible.