The measurement of fringe visibility (correlation) in a long baseline optical/infrared astronomical interferometer may be performed through a coherent integration of noisy data if a measurement of the phase producing the interference is available. That phase reference can be applied in hardware by rapidly servoing a delay line, or may be applied offline to a data stream produced while the phase was being monitored. In a spectrally dispersed detection system, the same data may be used for atmospheric delay tracking as well as visibility estimation. In that configuration one measures not only the magnitude, but the phase of the visibility. The squared magnitude of the measured interference need never be formed, so that all averaging is performed on the unbiased measurements of complex correlation, optimally reducing the effect of measurement noise. However accurate results depend on careful modeling of the system and correction for a number of effects which are detailed in this paper. The results, supported by simulations, are applicable to visibility determination in a wide range of astronomical interferometers utilizing analog detection or photon counting. In particular these methods are being developed and proposed for use with the MIDI 10 micron interferometric instrument being built for the VLTI.
Jeffrey A. Meisner,
"Coherent integration of fringe visibility: a generalized approach", Proc. SPIE 4006, Interferometry in Optical Astronomy, (5 July 2000); doi: 10.1117/12.390188; https://doi.org/10.1117/12.390188