Calibration of Coherently Integrated Visibilities

Coherent integration is an analysis approach which, can greatly increase the SNR of optical interferometric visibilities compared to those computed by the traditional squared visibility power spectrum technique. Co- herent integration relies on phase-referencing, optimally through post-processing fringe-tracking, to effectively create long coherent integrations of the fringe. At the Navy Precision Optical Interferometer (NPOI) this phase- referencing is achieved by a combination of wavelength bootstrapping and baseline bootstrapping. The result is that the complex visibility with full phase information is retrieved and that the poor noise associated with the power spectrum approach is greatly reduced. For small visibilities, which are most important in resolving objects, the SNR can be improved sometimes by orders of magnitudes, sometimes making the difference between easy and practically impossible observations. The fringe-tracking portion of coherent integration is limited by the SNR of the tracking signal and the noise of that causes some fringe smearing which must be calibrated. In this paper we develop a theoretical model of the resulting fringe smearing and its correction. We then demonstrated its validity through simulation and on observations from the NPOI.