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Atmospheric turbulence is a major impediment to ground-based optical interferometry. It causes fringes to move
on ms time-scales, forcing very short exposures. Because of the semi-random phase shifts, the traditional approach
averages exposure power spectra to build signal-to-noise ratio (SNR). This incoherent average has two problems:
(1) A bias of correlated noise is introduced which must be subtracted. The smaller the visibility/the fainter the
target star, the more diffcult bias subtraction becomes. SNR builds only slowly in this case. Unfortunately, these
most difficult small visibility baselines contain most of the image information. (2) Baseline phase information is
discarded. These are serious challenges to imaging with ground based optical interferometers. But if we were able
to determine fringe phase, we could shift and integrate all the short exposures. We would then eliminate the bias
problem, improve the SNR, and we would have preserved most of the phase information. This coherent averaging
becomes possible with multi-spectral measurements. The group delay presents one option for determining phase.
A more accurate approach is to use a time-dependent model of the fringe. For the most interesting low-visibility
baselines, the atmospheric phase information can be bootstrapped from phase determinations on high-visibility
baselines using the closure relation. The NPOI, with 32 spectral channels and a bootstrapping configuration,
is well-suited for these approaches. We will illustrate how the fringe modeling approach works, compare it to
the group-delay approach, and show how these approaches can be used to derive bias-free visibility amplitude
and phase information. Coherent integration provides the highest signal-to-noise (SNR) improvement precisely
in the situations where SNR builds most slowly using incoherent averaging. Coherent integration also produces
high-SNR phase measurements which are calibration-free and thus have high real uncertainties as well. In this
paper we will show how to coherently integration on NPOI data, and how to use baseline visibilities and calibrate coherently integrated visibility amplitudes.
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