We have simulated calibrator observations which look through the same model atmosphere as the target source, but removed by more than 10 degrees on the sky. The details of the atmospheric phase time series detected by the calibrator are not applicable to the target source, and the target source visibilities have not been corrected for these phase errors. This is the typical state of current interferometer observations: the calibration is not fast enough to track the atmospheric phase errors. We average the calibrator visibilities to determine the extent of the decorrelation. The statistics of the phase errors on each baseline of the calibrator will be similar to the statistics of the phase errors on the target source, and the level of decorrelation will be comparable. Ignoring the phase of the averaged calibrator data, we can make a table of baseline based amplitude corrections given by
We then average the target source visibilities to the same extent,
increase the averaged target source visibilities' amplitudes by
, Fourier transform and deconvolve by the standard Fourier
sampling based point spread function.
Averaging the visibilities in time will result in smaller phase
errors, but will also limit the field of view, so this method will
only work on smallish sources. The extent of the decorrelation and
the resulting images will depend upon the averaging time used. In
order to correct for the full 
decorrelation, we must average the visibilities over several baseline
crossing times. The short baselines in our simulations are maximally
decorrelated after averaging for a minute, while the 1 km baselines
require averaging over the full 18 minute observation.