If the target and calibrator are separated by an angle greater
than that subtended by the atmospheric cells responsible for the
amplitude and phase variations, the fluctuations seen in the
calibrator data may not correlate with those in the target data.
Corrections interpolated from the calibrator observations into the
rest of the data under these circumstances may worsen the
atmospheric amplitude and phase noise on the target by a factor of
. At the other extreme, if the target and calibrator
are typically within the same isoplanatic patch, the
fluctuations observed in the calibrator will faithfully track those
occurring in the target. Amplitude and phase corrections interpolated
into the target data from the calibrator data in time series may then
greatly improve the quality of the final image. The basic problem is
that the scale size of the isoplanatic patch will vary from day to day
and even from hour to hour (as a function of the
``weather'' and of the elevation of your target above
the horizon). It is therefore difficult to judge how reliable
amplitude and phase referencing from a distant calibrator may be
before the observations begin.
If you cannot, or do not wish to, rely on self-calibration to remove atmospheric effects from your data, you should choose external calibrator(s) as close as possible to the target(s), ideally within a degree or so of them. You must then hope that the amplitude and phase stability found in the calibrator data meet the needs of your experiment, and that the scale of the isoplanatic patch is typically greater than the calibrator-target separation.
If the within-scan and scan-to-scan amplitude or
phase fluctuations on a calibrator a degree or two from your target are
small (less than 10% or 
), it is unlikely that much larger
fluctuations are occurring on your target. Correcting the rest
of the data using long-term averages of the calibrator phases is
then likely to improve matters.
If you see large, rapid fluctuations on the calibrator, you are in trouble, which may or may not be mitigated by correcting the rest of the data by local (point-to-point) interpolation in the fluctuations. Because such interpolation may indeed make matters worse, you might then try making images (a) after long-term averaging, and (b) after local interpolation, of phase corrections from the calibrators. You can then judge empirically which gives better final images--using the final dynamic range, r.m.s. noise level, and/ or any prior knowledge about the source to make your judgment.
Deleting data from some or all baselines during periods of unusually bad phase stability will usually improve the quality of images made by external calibration. Imaging with less data but with good amplitude and phase stability can give better results than imaging with much poorly-calibrated data--if the synthesized beam is closer to the theoretical ``dirty'' beam, deconvolution algorithms work better, increasing the dynamic range of the images. Note that tapering the u-v data down-weights the visibilities from the longer baselines where phases are less stable. Be ready to sacrifice resolution in favor of forming the theoretical beam more closely when the phases are unstable, if your astronomical goals can be met at lower resolution.
Observers doing detection experiments are usually forced to use external calibration. Fortunately, they do not usually require such high dynamic range (and such good phase stability) as observers imaging bright emission complexes. The loss of point source response produced by poor phase stability in a detection experiment can be estimated by calibrating with a long (e.g., >2 hour) interpolation of the gains, then imaging the calibrators and comparing their apparent flux densities in these images with their assumed values.