We previously simulated a simple version of the primary beam as one of the fundamental direction dependent effects in an interferometer observation. As mentioned in the intro to that simulation, the beamshapes themselves are often complicated, with structure extending beyond the main lobe. They are naturally functions of frequency (although that can also involve subtle effects that are not obvious) but they can also be strongly time dependent. How they vary in time can also vary as a function of direction, so traditional '2GC' calibration where a single complex gain correction is applied to each antenna (or each feed) won't correct the sources that are blighted by this.

(Primary beams also introduce instrumental polarization effects: the elements in the array generally have a pair of dipoles that are sensitive to orthogonal modes of polarization. For aperture arrays the projection effects can lead to the instrumental polarization being quite severe, and for dish arrays it is definitely not neglible as the two receptors can never be co-spatial in the optical focal point.)

Although the title doesn't suggest it, this section introduces something that is very important in the context of direction dependent effects. Your interferometer doesn't care if a source is actually flaring over the course of your observation due to some astrophysical process, or if it's apparently variable due to an instrumental effect. Either way, they will both cause problems in your continuum image.

Here we simulate a source that flares over the duration of the observation. It's probably unlikely that a real radio source would do what we're about to pretend it does, and an instrumental effect is also unlikely to cause this, but it illustrates the point nicely. It also introduces the power of additive (or subtractive) simulations.