Ghost-busting

[JSKenyon]

Following some very cursory experiments, I can confirm that ghosts are indeed a concern. Much of this is rehashing the findings of ghost papers, but in the context of CubiCal:

1. Ghosts can and will appear during calibration based on completeness of the input model. This places some fundamental limits on how deep one can safely deconvolve whilst remaining certain that ghosts sources are not being frozen into the model. In theory, doing more, shallower self-cal loops can mitigate this problem. Additionally, we likely need to move away from component models which are increasingly difficult to generate.
2. Phase-only calibration (whether amplitude-free, true phase-only or normalised amp-phase) produces more noticeable ghosts. Note that all these methods produce effectively identical images/ghosts. This is an important discovery.
3. Amplitude calibration can "hide" ghosts as they will be affected by the gain amplitude. Practically we don't care if ghosts live in the noise, but this can be dangerous on fields around sources like 3C147. Even small errors can lead to very obvious ghosts.

[JSKenyon]

Some of these ghosts are explained by the use of the incorrect residual in the parameterised solvers. There is a degeneracy between amplitude (which may go negative if we let it) and a 180 degree phase rotation. QuartiCal no longer has this problem so the phase/amp only problem will be less severe. Model completeness is a separate issue.