  This work investigates a particular class of artefacts, or ghost sources, in
radio interferometric images. Earlier observations with (and simulations of)
the Westerbork Synthesis Radio Telescope (WSRT) suggested that these were due
to calibration with incomplete sky models. A theoretical framework is derived
that validates this suggestion, and provides predictions of ghost formation in
a two-source scenario. The predictions are found to accurately match the result
of simulations, and qualitatively reproduce the ghosts previously seen in
observational data. The theory also provides explanations for many previously
puzzling features of these artefacts (regular geometry, PSF-like sidelobes,
seeming independence on model flux), and shows that the observed phenomenon of
flux suppression affecting unmodelled sources is due to the same mechanism. We
demonstrate that this ghost formation mechanism is a fundamental feature of
calibration, and exhibits a particularly strong and localized signature due to
array redundancy. To some extent this mechanism will affect all observations
(including those with non-redundant arrays), though in most cases the ghosts
remain hidden below the noise or masked by other instrumental artefacts. The
implications of such errors on future deep observations are discussed.
