Revisiting the radio interferometer measurement equation. II. Calibration and direction-dependent effects

Context. Paper I of the series re-derived the radio interferometry measurement equation (RIME) from first principles, and extended the Jones formalism to the full-sky case, incorporating direction-dependent effects (DDEs).
Aims: This paper aims to describe both classical radio interferometric calibration (selfcal and related methods), and the recent developments in the treatment of DDEs, using the RIME-based mathematical framework developed in Paper I. It also aims to demonstrate the ease with which the various effects can be described and understood.
Methods: The first section of this paper uses the RIME formalism to describe self-calibration, both with a full RIME, and with the approximate equations of older software packages, and shows how this is affected by DDEs. The second section gives an overview of real-life DDEs and proposed methods of dealing with them.
Results: A formal RIME-based description and comparison of existing and proposed approaches to the problem of DDEs.