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.