Coherency-matrix formulation of self-calibration and some of its salient properties

Abstract Self-calibration has been known so far only in a scalar formulation. This paper translates it to a vector/matrix form that does justice to the true nature of the electromagnetic field. A number of interesting properties are derived for the case that a calibrator source known to be unpolarised can be used. This is often not the case; thus this paper is primarily a demonstration of the way matrix methods can be used in the analysis of polarisation self-calibration and to study unorthodox observing modes. Calibration on the unpolarised calibrator aligns the system to a very specific state. After this, self-calibration on an unknown polarised source will yield a source model with correct total brightness and percentage-polarisation distributions, but with its polarised-visibility vector rotated in QUV space. For an array with nominally identical feeds, this rotation may be only partly eliminated by a priori assumptions on the feeds: at least one phase measurement is needed in addition. For an inhomogeneous array (e.g., the EVN with linearly polarised feeds), feed parameters and receiver phases are coupled in such a way that the a priori feed characteristics alone suffice.