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Introduction

In a beautiful paper, Hamaker, Bregman and Sault (1995) described a new formalism for understanding and analysing the measurement of polarized radiation by radio-interferometers. Although the HBS paper was restricted to a point source, Bregman later developed the formalism for extended objects. Noordam (1995) pointed out that this leads to a measurement equation for a Generic Interferometer (GI), that provides a means of unifying the polarization calibration and imaging schemes for many different synthesis arrays.

In previous notes, I described mathematical approaches to imaging and calibration based upon a number of simple versions of the measurement equation (Cornwell, 1992a, 1992b). In this document, I will revisit the analysis performed in those two documents in the light of the new measurement equation.

I will avoid statements about design of software based upon these equations. Instead, analysis and design will be deferred to a later document. Hence I will try to separate concepts that are distinct, a discipline that will be useful later during the design phase.

The purpose of this document is to consider in more detail than HBS how calibration and imaging is to be performed for the Generic Interferometer. The formalism is very general and the equations seem somewhat different from those we have seen previously in interferometry. I will show that in fact straightforward generalizations of existing methods of calibration and imaging are possible. In calibration, one can derive update equations that resemble those usually seen. In imaging, the usual concepts of dirty image, residual image, and PSF can be similarly extended. I will show that the general formulas thus derived can be simplified to special cases to yield familiar results.