Understanding radio polarimetry - V. Making matrix self-calibration work: processing of a simulated observation

Context. This is Paper V in a series on polarimetric aperture synthesis based on the algebra of 2 x 2 matrices. Aims. It validates the matrix self-calibration theory of the preceding Paper IV and outlines the algorithmic methods that had to be developed for its application. Methods. New avenues of polarimetric self-calibration opened up in Paper IV are explored by processing a simulated observation. To focus on the polarimetric issues, it is set up so as to sidestep some of the common complications of aperture synthesis, yet properly represent physical conditions. In addition to a representative collection of observing errors, the simulated instrument includes strongly varying Faraday rotation and antennas with unequal feeds. The selfcal procedure is described in detail, including aspects in which it differs from the scalar case, and its effects are demonstrated with a number of intermediate image results. Results. The simulation's outcome is in full agreement with the theory. The nonlinear matrix equations for instrumental parameters are readily solved by iteration; a convergence problem is easily remedied with a new ancillary algorithm. Instrumental effects are cleanly separated from source properties without reference to changes in parallactic rotation during the observation. Polarimetric images of high purity and dynamic range result. As theory predicts, polarimetric errors that are common to all sources inevitably remain; prior knowledge of the statistics of linear and circular polarization in a typical observed field can be applied to eliminate most of them. Conclusions. The paper conclusively demonstrates that matrix selfcal per se is a viable method that may foster substantial advancement in the art of radio polarimetry. For its application in real observations, a number of issues must be resolved that matrix selfcal has in common with its scalar sibling, such as the treatment of extended sources and the familiar sampling and aliasing problems. The close analogy between scalar interferometry and its matrix-based generalisation suggests that one may apply well-developed methods of scalar interferometry. Marrying these methods to those of this paper will require a significant investment in new software. Two such developments are known to be foreseen or underway.