MeqTrees and direction-dependent effects

The classical self-calibration algorithm employed in radio interferometry associates a single direction-independent complex gain term (which can have a complicated behaviour in frequency and time) with each antenna of the interferometer. This has been spectacularly successful, and has allowed dynamic range (DR) in excess of 10⁶:1 to be reached [1], but only for relatively narrow fields with a single dominant source of emission. In many other regimes of current and future instruments, direction-dependent effects (DDEs) - that is, effects that vary across the field of view (FoV) as well as between antennas - become significant enough to produce DR-limiting calibration artefacts. The Westerbork Synthesis Radio Telescope (WSRT) is a particularly low-DDE instrument due to its careful design, but at sufficiently high DR, clear DDE-related artefacts are also evident (Fig. 1, left). In a previous study [2], we applied the differential gains (DG) technique using the MeqTrees package [3] to eliminate these artefacts. This was very successful at producing a noise-limited image (Fig. 1, right), but did not explain the ultimate cause of the DDEs in the 3C 147 dataset. The per-antenna DG solutions for the 3C 147 field showed continuity in time and consistency across frequency bands [2], which was a clear indication of some “global” effect at work. Crucially, this also demonstrated that sources as faint as few mJy could be used to solve for differential gains, and could thus be employed as “calibration beacons” in the various closed-loop methods proposed for the calibration of DDEs.