Self-Calibration, Imaging, and Deconvolution

Even after global fringe fitting, averaging, and editing, the phases on a VLBA target source can still vary rapidly with time. Most of these variations are due to inadequate removal of antenna-based atmospheric phases, but some variations also can be caused by an inadequate model of the source structure during fringe fitting. If the VLBA target source is sufficiently strong and if absolute positional information is not needed, then it is possible to reduce these phase fluctuations by looping through cyles of Fourier transform imaging and deconvolution, combined with phase self-calibration in a time interval shorter than that used for the fringe fit (Cornwell 1995; Walker 1995b; Cornwell & Fomalont 1999). Fourier transform imaging is straightforward (Briggs, Schwab, & Sramek 1999), and done with AIPS task IMAGR or the Caltech program DIFMAP (Shepherd 1997). The resulting VLBI images are deconvolved to rid them of substantial sidelobes arising from relatively sparse sampling of the $u$-$v$ plane (Cornwell, Braun, & Briggs 1999). Such deconvolution is achieved with AIPS tasks based on the CLEAN or Maximum Entropy methods or with the Caltech program DIFMAP.

Phase self-calibration just involves minimizing the difference between observed phases and model phases based on a trial image, by solving for antenna-based instrumental phases (Cornwell 1995; Walker 1995b; Cornwell & Fomalont 1999). After removal of these antenna-based phases, the improved visibilities are used to generate an improved set of model phases, usually based on a new deconvolved trial image. This process is iterated several times until the phase variations are substantially reduced. The method is then generalized to allow estimation and removal of complex instrumental antenna gains, leading to further image improvement. Both phase and complex self-calibration are accomplished with the AIPS task CALIB and with program DIFMAP in the Caltech VLBI Analysis Programs. Self-calibration should only be done if the VLBA target source is detected with sufficient signal-to-noise in the self-calibration time interval (otherwise, fake sources can be generated!) and if absolute positional information is not needed.

The useful field of view in VLBI images can be limited by finite bandwidth, integration time, and non-coplanar baselines (Wrobel 1995; Cotton 1999b; Bridle & Schwab 1999; Perley 1999b); the first two of these effects have been discussed in some detail in Section 13. Measures of image correctness - image fidelity and dynamic range - are discussed by Walker (1995a) and Perley (1999a).