An investigation of the telescope based calibration methods `redundancy' and `self-cal'

We give a description of self-calibration methods currently in use at radio synthesis arrays, with special emphasis on the Westerbork Synthesis Radio Telescope (WSRT). First we will introduce the basic observables in interferometry: visibilities, including the errors that can plague them. We then discuss self-calibration techniques which use the observed data themselves to (partly) correct the instrumental and atmospheric errors. The use of redundant baseline information allows a determination of telescope based corrections independent of knowledge about the sky brightness distribution. The method is very powerful: a map with greatly enhanced dynamic range can be obtained in a single step. We investigate the sensitivity of the redundancy solutions to noise and interference. We find that for arrays that are not optimally redundant there can be unwanted side effects such as a noise increase and a relatively high sensitivity to interference. Another calibration technique, self-calibration, solves for all complex telescope gains using a model of the sky brightness distribution. This method is subjected to a similar analysis, which now also includes an investigation of the dependence of the solution on the assumed model. In particular, we point out the artificial noise decrease and the potential removal of structure inherent in the self-calibration method. We also discuss constrained self-calibration which solves only for the remaining free parameters after redundant baseline calibration has been applied. We show that the noise increase in the redundancy solution can be reduced by about a factor of 2 by redetermining the ill-constrained telescope gains using a self-cal technique, once a good model of the sky brightness has been obtained. An investigation of algorithms which combine model information and redundant information leads to the conclusion that they work well, i.e., improve on both redundancy and self-calibration, in cases where a reasonable model can be obtained on (a possibly limited set of) the non-redundant baselines. They may fail (just like self-cal) if no adequate first model can be obtained, not even for a limited set of baselines.