Clustered calibration : An improvement to radio interferometric direction-dependent self-calibration

The new generation of radio synthesis arrays, such as Low Frequency Array and Square Kilometre Array, have been designed to surpass existing arrays in terms of sensitivity, angular resolution and frequency coverage. This evolution has led to the development of advanced calibration techniques that ensure the delivery of accurate results at the lowest possible computational cost. However, the performance of such calibration techniques is still limited by the compact, bright sources in the sky, used as calibrators. It is important to have a bright enough source that is well distinguished from the background noise level in order to achieve satisfactory results in calibration. This paper presents `clustered calibration' as a modification to traditional radio interferometric calibration, in order to accommodate faint sources that are almost below the background noise level into the calibration process. The main idea is to employ the information of the bright sources' measured signals as an aid to calibrate fainter sources that are nearby the bright sources. In the case where we do not have bright enough sources, a source cluster could act as a bright source that can be distinguished from background noise. For this purpose, we construct a number of source clusters assuming that the signals of the sources belonging to a single cluster are corrupted by almost the same errors. Under this assumption, each cluster is calibrated as a single source, using the combined coherencies of its sources simultaneously. This upgrades the power of an individual faint source by the effective power of its cluster. The solutions thus obtained for every cluster are assigned to each individual source in the cluster. We give performance analysis of clustered calibration to show the superiority of this approach compared to the traditional unclustered calibration. We also provide analytical criteria to choose the optimum number of clusters for a given observation in an efficient manner.