Beam Shape Calibration for Multi-Beam Radio Astronomical Phased Arrays

The ability of phased array systems to form multiple beams simultaneously holds great promise to revolutionise radio astronomy by enlarging the instantaneous sky coverage. Currently, measurements obtained by different beams are largely treated as separate observations. In this paper, a new approach to beam shape calibration, i.e., the calibration of direction dependent instrumental gains, is presented, in which the fact that these observations are done simultaneously is adequately exploited. It follows from imposing a novel spatial constraint on the direction dependent instrumental gain model. It may provide better calibration performance and may even allow beam shape calibration in scenarios in which the observations with the individual beams provide insufficient information to do so when they are treated as separate observations.