Spatially constrained direction dependent calibration

Direction dependent calibration of widefield radio interferometers estimates the systematic errors along multiple directions in the sky. This is necessary because with most systematic errors that are caused by effects such as the ionosphere or the receiver beam shape, there is significant spatial variation. Fortunately, there is some deterministic behavior of these variations in most situations. We enforce this underlying smooth spatial behavior of systematic errors as an additional constraint onto spectrally constrained direction dependent calibration. Using both analysis and simulations, we show that this additional spatial constraint improves the performance of multi-frequency direction dependent calibration.