Probabilistic direction-dependent ionospheric calibration for LOFAR-HBA

Direction dependent calibration and imaging is a vital part of producing deep, high fidelity, high-dynamic range radio images with a wide-field low-frequency array like LOFAR. Currently, state-of-the-art facet-based direction dependent calibration algorithms rely on the assumption that the isoplanatic-patch size is much larger than the separation between bright in-field calibrators. This assumption is often violated due to the dynamic nature of the ionosphere, and as a result direction dependent errors affect image quality between calibrators. In this paper we propose a probabilistic physics-informed model for inferring ionospheric phase screens, providing a calibration for all sources in the field of view. We apply our method to a randomly selected observation from the LOFAR Two-Metre Sky Survey archive, and show that almost all direction dependent effects between bright calibrators are corrected and that the root-mean-squared residuals around bright sources is reduced by 32\% on average.