Liying Wei and Stefan J. Wijnholds, "Joint calibration and imaging for phased array radio telescopes," Monthly Notices of the Royal Astronomical Society, V483, no. 4, pp5672-5686, March 2019.
We propose a novel compressed sensing based self-calibration and imaging algorithm for phased array radio telescopes, whose receiving elements are subject to the same direction dependent effects. Our approach simultaneously estimates the apparent sky brightness distribution and the direction independent receiver path gains from the observational data. The estimated source model may contain point sources and extended structures. Moreover, our algorithm allows to tune the accuracy of gain calibration and reconstructed image quality by controlling the detail level in the reconstructed image by a threshold value. We demonstrate the accuracy, robustness to extremely low Signal-to-Noise Ratio (SNR) and large sensor phase variability using Monte Carlo simulations for various array configurations. We also display the main advantages of our algorithm on actual data from a Low Band Antenna (LBA) station of the Low Frequency Array (LOFAR): firstly, our algorithm is sufficiently fast for practical applications such as LOFAR station calibration; secondly, the gain calibration accuracy improves with increasingly detailed reconstructed image; thirdly, the method is capable of handling a complex observed field that is a combination of a few dominant point sources and diffuse emission from the Galactic plane. The latter point is interesting as it poses a difficult scenario for sky source model based calibration approaches, in which the short baselines are often flagged to avoid visibility modelling issues. This feature could make our method very attractive for calibration of the Square Kilometre Array (SKA) or a future low-frequency instrument in space.
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