Calibration of an SKA-low prototype station using holographic techniques

Performance of digitally beamformed phased arrays relies on accurate calibration of the array by obtaining gains of each antenna in the array. The stations of the Square Kilometer Array-Low (SKA-Low) are such digital arrays, where the station calibration is currently performed using conventional interferometric techniques. An alternative calibration technique similar to holography of dish based telescopes has been suggested in the past. In this paper, we develop a novel mathematical framework for holography employing tensors, which are multi-way data structures. Self-holography using a reference beam formed with the station under test itself and cross-holography using a different station to obtain the reference beam are unified under the same formalism. Besides, the relation between the two apparently distinct holographic approaches in the literature for phased arrays is shown, and we show that under certain conditions the two methods yield the same results. We test the various holographic techniques on an SKA-Low prototype station Aperture Array Verification System 2 (AAVS2) with the Sun as the calibrator. We perform self-holography of AAVS2 and cross-holography with simultaneous observations carried out with another station Engineering Development Array 2. We find the results from the holographic techniques to be consistent among themselves as well as with a more conventional calibration technique.