Beam modelling accuracy for flux calibration of phased array radio telescopes

The gain of radio telescopes is calibrated using well-known radio astronomical sources. Due to the limited number of suitable calibration sources, the angle between the directions towards the calibrator and towards the observed field can be as large as similar to 60 degrees. This poses an instrument characterization and modelling challenge for phased array radio telescopes like LOFAR and SKA, which are steered electronically, as the gain of the antennas varies over the sky. We derive a requirement on the accuracy of the instrument model and assess the impact of two simplified calculations of the main beam peak gain of the subarrays (stations) of the low-frequency receiving system of the SKA. We show that station beam peak gain modelling can be simplified by using the average EEP, while the isolated antenna pattern is an oversimplification.