Low order beam models for the calibration of large aperture arrays for radio astronomy; The case of the SKA-low instrument

Modern aperture array radio-telescopes at MHz frequencies (like the SKA-low instrument) will be made of a very large number of wideband antennas possibly arranged in an irregular configuration, with many imperfections to be corrected for, like mutual coupling. Here, low-order beam representations of array beams are given by using simulated embedded element radiation patterns, multiplied by low-order Zernike functions spanning the whole aperture, and a few measurement points of the actual beam. This allows an accurate representation of the main beam and first few slide lobes with order of tens of coefficients for arrays of hundreds and up to thousands of elements.