Main Beam Modeling for Large Irregular Arrays: The SKA1-LOW telescope case

Large radio telescopes in the 21st century such as the Low-Frequency Array (LOFAR) or the Murchison Widefield Array (MWA) make use of phased aperture arrays of antennas to achieve superb survey speeds. The Square Kilometer Array low frequency instrument (SKA1-LOW) will consist of a collection of non-regular phased array systems. The prediction of the main beam of these arrays using a few coefficients is crucial for the calibration of the telescope. An effective approach to model the main beam and first few sidelobes for large non-regular arrays is presented. The approach exploits Zernike polynomials to represent the array pattern. Starting from the current defined on an equivalence plane located just above the array, the pattern is expressed as a sum of Fourier transforms of Zernike functions of different orders. The coefficients for Zernike polynomials are derived by two different means: least-squares and analytical approaches. The analysis shows that both approaches provide a similar performance for representing the main beam and first few sidelobes. Moreover, numerical results for different array configurations are provided, which demonstrate the performance of the proposed method, also for arrays with shapes far from circular.