Main beam modeling for large irregular arrays

Abstract

Large radio telescopes in the 21 st 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.

Patterns of primary beam non-redundancy in close-packed 21 cm array observations

“…While it would be possible to construct a more general perturbation scheme, for example using a 2D Zernike polynomial basis, principal component representations, or similar (e.g. Bui- Van et al 2017;Eastwood et al 2018;Iheanetu et al 2019;Sekhar et al 2019), our goal here is to minimise the number of additional parameters that must be introduced to the beam model, and to directly connect these parameters to physical effects. Directly perturbing a general polynomial representation of the beam would typically require the coefficients to be adjusted in specific, highly-correlated ways in order to model different effects, since small changes to individual coefficients tend to result in wildly different beam patterns that do not correspond to realistic beam variations.…”

All Sky Modelling Requirements for Bayesian 21 cm Power Spectrum Estimation with BayesEoR

“…In this way, the input data to BayesEoR exclusively contain information about the sky on the scales accessible to the forward model. However, real instruments are in general sensitive to emission from horizon to horizon due to the primary beam response of the antennas 2 (Fagnoni et al 2021;Virone et al 2021;Line et al 2018;Mort et al 2017;Bui-Van et al 2017). Visibilities from a real instrument thus contain information about the entire sky.…”

Holographic Calibration of Phased Array Telescopes

“…A common challenge of phased‐array radio telescope systems is the characterization and calibration of the phased‐array antenna pattern, which can change significantly depending on the pointing direction on the sky. Substantial effort has been made to form predictive models of the phased‐array response (e.g., Bui‐Van et al., 2017, 2018; Sokolowski et al., 2017; Sutinjo, O'Sullivan, et al., 2015; Warnick et al., 2018), which in turn requires an accurate electromagnetic model of the elements in the phased‐array, including mutual coupling effects. Work to characterize the element or primary beam pattern of the telescope includes the use of Unmanned Aerial Vehicles (UAVs) with radio transmitters, low earth orbit satellites and astronomical sources (Bolli et al., 2016; Jacobs et al., 2017; Line et al., 2018; Neben et al., 2015; Sutinjo, Colegate, et al., 2015).…”