Mutual Coupling Effects Between Test and Reference Antennas in Near-Field Measurements Scott G. H. Kriel and Dirk I. L. de Villiers Abstract – This study considers near-field (NF) measurements performed by using a reference antenna to extract phase information from an unknown probe source. We simulate such a measurement of a prototype antenna element, designed for the proposed midfre- quency aperture array of the Square Kilometre Array and attempt to transform the phase-extracted NF measurement into the far-field (FF) pattern of the antenna. The separation distance between the antenna under test and the reference antenna has a substantial effect on the resulting predicted FF pattern. Further- more, this mutual coupling effect is found to be more pronounced in the NF region surrounding the antennas, leaving one to consider increasing the height of the scan plane to improve results. The analysis shows that one must carefully consider the effect that specific config- urations have on NF measurements performed in this manner. 1. Introduction The far-field (FF) radiation pattern of an antenna is a major consideration in the design and calibration of radio telescopes. Given the large scale of modern radio telescopes, such as the proposed midfrequency aperture array (MFAA) of the Square Kilometre Array, pattern verification via traditional methods becomes problem- atic. In light of this, there is interest in field measurements based on an unmanned aerial vehicle (UAV), whereby a UAV equipped with a transmitting source signal can be maneuvered throughout the observation domain of the antenna under test (AUT). This methodology is used in [1], where a UAV equipped with transmitting dipole antennas determines the FF pattern of various antenna systems. Here, the direct FF of the AUT is sampled, thus requiring the UAV to remain suitably far away in the FF region, commonly approximated as r far  2D 2 /k, where k is the wavelength at the frequency in question and D is the maximum dimension of the antenna. This poses a problem when considering the MFAA, where the large aperture size of its various array stations (on the order of 50 m 2 ) may result in the FF region being located at distances that place unrealistic requirements on the UAV. This has led to the consideration of performing such UAV-based measurements in the near field (NF) of the AUT, whereby a suitable transform can be applied to calculate the required FF pattern. Although FF measurements only require the magnitude of the received power to be recorded, NF measurements require both amplitude and phase. The added necessity of measuring phase proves troublesome when consid- ering a UAV-based system, as a common reference signal must be distributed between the probe and AUT for a relative phase measurement between the two to be performed. Although a direct cable link to the UAV may be realizable, as with the system proposed in [2], this will no doubt prove cumbersome in practice. We investigate a method in which a common reference signal can be established between the UAV and AUT in a detached fashion, using a reference antenna with well- known receiving characteristics. This phase reconstruc- tion technique is performed in [3], which considers the practical UAV NF measurement of an aperture array. Although the article reports good agreement between the simulated and reconstructed phase of the AUT, no attempt is made at calculating the predicted FF pattern from the reconstructed data, as can be accomplished by using a suitable field transformation. Expanding on this topic, we first present a brief description of the fast irregular antenna field transformation algorithm (FIAF- TA), which is subsequently used in a NF measurement simulation with a reference antenna to extract phase. Simulation of the problem illustrates how the position of the reference antenna relative to the AUT plays a vital role in the resulting accuracy of the predicted FF. Suspecting mutual coupling between the AUT and reference antenna as the main source of these discrepancies, we move on to analyze the extent to which the addition of a reference antenna serves to alter the NF of the AUT. Performing this for a number of measurement configurations, a suitable spacing between the AUT, reference, and probe antennas is established. 2. Field Transformation To predict the FF pattern from the given NF measurements, a suitable transformation algorithm must be used. In this article, we use the FIAFTA developed and reviewed in [4]. Allowing for arbitrary sample locations, FIAFTA uses the diagonal translation oper- ator T L given as T L ð ^ k ; ^ r M Þ¼ jk 4p X L l¼0 ðjÞ l ð2l þ 1Þh ð2Þ l ðkr M ÞP l ð ^ k  ^ r M Þ ð1Þ where h ð2Þ l is the spherical Hankel function of the second kind and P l a Legendre polynomial. The choice Manuscript received 26 August 2020. Scott G. H. Kriel and Dirk I. L. de Villiers are with the Department of Electrical and Electronic Engineering, Stellenbosch University, 14 Bosman Street, Stellenbosch Central, Stellenbosch, 7600, South Africa; e-mail: scottkriel@gmail.com, ddv@sun.ac.za. URSI RADIO SCIENCE LETTERS, VOL. 2, 2020 DOI: 10.46620/20-0025 1