## 1 Introduction  
Feed antennas are typically employed to operate various electrical large-aperture antennas, such as dielectric lens antennas, frequency selective surfaces, and metasurface transmissive arrays [1; 2; 3; 4; 5; 6; 7; 8; 9]. The feed antennas make it possible to generate a desired electric field distribution over the surface of a large-aperture antenna, enabling a high gain and beam steering while maintaining low design complexity and manufacturing costs [10; 11; 12]. In general, patch antennas [13], horn antennas [14], and log-periodic dipole antennas [15] are used as feed antennas. However, these feed antennas are often mounted in the far-field region several wavelengths away from a large-aperture surface, which poses the problem of increasing the overall volume of the antenna system. To resolve this problem, research has been conducted on near-field feed antennas that can be placed within a specific wavelength from the large-aperture antenna [16; 17]. In the near-field region, since it is difficult to generate a uniform electric field distribution using a single-element feed antenna, studies on array feed antennas including multiple elements have recently been conducted [18; 19; 20]. In particular, array feed antennas are competitive for near-field feeding because they can adjust the amplitude and phase of each element to achieve more uniform field generation in the near-field region.  
In this paper, we propose a novel feed array antenna to achieve a uniform electric field distribution in the near-field region for feeding a large-aperture antenna. The feed antenna has a \(4\times 4\) rectangular array configuration to obtain uniform near-field distribution on a virtual target surface. The virtual target surface was set as a flat surface with dimensionsof 200 \(\times\) 200 mm\({}^{2}\). The size of the virtual surface can be flexibly determined to suit the requirements of the specific application. Each element of the array consists of a Vivaldi radiator and parasitic rings, where the parasitic rings are placed on top of the Vivaldi radiators. The Vivaldi radiator and the parasitic rings have different radiating modes, and, in particular, the near-field pattern of the parasitic rings can be varied by adjusting their radii. Thus, the required near-field distribution on the virtual target surface can be achieved by optimizing the radii of the parasitic rings. To further improve the uniformity of the field distribution, the input phase of each Vivaldi radiator is adjusted by applying different transmission line lengths to the Vivaldi radiators depending on their positions in the array. This configuration can easily control the phase distribution in the array without the use of a complex phase shifter. Then, three variables such as array spacing, an input phase for each element, and a separation distance between the feed array and the virtual target surface are optimized using the genetic algorithm (GA) [21]. Herein, the cost function of the GA is determined by considering both the average and the deviation of the near-electric field distribution on the virtual target surface. The feed array antennas with the optimum design variables are then fabricated, and the electric field distribution is measured on a target surface using a near-field scanner. The results demonstrate that the feed array with the optimum array configuration and parasitic rings can obtain uniform near-field distribution with an average of 1.7 dB and a deviation of 6.8 dB on the virtual target surface placed within half a wavelength from the antenna aperture.