# Mechanically Reconfigurable, Beam-Scanning Reflectarray and Transmitarray Antennas: A Review
## 4 Feed Movement
### Feed Displacement on Fully Illuminated Apertures
#### 4.1.2 Arrays with Multi Focal points  
The spatial phase error will increase when the feed antenna's phase center deviates from the focal point of the lens or RA, resulting in degradation of antenna gain and beam scanning performance. Each element on a RA/TA can provide a different phase delay independently, rendering it possible to use RAs/TAs to mimic conventional multifocal antennas by dynamically changing the phase shift on each element. Inspired by multifocal lenses and reflector antennas [44; 45; 46], a multifocal design approach was adopted for beam scanning of RAs [47; 48] and TAs [65; 66; 67; 68]. In the synthesis of multifocal RAs/TAs, it is required to find a compromise in the phase shift on each array element since they need to adjust the phase shift for multiple focal points. However, the phase error resulting from this method will slightly degrade the antenna gain at the initial scan angle, which is generally at broadside for single focal systems. Inspired by the enhanced scanning performance of bifocal reflector antennas [49; 46], multifocal RA systems were reported to increase the scan range in numerous studies [49; 50; 51; 52; 53]. A bifocal RA antenna based on a dual-offset reflector configuration was investigated in [50]. While the beam scanning performance was considerably improved, high complexity and fabrication cost render this configuration undesirable. In [49], an RA with multiple focal points was designed that showed enhanced scanning performance compared to a single focal RA. Figure 9a shows the schematic of a bifocal RA system, where the aperture phase distribution needs to compensate for two different feed positions and beam directions. For a symmetric feed configuration and by using the average phase of both feed beams for each unit cell, it can be proved that the direction of the main beam of the RA will depend on the feed offset. Figure 9b shows the scanned gain patterns of a single-focal and a bifocal RA presented in [49]. As shown, the bifocal design provides better scan range in comparison with the single focal design. Moreover, while bifocal RAs provide a larger scan range, they have higher side lobe levels, which may be critical in some applications such as radar systems. This is probably due to the high dissimilarity in the spatial delay of the two feeds for larger scan angles and, therefore, causes higher phase errors while averaging the phases of the two feeds. By using pattern synthesis optimization and quadrufocal phase distribution for a single reflector, Reference [49] reported a wide beam scanning RA with scan coverage of \(60^{\circ}\), aperture efficiency of \(40\%\) and side lobe level better than 15 dB. However, this improved performance compared to the single-focal parabolic-type design is achieved at the cost of lower aperture efficiency. The aperture efficiency of the quadrufocal RA reported in [49] is \(15\%\) lower than that of the single focal RA. A similar method was also used in designing a TA reported in [65]. In this design, four focal points were divided into two groups and located on the focal arcs in the E-plane and H-plane, respectively. This achieved a \(\pm 30^{\circ}\) scanning coverage in both E-plane and H-plane with directivity variation less than 1 dB in the Ka-band. Optimization algorithms were used to balance both beam-scanning coverage and directivity and to maintain a stable directivity over the entire scanning coverage [69]. Conventionally, the phase distribution on a RA/TA is calculated by averaging the phase compensation of both feeds [65; 66]. However, simply averaging spatial phase delay from multiple focal points will cause significant phase error and radiation degradation since illumination from different focal point on array unit cells has non-negligible intensity difference [65; 66]. In order to further reduce this phase error, a new formula in [67] was proposed to calculate the phase distribution on each unit cell.