# HERAS: A Modular Matlab Tool Using Physical Optics for the Analysis of Reflector Antennas
## 4 Applications of the Tool
### Efficient Estimation of Antenna System Performance for VHTS Applications in a SFPB Scenario  
In a first example, we use HERAS for the analysis of passive (e.g., SFPB/MFPB) antenna architectures. The degrees of freedom in the design of these systems, such as the definition of the optics and the feed array characteristics, call for multidisciplinary optimisations in which the antenna parameters need to be modified multiple times to meet mission requirements. In reflector-based configurations, this is translated to thousands of time-consuming numerical integrations. This is often the bottleneck in the system optimisation time. In this case, computational time is a primary driver provided the coverage metrics are evaluated with an acceptable level of accuracy. Some acceleration techniques applied to the tool described in this paper were presented in [56] in the case of an SFPB configuration with thousands of feeds. While the beams typically have high directivity in the main lobe, the gain envelope decreases rapidly at the side lobes. Consequently, only a limited area around the main beam is relevant for \(C/I\) computation. Since the PO integral is numerically computed for every far-field direction defined in the coverage grid, the computational time is highly dependent on the number of far-field points to be computed. The above observations form the basis of one of the acceleration techniques (in the remaining, referred to as the _threshold_ method) which can be implemented directly in HERAS. Instead of computing the far-field pattern for every beam at every coverage point, the computation starts at the estimated centre of the beam and continues with surrounding coverage points until the ratio of the computed field to the peak directivity is below a given threshold. This threshold enables the user to find a suitable compromise between computation time and accuracy. In order to avoid stopping at a null of the far-field pattern, a number of surrounding points are checked in every iteration. Another acceleration method exploits _interpolation_ between beams across the coverage as means to reducing the number of beams numerically evaluated using PO. In particular, this technique exploits the fact that, with the exception of a shift in the pointing direction along the angular domain, neighbouring feeds otherwise produce very similar radiation patterns. The interpolation process is thus performed using two or more surrounding beams to estimate the far-field pattern of a given unevaluated beam. Using the corresponding local coordinates of each beam allows to account for the shift in the angular domain observed between successive beams. The estimated centre point of the beam is therefore computed as the average of the far-field strength obtained in the centre point of the surrounding beams, and the process is repeated for every point, considering the relative distance from the beam centre. This can be performed with one command by virtually aligning the centre of the beams and obtaining the average of their far-fields' strength. An interpolation path specifies which beams in the coverage are computed with PO and which are interpolated. Since the computational time associated with taking a weighted average to interpolate a beam is negligible compared to the time required to perform the PO integral, the acceleration obtained with this method is directly related to the percentage of beams that are interpolated. Further computational savings can be achieved by adjusting the number of points defining the reflector mesh grid. This grid defines the discrete set of points along which the surface currents on the reflector, \(\overline{j}_{s}\), are estimated. This set of points is used to apply the associated PO numerical integration to obtain the far-field, and their number is highly correlated to the computational effort and the accuracy of the results. A coarser mesh reduces the computational time, typically at the expense of a higher error in the side lobe level of the far-field pattern and on the cross-polarisation results.