Optimization of the efficiency of large deployable reflectors by measuring the error around the feed

Large Deployable Reflector (LDR) systems are commonly used as mesh reflectors for large aperture space antennas in aerospace applications since they provide affordability while guaranteeing at the same time a high gain and a high directivity. To improve the surface accuracy several methods have been studied, most of which measure the distance between the cable-net system that forms the reflector surface and the desired paraboloid. In this paper we want to improve the reflector's ability to convey a greater concentration of reflected rays in the direction of the feed. To deal with this issue, a numerical optimization algorithm has been proposed, both in the case of prime-focus reflector and with offset. During the explanation of the algorithm, numerical examples will be reported, thus demonstrating the goodness of the algorithm, and its effectiveness will also be demonstrated using the Monte Carlo method.