基于Zernike拟合的三反射面天线赋形设计

多反射面天线系统受空间、位置和尺寸等因素的影响，其主反射面口面存在相位差，从而导致天线辐射性能下降，文章提出了一种利用Zernike多项式赋形多个反射面的方法，通过对副反射面赋形，在主反射面口面得到期望的幅度相位分布。该方法利用Zernike拟合来处理反射面间的光程差，并将主反射面作为固定面，根据几何光学法和光程条件，在Matlab中建立副反射镜初始模型，通过遗传算法优化Zernike系数调整光程差，对副反射镜面形进行优化设计，避免了复杂的微分计算。使用Grasp仿真软件对设计的三反射面天线系统进行了分析，计算表明，与未赋形的三反射面天线相比，赋形反射面天线系统主波束效率提升了10.67%,达到95%以上，验证了该赋形方法的可行性及对天线系统性能提升的有效性。

Design of shaped tri-reflector antennas by using Zernike polynomials

The multiple reflector antenna system is affected by the available space, position and size, which would result in phase differences at the main reflector aperture and consequently degrade the antenna radiation performance. This paper proposes a method of shaping multiple reflector surfaces using Zernike polynomials. By shaping the sub-reflector surfaces, the desired amplitude and phase distribution at the main reflector aperture are achieved. This method uses the Zernike polynomials fitting to handle phase differences and treating the main reflector as a fixed surface. Base on geometric optics and the optical path condition, an initial model of the sub-reflectors established in Matlab. The genetic algorithm is used to optimize the Zernike coefficients to adjust phase and achieve an optimized design of the sub-reflectors, which effectively avoids the complex differential calculations. The designed tri-reflector antenna system was analyzed using Grasp simulation software. The calculation results show the main beam efficiency is improved by 10.67% and reach 95% compared to the unshaped tri-reflector antenna, which validated the feasibility and effectiveness of this shaping method.