Radiation pattern captures the electromagnetic performance of reflector antennas, which is significantly affected by the deformation of the primary reflector due to gravity and the displacement of the secondary reflector. During the design process of large reflector antennas, a substantial amount of time is often dedicated to iteratively adjusting structural parameters and validating electromagnetic performance. To improve the efficiency of the design process, we first propose an approximate calculation method of optical path difference (OPD) for the deformation of the primary reflector under gravity and the displacement of the secondary reflector. Then an OPD fitting function based on the modified Zernike polynomials is proposed to capture the phase difference of radiation over the aperture plane, based on which the radiation pattern will be obtained quickly by the aperture field integration method. Numerical experiments demonstrate the effectiveness of the proposed quick calculation method for analyzing the radiation pattern of a 10.4 m submillimeter telescope antenna at its highest operating frequency of 856 GHz. In comparison with the numerical simulation method based on GRASP (which is an antenna electromagnetic analysis tool combining physical optics (PO) and physical theory of diffraction (PTD)), the quick calculation method reduces the time for radiation pattern analysis from more than one hour to less than two minutes. Furthermore, the quick calculation method exhibits excellent accuracy for the figure of merit (FOM) of the radiation pattern. Therefore, the proposed quick calculation method can obtain the radiation pattern with high speed and accuracy. Compared to the time-consuming numerical simulation method (PO and PTD), it can be employed for quick analysis of the radiation pattern for the lateral displacement of the secondary reflector and the deformation of the primary reflector under gravity in the design process of a reflector antenna.

中文翻译：

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亚毫米望远镜变形位移辐射方向图快速计算方法

辐射方向图捕获反射器天线的电磁性能，该性能受到主反射器由于重力导致的变形和副反射器的位移的显着影响。在大型反射面天线的设计过程中，通常需要花费大量时间迭代调整结构参数和验证电磁性能。为了提高设计过程的效率，我们首先提出了一种主反射镜在重力作用下的变形和副反射镜的位移的光程差（OPD）的近似计算方法。然后提出一种基于修正Zernike多项式的OPD拟合函数来捕获孔径平面上辐射的相位差，在此基础上通过孔径场积分方法快速获得辐射方向图。数值实验证明了所提出的快速计算方法在分析 10.4 m 亚毫米望远镜天线在最高工作频率 856 GHz 下的辐射方向图时的有效性。与基于GRASP（物理光学（PO）和物理衍射理论（PTD）相结合的天线电磁分析工具）的数值模拟方法相比，快速计算方法将辐射方向图分析时间从1个多小时缩短到不到两分钟。此外，快速计算方法对辐射方向图的品质因数（FOM）表现出出色的精度。因此，所提出的快速计算方法可以高速、准确地获得辐射方向图。与耗时的数值模拟方法（PO和PTD）相比，它可以在反射器设计过程中快速分析次反射器横向位移和主反射器在重力作用下的变形的辐射方向图天线。