中文摘要：

以大型光学系统主镜为研究对象,基于经典标量衍射理论分析了中高频误差对环围能量比（FEE）的影响。根据光学镜面面形误差近似为高斯平稳随机过程以及全频段面形误差对光强分布和FEE的影响,建立了光学镜面中高频误差梯度均方根（GRMS）与FEE之间的数学关系模型,进行了仿真分析并利用实际面形误差数据进行了验证。研究表明,FEE随着中高频误差GRMS的增加近似呈指数规律衰减,同时各频段误差将无误差时对应的光强分布边缘部分能量转移到光强分布的中心以及更宽范围,并且随着中高频误差的增大,能量转移曲线出现反复振荡。结果表明,在特定光学口径下,中高频误差GRMS值分别〈12nm/mm以及30nm/mm时,中高频误差对FEE的影响均〈5%,可用于控制中高频误差对FEE的影响,为中高频误差的进一步修形提供理论支持。

英文摘要：

With respect to the primary mirror of a large optical system, the influence of mid- and-high frequency errors on the Fractional Encircled Energy （FEE） based on classical scalar diffraction theory was analyzed. With the relation between full frequency errors and FEE, the mathematical model between the Gradient Root-mean Square （GRMS） errors of mid- and-high frequency errors and FEE was established by assuming that the surface error is a stationary Gaussian random progress.The numerical computation and actual surface profile data of the model were validated. It is found that the FEE almost declines in an exponential form with the increase of GRMS of the mid- and-high frequency errors, and the various frequency errors transform the edge energy of the ideal intensity distribution to the centre and wider domain of the intensity distribution.The energy transfer curve oscillates with the increase of the GRMS. It is concluded that the influence on FEE is less than 5% when the GRMS of the mid- and-high frequency errors are less than 12 nm/mm and 30 nm/mm,respectively, under the special optical diameter,and obtained results can be used to control the influence of mid-and-high frequency errors on the FEE and can provide a support for the further finishing and figuring of the optical surface profile.