离轴三反望远镜主镜和三镜面形误差补偿机理

Compensation mechanism of primary mirror and the third mirror figure error of off-axis three-mirror telescope

为保证大口径离轴三反消像散(Three-Mirror Anastigmat,TMA)光学系统在轨成像质量,探明离轴TMA系统中次镜位姿与主镜及三镜面形误差补偿机理,以矢量像差理论为基础,用Zernike多项式表述离轴TMA系统镜面面形误差,并对系统镜面面形误差进行解析。通过分析发现,位于非光阑位置三阶彗差经光瞳坐标变换衍生出与视场线性相关像散;提出结合失调离轴系统矢量像差校正解析式,以系统出瞳波像差RMS值为评价标准,构建离轴TMA系统像差补偿模型,利用次镜位姿对主镜及三镜存在面形误差的离轴TMA系统进行补偿。仿真实验表明:系统主镜存在0.5λ像散与彗差时,所构建像差补偿模型可将系统出瞳波像差由0.18λ补偿至0.08λ;系统三镜存在0.05λ像散与彗差时,可将出瞳波像差由0.3λ补偿至0.1λ,且当三镜面形误差在(-0.03λ,0.03λ)范围内时,可将系统各视场RMS值补偿至系统设计值,使系统成像质量满足要求,为大口径反射式空间望远镜在轨主动装调提供进一步理论指导。

Objective When the large aperture off-axis three-mirror anastigmat(TMA)is launched to space,surface degradation appear on the the optical surface of its components due to gravity unloading,which will affect the imaging quality of the system.In order to ensure the imaging quality of the large aperture space reflecting telescope in orbit,it is necessary to explore the surface figure error compensation mechanism of the position of optical elements.Then the compensation mechanism of the secondary mirror position for the primary mirror and the third-mirror shape of the off-axis TMA system was investigated.So that the space telescope can actively use the element pose adjustment to compensate the impact of surface figure degradation on the imaging quality of the system.Methods In order to analyze the progressive compensation mechanism of the surface figure error,the compensation mechanism and compensation amount are defined and calculated based on the nodal aberration theory(NAT).Firstly,the Zernike polynomial vector form is used to describe the surface figure error of the offaxis TMA system based on the vector multiplication rule,and its derived aberration distribution is analyzed.Different from the aberration characteristics of the position of the primary mirror at the stop,the third mirror in the non-stop position of each field of view on the surface of the beam trajectory is different(Fig.1).Therefore,when compensating for the surface figure error of the third mirror,the situation of each field of view is different.This is also the focus of the investigation on the analysis and discussion of using pupil position transformation and least square method to solve the problem.Then a vector aberration correction model is proposed and an aberration compensation model of off-axis TMA system is constructed.In order to objectively evaluate the imaging quality of the imaging system,the exit pupil wave aberration RMS value is taken as the evaluation standard,and the secondary mirror adjustment with small aperture and the highest sensitivity in the TMA system is used to compensate the system exit pupil wave aberration with surface figure errors in the primary mirror and the third mirror.Results and Discussions Simulation experiments show that when the primary mirror of the system has 0.5λastigmatism and coma,the constructed aberration compensation model can compensate the exit pupil wave aberration RMS value from 0.18λto 0.08λ(Tab.5).When 0.05λastigmatism and coma exist on the system's third mirror,the exit pupil wave aberration RMS value can be compensated from 0.3λto 0.1λ(Tab.8).In order to verify the applicability of the aberration compensation model,Monte Carlo experiment was carried out,which proved that when the third-mirror figure error(astigmatism and coma)was within the range of(−0.03λ,0.03λ),the RMS value of each field of view of the system could be compensated to the design value of the system(Fig.9).Conclusions A portable surface figure error compensation model of the TMA system is designed.It can compensate the RMS value of the TMA system with 0.5λin the primary mirror and 0.05λin the third mirror respectively to the nominal state.Through analysis,it is found that the third-order coma in the non-stop position is derived from the linear correlation astigmatism with the field of view by optical symmetry coordinate transformation.The astigmatism and coma distribution rules can be verified during the analysis of the surface error of each position of the system,which provides a theoretical reference and basis for other types of aberrations and further theoretical guidance for the active in-orbit installation of large aperture reflecting space telescopes.It provides the basic theory and framework for constructing the surface figure error compensation model of the primary mirror and the third-mirror of off-axis TMA system.