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空间相机运行在500 km的轨道高度上,相机质量在5 kg以内,并具有全色、RGB 以及近红外五个谱段。光学系统采用同轴两反加校正镜的形式。该相机由于光学系统的跨距较大,同时镜头口径较大,采用传统的承力筒或桁架式结构很难满足相机的质量要求。因此采用单杆支撑作为主承力结构,其设计过程困难、复杂,仅应用在部分国外的空间遥感相机上,如日本/欧盟联合开发的地球云和气溶胶辐射探测卫星(EarthCARE)中的大气激光雷达(ATLID)相机及美国研制的GIFTS无焦望远镜。单杆主承力结构由主承力板、主支撑杆及次镜支架三部分组成,如图2所示。
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光学系统设计完成后,为了得到主镜(primary mirror, PM)、次镜(secondary mirror, SM)失调量对于系统波像差的影响,从而指导光机系统的设计,分别进行了主镜、次镜在平移和旋转方向的波像差灵敏度分析。平移和旋转的单位失调量增量分别设置为1 μm和1″。通过分别分析主、次镜各失调量引起的光学系统波像差,获得在各个失调位置处对应的系统波像差,并将结果绘制如图3和图4所示。
Figure 3. Relationship between displacement and wavefront aberration of primary mirror and secondary mirror
可以看出,主镜和次镜的位移和倾斜失调量与系统波像差具有非常好的线性关系,根据平面直线公式进行拟合,得到各线性关系的斜率和截距如表1所示。
Misalignment Sensitive
(λ/μm; λ/(″))Intercept/λ PM-Dx 2.67E-03 5.16E-06 PM-Dy 2.67E-03 5.16E-06 PM-Dz 1.33E-02 5.29E-02 PM-Tx 6.35E-03 −3.90E-06 PM-Ty 6.35E-03 −3.90E-06 SM-Dx 2.84E-03 −1.33E-05 SM-Dy 2.84E-03 −1.33E-05 SM-Dz 9.55E-04 2.67E-03 SM-Tx 8.75E-04 −1.85E-04 SM-Ty 8.75E-04 −1.85E-04 Table 1. Fitting parameters
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光机结构有限元模型如图5(a)所示,网格数量为137337,重力方向为−X方向。其在重力条件下的静力学变形云图如图5(b)所示。对有限元分析结果进行后处理,提取主镜和次镜的有限元节点坐标及位移量,进行叠加得到变形后的节点坐标位置,并分别使用主镜和次镜表面的节点基于公式(3)和公式(4)进行主镜和次镜六个方向刚体位移的计算,结果如表2所示,其在X方向的平移量和绕Y方向的旋转量与变形云图一致。将主镜和次镜的刚体位移量分别与表1中对应的灵敏度系数相乘,得到每个位移量引起的系统波像差变化如表2所示。并基于公式(2)计算得到系统波像差变化为0.0569λ。
Subassembly Direction Dx Dy Dz Tx Ty Tz PM Misalignment/mm; (″) −2.324E-03 1.233E-06 3.684E-04 −1.63E-06 4.70E-04 2.075E-08 Wavefront aberration/λ 6.20E-03 3.29E-06 4.90E-03 3.73E-05 1.07E-02 0 SM Misalignment/mm; (″) −1.903E-02 −1.415E-04 7.777E-03 3.59E-06 −6.83E-04 8.248E-07 Wavefront aberration/λ 5.40E-02 4.01E-04 −7.38E-03 1.13E-05 −2.15E-03 0 Table 2. Rigid body displacements of primary mirror and secondary mirror
最后,为了进行对比,根据表2中主镜和次镜的刚体位移量修改光学软件中的主镜和次镜的位置和倾斜量,进行分析得到重力条件下的系统波像差为0.0487λ,如图6所示,可见该光机结构的设计具有非常好的静刚度,使主镜和次镜的位移量和角度偏移量都非常小,从而使重力对光机系统成像质量的影响非常小。基于公式 (5)计算所提出方法相对于软件仿真结果的误差为16.8%,说明灵敏度分析具有足够的精度,在初步设计阶段用于快速对系统波像差预测。
式中:WE 为两种方法的计算误差;WM为基于灵敏度分析模型的波像差计算结果;WS为基于软件仿真的波像差计算结果。
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装调后的光机系统采用自准方法进行各视场波像差的检测。如图7所示,在相机焦面位置放置干涉仪,相机入光口处放置平面反射镜,干涉仪发出的光经过光学系统,经平面反射镜反射后再入射到光学系统中,光线原路返回至干涉仪中产生干涉条纹,从而进行波像差检测。为了进一步验证所设计的主承力结构的性能对系统波像差的影响,分别进行了正向和反向重力工况下的波像差测试。其中,反向重力工况为相机倒置稳定后进行波像差测试。
图8所示为两种工况下的中心视场波像差测试结果,并汇总于表3中。可见系统波像差在正向和反向重力工况下的差别非常小,最大误差在10%以内,证明了光机结构具有非常好的力学稳定性。
Direction Positive/λ Negative/λ Error Central FOV 0.0531 0.0518 −2.45% Right FOV 0.0748 0.0814 8.82% Left FOV 0.0683 0.0694 1.61% UP FOV 0.06543 0.0639 −2.34% Down FOV 0.0539 0.0565 4.82% Table 3. Wavefront aberration measurement results
Wavefront aberration sensitivity and integrated analysis method for spaceborne camera
doi: 10.3788/IRLA20220109
- Received Date: 2022-02-17
- Rev Recd Date: 2022-05-07
- Publish Date: 2022-11-30
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Key words:
- micro-nano satellite /
- spaceborne camera /
- optomechanical integrated optimization /
- mechanical performance /
- wavefront aberration
Abstract: Aiming at a new type of single cantilever main support structure of space camera, both wave aberration sensitivity model and integrated simulation analysis are proposed to calculate the camera's wave aberration in the lightweight design of optomechanical structure, so as to ensure the imaging quality under mechanical conditions. The proposed wave aberration sensitivity method can model based on the linear relationship between wave aberration and misalignment, which is of great significance to guide the optimal design of optomechanical structure under the constraint of the camera imaging quality. Firstly, the sensitivity model of optical element misalignment and wavefront aberration is derived based on the principle of optical system misalignment. Then, the nodal displacements under mechanical condition are obtained by finite element method, and the misalignment of primary and secondary mirrors is calculated based on best-fit fitting method. The wavefront aberration of the camera is obtained by the optical analysis of the misaligned system. Finally, the two methods proposed in this paper are used for modeling and analysis of a 5 kg level space optical camera, and the corresponding gravity condition analysis and test are also performed. The error of sensitivity model is 16.8% compared with the optomechanical integrated simulation method, and the sensitivity model can be applied to the rapid calculation of system imaging performance in the design phase.