Structure design of flat mirror with large aspect ratio for space camera
  • Abstract

    The flat mirror with the characteristics of large aspect ratio and high lightweight rate is one difficulty in the opto-mechanical design of a large off-axis three-mirror anastigmat cameras. For a certain flat mirror with a clear aperture of 1220 mm×198 mm, the assembly structure combining a semi-closed mirror blank made of silicon carbide with the three-point back support scheme was proposed, resulting in a total design weight of 30.5 kg. The supporting effect of the mirror was improved through the optimization of support positions. Both the size and position of hinges in the flexure were adjusted, taking into account gravitational deformation, thermal stability, and dynamic characteristics of the assembly. Simulation reveals that, under the condition of gravity during the test, the root mean square (RMS) of the surface accuracy change of the flat mirror is 1.812 nm, together with the tilt of 3.639" for the mirror blank. The measured fundamental frequency of the assembly is 132.5 Hz. After polishing, the tested RMS values of surface accuracy are 0.0203λ, 0.0197λ, and 0.0204λ (λ=632.8 nm), corresponding to the left, middle, and right sub-zones of the flat mirror respectively. The surface accuracy can remain basically unchanged after environmental tests, which meets the requirements of high-performance space cameras.

    Keywords

  • 上述文献中报道的反射镜长宽比均较小,以某大型离轴三反相机中通光口径为1220 mm×198 mm的平面反射镜(后文简称“平面镜”)为研究对象,其长宽比大于6∶1,主要阐述具备大长宽比特征的高轻量化率空间反射镜的设计方法,重点讨论了镜体的轻量化设计、背部三点支撑方案的实现、柔性支撑的参数优化、大尺寸平面的面形精度检测等技术要点,并通过环境试验,对所研制的平面镜的力学特性和面形精度稳定性进行充分验证。

    离轴三反光学系统具有焦距长、视场大、无遮拦、传函高等特点[-],因其具备的突出商业价值,在现代商业航天遥感领域内得到广泛应用,其中较为成功的是美国DigitalGlobe公司于2001年研制的Quickbird-2卫星和2007年研制的Worldview-1卫星,其全色分辨率和幅宽分别达到0.61 m和16.5 km,以及0.5 m和17.6 km。近年来,我国也成功研制了多颗配备了离轴三反相机的大型商业遥感卫星,如中国四维测绘技术有限公司于2024年发射的“四维高景三号”卫星,其幅宽超过130 km,可向用户提供0.5 m分辨率的图像产品。此类空间相机普遍采用推扫成像模式[],光学系统垂轨向视场远大于沿轨向视场,使得除位于孔径光阑外的其他反射镜均呈现近似长方形轮廓;随着用户对图像分辨率和观测效率的要求不断提高,离轴三反相机的口径和幅宽随之增长[-],导致长方形反射镜的尺寸不断拓展,其长边尺寸现已超过1 m量级,反射镜的长宽比随之快速提高,非对称的镜体大大增加了组件支撑结构的设计难度。具备大长宽比、高轻量化率特征的反射镜组件结构设计已成为离轴三反相机光机结构研制中的主要难点之一。

    近年来,学者们针对大尺寸长条形空间反射镜的研究不断深入。曲慧东等[]提出一种新型柔性支撑结构,并完成了某700 mm×249 mm长方形空间反射镜组件的结构设计,改善了反射镜组件的力、热环境适应能力;袁健等[]介绍了某空间相机中通光口径为1250 mm×460 mm的长方形反射镜的设计过程,其全口径面形精度实测值均方根(RMS)为0.016λ (λ为波长,λ=632.8 nm),且在大量级的环境试验前后体现出良好的面形精度稳定性;刘朋朋等[]针对某口径为540 mm×180 mm、材料为超低膨胀石英玻璃的长方形反射镜建立了组件参数化模型,使用多种优化方法确定了全封闭式镜体结构的轻量化参数以及柔性支撑的尺寸参数,并运用基于点云三维重建的点阵结构仿真方法完成了背板的优化设计;李宗轩等[,]重点研究了某1.8 m×0.5 m口径的长方形反射镜的柔性支撑技术,对柔性支撑的关键尺寸进行了优化设计,提出了柔性支撑最佳安装位置,即长条形反射镜中性面位置的确定方法,反射镜在0°/180°自重作用下的面形精度实测值RMS均优于0.03λ (λ=632.8 nm)。

    Figure 1. Flat mirror assembly in large off-axis TMA camera
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    Flat mirror assembly in large off-axis TMA camera

    大型离轴三反相机(TMA camera)中,入射光线依次经主镜、次镜、三镜反射后,再经平面镜的折转,最终会聚在焦面上,虽然平面镜没有光焦度、对像差校正没有贡献,但能够将焦平面从次镜一侧折转至主镜一侧,起到有效压缩系统光轴向尺寸的作用[],因此,平面镜成为大型离轴三反相机的重要组件。

    文中相机采用桁架式支撑结构[],前、后框架间由碳纤维桁架连接,主镜、三镜及焦平面布置在后框架上,次镜和平面镜安装于前框架上,如图1所示。相机内除次镜为圆形口径外,其余反射镜的轮廓均近似为长方形,而平面镜处于光路后端,成像光束的截面经压缩后在此处变得更加扁平,使平面镜的通光口径达到1220 mm×198 mm,长宽比则扩大至6.16∶1。反射镜的长宽比越大,镜体整体刚度越差、镜面边缘越易变形,轻量化镜体以及组件支撑结构的设计难度也随之提升。开展系统装调及测试时,空间相机通过后框架上的安装支腿固定在检测工装上,相机处于图1所示的光轴水平状态,此时的相机可视作“简支梁”,相机前端的挠度和转角将使光学元件间的相对位置精度发生变化,造成相机入轨后工作性能的衰退,因此,为减轻系统重量,平面镜组件的轻量化设计非常重要。

    Main design metrics for flat mirror assembly

    平面镜组件主要设计指标

    No. Item Requirement
    1 Clear aperture 1220 mm×198 mm
    2 Testing attitude Optical axis horizontal
    3 Gravitational deformation Tilt: θM≤10″
    4 Working temperature (20±4) ℃
    5 Surface accuracy RMS≤1/50λ over sub-aperture of φ140 mm (λ=632.8 nm)
    6 Mass ≤40 kg
    7 Frequency ≥100 Hz
    CSV Show Table

    除显著的大长宽比和高轻量化率特征外,为了能够适应高性能可见光波段遥感器的使用需求,平面镜的动、静力学特性和热稳定性也应满足相应的技术指标。综上,给出平面镜组件的主要设计指标,如表1所示,其中θM为镜体绕图1X轴的转角,φ为镜面直径。

    Figure 2. Lightweight structure of mirror blank
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    Lightweight structure of mirror blank

    对于长条形反射镜而言,单纯增加镜体厚度对提高反射镜刚度的效果有限,镜体厚度通常为镜体长度的1/10左右[],若反射镜的长宽比较大,镜体厚度与长度间的比值可以适当放宽;为控制镜体重量,结合本文空间相机中前框架沿光轴向的尺寸限制,确定平面镜镜体厚度为87.5 mm。

    为减轻镜体质量,增强光学元件的环境适应能力,用来制备大口径空间反射镜的材料应具备高比刚度、高热稳定性等特点[,],在可见光波段高性能遥感器中常见的镜坯材料物理属性如表2所示。其中,比刚度参数(即弹性模量与密度之比)对于提升大长宽比反射镜的力学性能、降低镜坯重力变形尤为重要,镜坯材料的高热稳定性(即导温系数与线胀系数之比)有助于大尺寸长条形镜体各处保持温度一致,因此文中平面镜镜坯选用三种材料中比刚度和热稳定性均最高的碳化硅(SiC)制造。

    文中碳化硅镜坯采用反应烧结方法制备,在制坯阶段使用消失模铸造工艺,镜体内部的减重腔体呈半封闭式结构,翻边宽度为10 mm,加强筋交叉构成等边三角形,支撑孔处于加强筋交点上,如图2所示,该轻量化形式可显著提升镜体刚度。随着高精度数控铣磨、磁流变抛光等新型光学加工工艺的日益成熟,有效地削弱了高轻量化率反射镜在抛光时产生的“印透效应”,对各处板壳的厚度和加强筋密度等参数的限制也逐步放松[];同时,采用的平面镜短边长度小,镜体四周侧壁对镜面起到较好的支撑作用,使得抛光时的镜面变形得到有效控制。基于以上考量,在确定平面镜镜体轻量化参数时,主要考虑制坯时的工艺因素,如保证腔体壁厚均匀、减少疏松气孔、方便操作等,最终将镜坯的面板厚度T1定为5 mm,背板厚度T2为4 mm,四周侧壁厚度T3为4 mm,加强筋厚度T4为3 mm,三处锥孔壁厚T5为10 mm。

    制坯过程中,在平面镜镜坯背面及底面等位置还增设了多处矩形或圆环形凸台,如图2所示,后续经铣磨后可用作基准面,供光学加工、系统装调时定位用。此外,还在远离支撑点的镜体两侧设置斜面、在镜体中部布置削边,这些措施起到了进一步去除镜体冗余质量、提升镜体轻量化率的作用。综上,最后得到平面镜镜体的设计质量为17.4 kg、面密度约为70 kg/m2,与未做减重处理的结构相比,镜体轻量化率约为74%。

    Properties of spatial reflector materials in main visible light band

    主要可见光波段空间反射镜材料属性

    Property SiC ULE Zerodur
    Density ρ/(kg·m−3) 3050 2210 2530
    Elastic modulus E/Gpa 340 67 91
    Specific stiffness E/ρ 111.5 30.3 36
    Thermal conductivity λ1/(W·K−1·m−1) 155 1.31 1.64
    Thermal expansion coefficient α/(10−6·K−1) 2.50 0.03 0.05
    Thermal stability λ1/α 62 43.7 32.8
    CSV Show Table
    Figure 3. Relative position between supports of mirror
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    Relative position between supports of mirror

    Figure 4. Influence of three-point back support position on gravitational deformation of mirror. (a) δy=50 mm; (b) δy=80 mm; (c) δy=110 mm
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    Influence of three-point back support position on gravitational deformation of mirror. (a) δy=50 mm; (b) δy=80 mm; (c) δy=110 mm

    δy数值较小(50 mm)时,Dy对镜体变形量起决定作用,Dy数值越大,对镜体的支撑效果越佳,但此时镜体自重变形RMS均偏大,如图4(a)所示;当δy数值较大(110 mm)时,下方支撑点近似位于镜体短边方向的中间位置,此时Dy对镜体变形量的影响趋同,如图4(c)所示,镜体自重变形体现为两侧边缘位置的凹陷,其RMS主要由下方支撑点的水平距离Dx决定,可见此时中心支撑点并未对镜体起到明显的支撑作用。当δy取值适中(80 mm)时,如图4(b)所示,各支撑点间存在最佳的相对位置使得镜体自重变形量最小,且随着Dy的缩小,最佳位置对应的Dx快速扩大,镜体自重变形RMS逐步减小;注意到当Dy取值偏小时,三个支撑点趋于构成一条直线,此时镜体沿短边方向缺乏支撑,组件将出现绕镜体长边方向的旋转模态,故Dy取值不能过小,以避免削弱大长宽比反射镜组件的动态刚度。综上,最终选取了δy=80 mm、Dy=90 mm作为平面镜的支撑位置,此时,在典型的Dx取值下,平面镜镜面的自重变形趋势如图5所示,其中,当Dx=650 mm时,镜面的变形量最小;为了使各支撑点与轻量化镜体内部加强筋的交汇点重合,将Dx在上述最佳支撑位置附近适当调整,最终确定Dx=624 mm。

    平面镜采用背部三点支撑形式,镜体背部三个支撑点间的相对位置对大长宽比平面镜组件的动、静力学特性有显著影响。为提高镜体刚度,支撑点的布置应使镜体重量均匀地分散至各处、整个镜面得到有效支撑,支撑点间的相对位置主要由支撑点间的水平距离Dx、垂直距离Dy,以及下方支撑点距离镜体侧面的距离δy三个参数确定,如图3所示;由于镜体长宽比达到6∶1量级,镜体短边方向的长度仅208 mm,为增加支撑点构成的三角形的覆盖面积,将上方支撑点适当向上移动,在镜体上方形成拱形突出部。

    Main parts materials and their physical properties

    主要零件材料及其物理属性

    Parameter Main parts material
    Mirror Cone Flexure Base
    Material SiC Invar TC4 SiC/Al
    Density ρ/(kg·m−3) 3050 8100 4400 3000
    Elastic modulus E/Gpa 340 141 114 180
    Poisson ratio μ 0.27 0.25 0.34 0.18
    Thermal expansion coefficient α/(10−6·K−1) 2.5 2.5 9.1 8.4
    CSV Show Table

    平面镜组件主要由镜体、锥套、柔性支撑和基板四部分组成,其结构如图6所示。其中,锥套材料为铟钢、其线胀系数与SiC镜体接近,锥套与镜体之间使用光学环氧胶粘接固定;柔性支撑使用具备高屈服极限的钛合金(TC4)制造,可保证组件可靠性、防止组件在恶劣的力学条件下破坏失效;基板采用铝基碳化硅复合材料(SiC/Al),该材料比刚度高,有助于进一步减轻组件质量。平面镜组件设计质量为30.5 kg,镜体质量在设计质量中的占比为57%,各主要零件使用的材料及物理属性如表3所示;该组件结构方案不仅对外的机械接口简单,且内部受力状态稳定,有助于维持大长宽比反射镜面形精度的长期稳定。

    Figure 6. Back three-point support structure for flat mirror. (a) Assembly relationship; (b) Component physical object
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    Back three-point support structure for flat mirror. (a) Assembly relationship; (b) Component physical object

    为确定合适的支撑点位置,可以分析上述三个参数DxDyδy对镜体处于光轴铅垂状态时自重变形的影响[];对大长宽比镜体而言,该变形量既表征了支撑点分布对镜体自身重力的均匀卸载情况,也在一定程度上反映了振动、热胀冷缩等其他外部载荷通过支撑点作用于镜体时的变形情况,以该变形量为关注对象有助于在镜体设计阶段获得良好的综合支撑效果。仿真时约束镜体背面各支撑点对应位置,计算上述重力状态下镜面面形的均方根值。

    Figure 5. Gravitational deformation of flat mirror under typical support positions. (a) Dx=610 mm; (b) Dx=650 mm; (c) Dx=690 mm
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    Gravitational deformation of flat mirror under typical support positions. (a) Dx=610 mm; (b) Dx=650 mm; (c) Dx=690 mm

    由式(3)可知,铰链的长度L越大、截面惯性矩I越小,铰链的转动刚度K就越小,且铰链厚度T对铰链转动刚度K的影响最大,数值上为立方关系。虽然降低铰链转动刚度使得柔性支撑更易于发生变形,有利于减小环境温度变化时组件内部的热应力,进而控制平面镜的热畸变,然而,大幅降低铰链转动刚度会导致组件基频迅速下降,增加空间相机在发射过程中出现破坏的风险。为兼顾组件的热稳定性和动力学特性,可采用多目标优化的方法,确定柔性支撑最终的结构参数。以4 ℃均匀温度变化工况下的平面镜面形精度RMS为热稳定性的评价指标,以组件基频f1为动力学特性的评价指标,上述优化问题的数学描述可以记为

    式中:W、T分别为铰链的宽度(即零件壁厚)和厚度。记铰链的转动刚度为K,则由以上两式可得

    K=(EI)/L=(EWT3)/12L.
    I=WT3/12,

    式中:X代表由铰链的宽度W、厚度T及长度L构成的参数组合,各参数的取值范围主要根据制造工艺限制确定,单位均为mm。为求解上述优化问题,首先通过实验设计(design of experiment, DOE)的手段,对该问题的响应面模型进行拟合,在选择样本点时,应保证其在设计空间内的随机性与均匀性;进而使用全局响应面法对拟合得到的近似模型进行多目标寻优,优化中最大评估数设置为200,得到的计算数据及帕雷托前沿如图7(b)所示。帕累托前沿对应的组件基频f1变化范围较小且数值均较高,而温度变化工况下的面形精度RMS则变化剧烈,故选择帕累托前沿的底部作为最优解,综合考虑制造工艺并经过圆整后,最终确定柔性支撑中铰链的结构参数为W=9 mm、T=6 mm、L=13 mm。

    使用柔性支撑是提升空间反射镜热稳定性的有效途径之一,也是卸载大长宽比镜体自身重力作用、确保面形精度检测数据准确无误的关键环节。平面镜采用双轴正交铰链式柔性支撑,零件整体呈中空的圆柱形,顶部有盖、底部有法兰,如图7(a)所示;使用线切割工艺,在零件靠近顶部的位置加工两层柔性环节,每层柔性环节均包含一对相向布置的柔性铰链,可认为其旋转轴位于两铰链根部中点的连线上,两层柔性环节的结构参数一致、旋转轴互相垂直且位于同一平面内,构成类似“万向节”的结构。

    各柔性铰链均可简化为悬臂梁结构,当平面镜发生热胀冷缩时,组件内的柔性铰链将受力产生微小变形,这一过程中可视作各铰链仅承受弯矩M作用,根据材料力学相关知识,此时铰链一端的转角θ可以记为

    Figure 7. Flexure support with biaxial orthogonal hinge. (a) Main flexure parameters; (b) Optimization of hinge structure parameters; (c) Relation between hinge position and mirror deformation
    Full-Size Img PowerPoint

    Flexure support with biaxial orthogonal hinge. (a) Main flexure parameters; (b) Optimization of hinge structure parameters; (c) Relation between hinge position and mirror deformation

    开展平面镜面形检测时,组件处于光轴水平状态,此时平面镜将在图1中-Y方向重力作用下产生变形,镜体的大长宽比特征将使上述自重变形更加显著;该变形量既影响面形检测的精度,又可以表征空间相机入轨后处于微重力环境时镜面回弹量的大小,必须对其加以控制。相关研究表明,柔性支撑中铰链结构的轴向位置对大口径反射镜在光轴水平重力工况下的变形量有重要影响,可以通过优化铰链结构的轴向位置获得最佳的重力卸载效果[-]。在有限元模型中,仅将铰链结构沿光轴向整体移动、其它结构参数保持不变,分析得到铰链结构的高度H与检测状态下镜面面形变化RMS间的数值关系,如图7(c)所示,其中,横轴表示高度H,即上层铰链切槽与顶面间的距离,纵轴表示-Y向重力工况下的镜面RMS。可见,平面镜在铰链结构逐步下移的过程中存在面形变化量最小点,其原因可以用“中性面”理论解释:在该位置,铰链结构的旋转轴与镜体的中性面基本重合,此时镜体仅受重力作用,镜面面形精度变化量最小,一旦偏离该位置,镜体除受重力作用外,还要承受附加转矩,使镜面面形RMS值快速增大。综上,确定柔性支撑中铰链结构的高度H为9.5 mm。

    式中:E为铰链材料的弹性模量;LI分别为铰链长度和截面惯性矩。铰链截面为矩形,故I可记作

    θ=(ML)/(EI),
    FindX=(W,T,L)WhereMinimize(RMS), Maximize(f1) s.t. 6W9,5T8,12L16

    开展面形检测和系统装调时,平面镜的长边保持水平状态,此时组件会因重力作用发生变形,导致镜面面形精度退化以及镜体倾斜;地面测试及在轨工作过程中,平面镜所处的环境温度存在一定的变化范围((20±4) ℃),此外,基板对外安装接口位置的表面不平整(不平度最大可达0.02 mm),以上因素也会造成平面镜变形。

    Figure 8. Fitting nephograms of mirror deformation under typical conditions. (a) 1 G, -Y gravity; (b) 4 ℃ temperature change; (c) 0.02 mm forced displacement; (d) Compound
    Full-Size Img PowerPoint

    Fitting nephograms of mirror deformation under typical conditions. (a) 1 G, -Y gravity; (b) 4 ℃ temperature change; (c) 0.02 mm forced displacement; (d) Compound

    对平面镜组件进行模态分析,组件前6阶自然频率及对应振型如表5所示。平面镜组件基频仿真值达到129.1 Hz,与100.0 Hz的设计要求之间存在较大裕量,背部三点支撑形式可以满足米级大长宽比空间反射镜的组件基频要求;平面镜的一阶振型表现为镜体绕Z轴的旋转,如图9所示,这主要是由于大长宽比平面镜在镜体长边两侧的刚度相对较低所致,与柔性支撑相比,镜体的大长宽比因素是决定平面镜动力学特性的主要因素。此外,若以无约束状态下镜体自身的基频为关注对象,发现采用开放式结构的镜体的基础频率为532.0 Hz,而采用半封闭式结构时,镜体基础频率则为656.0 Hz,较前者提升了约23%,可见,半封闭式结构使得大长宽比镜体自身的刚度得到了显著改善。

    Figure 9. First order vibration mode of flat mirror assembly
    Full-Size Img PowerPoint

    First order vibration mode of flat mirror assembly

    表4中数据可知,平面镜在检测重力工况下的面形精度变化量RMS为1.812 nm,虽然通过调整柔性支撑中的铰链高度,实现了对重力作用较好的卸载效果,但镜体仍存在微小的刚体转角θX,其数值为3.639″;复合工况代表了全使用周期内可能出现的最恶劣情况,对应的平面镜面形精度变化RMS为 5.044 nm。可见,平面镜在各工况下的变形数据均满足设计指标要求,所提大长宽比平面镜结构方案具有良好的环境适应能力。

    为评估自重、温度、装配等因素对平面镜工作性能的影响,分别用-Y向1 G重力、4 ℃均匀温度变化、0.02 mm强迫位移三种工况对上述因素加以仿真,分析得到各因素分别作用及同时作用(即复合工况)时的组件变形数据,包括镜面的面形精度变化RMS以及镜体的倾角等如表4所示,相应的镜面节点拟合云图如图8所示。

    Deformation data of the flat mirror assembly under typical conditions

    典型工况下平面镜组件变形数据

    Typical condition RMS/nm θX/″
    Condition 1 Gravity/(1 G, −Y) 1.812 3.639
    Condition 2 Temperature change/4 ${}^ \circ {\mathrm{C}} $ 3.302 /
    Condition 3 Forced displacement/0.02 mm 0.948 /
    Condition 1+2+3 Compound 5.044 /
    Requirement ≤1/50λ (λ=632.8 nm) ≤10″
    CSV Show Table

    Modal analysis results of flat mirror assembly

    平面镜组件模态分析结果

    No.Frequency/HzVibration mode
    1129.1Mirror rotation around Y-axis
    2134.6Mirror rotation around X-axis
    3174.9Mirror rotation around Z-axis
    4178.5Mirror translation along Y-axis
    5193.3Mirror translation along X-axis
    6201.5Mirror translation along Z-axis
    CSV Show Table

    建立组件有限元模型,零件材料及物理属性根据表2设置,其中,胶层由于厚度较薄(约0.02 mm),建模时加以省略,镜体与衬套间的粘接界面通过镜体锥孔内壁全部节点耦合加以模拟,柔性支撑与衬套和基板间的螺钉紧固关系则通过螺钉孔开口处节点耦合来模拟,固定三角基板的对外接口位置作为约束条件,将镜面节点的原始位置及分析得到的节点位移量导出,通过拟合得到镜面的面形精度数据。

    环境温度对大长宽比平面镜的面形检测影响较大,变化的温度场不仅会使待检组件自身产生热变形,还会导致干涉仪内部腔体处于不稳定状态,向测量结果中引入系统误差。为获得准确的测量结果,平面镜的面形精度检测在独立且相对封闭的检测室内开展,室内配备大功率空调,使环境温度恒定在(20±0.5) ℃范围内,每次检测前,组件放置在检测室内静置4 h以上;测试时,待面形云图中的高低点分布及面形数据稳定时记录数据,对各区域进行多次测量并求平均值,从而减少气流扰动、环境振动等不利因素对面形精度检测的影响。

    使用的干涉仪为国产品牌成都泰科的INF600-LP-WM型激光平面干涉仪,其检测口径φ=600 mm、检测重复性精度RMS优于 1/2000λ (λ=632.8 nm)。搭建好的平面镜检测光路如图10(b)所示,干涉仪整体放置于隔振光学平台上,检测时平面镜组件安装在特制的检测工装内,以模拟平面镜与前框架之间的连接方式,平面镜与干涉仪窗口距离约为400 mm;检测工装固定在气浮调整架上,切换区域时,平面镜与工装可以在光学平台上平稳移动;借助干涉仪的对准光束,可将各子区域与干涉仪窗口对中布置,并保证各子区域每次的检测范围基本一致。

    测得平面镜各分区的面形云图如图11所示,各子区域RMS分别为左侧0.0203λ、中部0.0197λ、右侧0.0204λ,各子区域残留像差以中高频成分为主、power项系数均小于0.05,同时注意到,中部区域面形云图中的两侧相对偏低,与左侧、右侧区域中的重叠区域位置相对应;使用干涉仪自带的测量软件,在各子区域内任意框选直径φ=140 mm的圆形区域并分析此处子口径的面形精度,其RMS均优于1/50λ,满足设计指标要求。

    Figure 11. Zonal surface nephograms of flat mirror. (a) Left, RMS of 0.0203λ; (b) Middle, RMS of 0.0197λ; (c) Right, RMS of 0.0204λ
    Full-Size Img PowerPoint

    Zonal surface nephograms of flat mirror. (a) Left, RMS of 0.0203λ; (b) Middle, RMS of 0.0197λ; (c) Right, RMS of 0.0204λ

    Figure 10. Surface accuracy test of flat mirror. (a) Schematic of surface zoning; (b) Test scene using large aperture interferometer
    Full-Size Img PowerPoint

    Surface accuracy test of flat mirror. (a) Schematic of surface zoning; (b) Test scene using large aperture interferometer

    待平面镜组件完成装配和抛光后,对其面形精度进行了检测。平面镜长边方向超过1.2 m,由于缺乏与之匹配的更大口径标准球面镜检具,未搭建常规的“瑞奇-康芒”法检测光路,而是使用分区检测方法开展大长宽比平面镜的面形精度检测,具体做法是:将平面镜镜面划分为左、中、右三个直径约为600 mm的子区域,相邻区域间有约150 mm宽的重叠带,如图10(a)所示,使用大口径平面干涉仪分别检测并记录各子区域的面形精度RMS及面形云图;当全部子区域的RMS均满足设计指标时,可认为平面镜满足系统使用要求。分区检测方法不需要更大口径的光学元件作为辅助检具,利用大口径干涉仪直接对待检平面进行检测[],具有成本低、效率高等优点,在大长宽比平面镜的光学加工领域中被广泛采用。

    Surface accuracy data of flat mirror before and after overturn

    翻转前后平面镜面形精度数据

    Zone RMS/λ
    Left Before 0.0203
    After 0.0213
    Middle Before 0.0197
    After 0.0204
    Right Before 0.0204
    After 0.0207
    CSV Show Table

    为了验证背部三点支撑形式能否充分卸载大长宽比镜体自身的重力作用,以及柔性支撑关键参数设计的正确性,对平面镜开展了面形翻转测试[,],即将检测光路中的平面镜组件连同其检测工装绕光轴旋转180°,再复检此时平面镜各区域的面形精度。测试结果如表6所示,翻转后平面镜各子区域的面形精度RMS值分别为左侧0.0213λ、中部0.0204λ、右侧0.0207λ,相同子区域在翻转前后的RMS变化量不超过1/1000λ。以上数据表明,所提平面镜组件具有良好的静态刚度,可以有效地控制重力作用对检测状态中反射镜面形精度的不良影响。

    为了考核所提平面镜面形精度的稳定性以及组件结构方案的可靠性,参考典型的空间遥感器环境试验方法,对平面镜开展了振动试验和高低温循环试验。

    将平面镜组件置于快速温变箱内,开展高低温循环试验。在试验过程中,控制温度范围为0~40 ℃、温变速率为1~2 ℃/min,总持续时间超过48 h;试验结束后,取出平面镜并复检面形精度,各分区RMS基本维持不变,表明平面镜组件结构稳定,其面形精度具备良好的长期稳定性。

    振动试验分为扫频试验和随机振动试验两部分:通过幅值为0.2 g、频率范围为0~2000.0 Hz的扫频试验,实测得到平面镜组件的基频为132.5 Hz,与仿真值间的误差约为2.5%,可见所提平面镜具有良好的动态刚度、能够满足空间反射镜的设计要求,也侧面表明所提仿真建模方法正确、分析数据的可信度较高;随机振动试验中,振动台的输入量级为2 g RMS且持续加载时间均超过120 s,实测镜体中部的最大加速度响应超过8 g RMS、镜体两侧达到14 g RMS,试验后复检平面镜面形精度,各子区域RMS未发生明显变化,说明平面镜组件动态刚度较高且装配可靠,可以抵御恶劣的振动环境并保持高精度面形质量。

    Overview: The flat mirror with the characteristics of a large aspect ratio and high lightweight rate is one difficulty in the opto-mechanical design of large off-axis three-mirror anastigmat cameras. For a certain flat mirror with a clear aperture of 1220 mm×198 mm, the assembly structure combining a mirror blank made of reaction-sintered silicon carbide with a three-point back support scheme was proposed. The assembly mainly consists of four parts, namely mirror, cone, flexure, and base, with a designed weight of 30.5 kg. Due to the special preparation process, the semi-closed mirror blank has a thin-walled structure with a facepanel of only 5 mm thick and the discretely arranged datums as a reference for positioning. Different supporting effects for mirrors with a large aspect ratio were discussed, and thus the optimal support position was determined. The working principle of the flexure with biaxial orthogonal hinges was explained, and the size parameters of the flexible hinges were determined to balance the thermal stability and dynamic characteristics of the assembly. Based on the neutral plane theory, the position of the hinges was also optimized to achieve the best gravity-unloading effect. Simulations reveal that the root mean square (RMS) value of surface accuracy change of the flat mirror caused by gravity during the test is 1.812 nm, with a tilt of 3.639" for the mirror blank. In the compound working condition where factors such as gravity, temperature change, and interface unflatness work together, the surface accuracy change is RMS only 5.044 nm. Using a large interferometer with an aperture of 600 mm, zonal detection was adopted in the surface accuracy test for the flat mirror after polishing, and the tested RMS values were 0.0203λ, 0.0197λ, and 0.0204λ (λ=632.8 nm), corresponding to the left, middle, and right zones respectively. The surface accuracy of each zone reaches an RMS of λ/50, and for any sub-aperture within φ=140 mm, it is significantly better than RMS λ/50, fully meeting the design metrics. In the overturn test, the assembly was rotated 180° around its optical axis, and the surface accuracy of each zone was retested, achieving the results of RMS 0.0213λ for the left, 0.0204λ for the middle, and 0.0207λ for the right. The RMS value change of the same zone does not exceed λ/1000, indicating that the developed structure can effectively control the gravitational deformation during the test. The measured fundamental frequency of the assembly is 132.5Hz, with a difference of about 2.5% from simulations. The surface accuracy of each sub-zone remains basically unchanged after the vibration test and thermal recycle test, indicating that the assembly structure is reliable and the high-precision surface of the flat mirror has good stability. The related work has important reference significance for the development of large-sized and high-precision space mirrors.

    使用大口径平面干涉仪和分区检测方法,对研制的平面镜实物开展了面形精度检测,左、中、右三处子区域的RMS分别为0.0203λ、0.0197λ、0.0204λ,且翻转测试中各子区域的面形精度基本维持不变;平面镜组件的基频实测值为132.5 Hz,经历大量级的振动试验和长期的高低温循环试验后,平面镜均能维持高精度的面形质量。所提平面镜的工作性能可以满足高性能空间相机的使用需求,该工作可以为大长宽比、高轻量化率平面镜的研制提供参考。

    以某大型离轴三反相机内的平面镜为研究对象,其通光口径为1220 mm×198 mm,详细讨论了大长宽比特征对高性能平面反射镜工作性能的影响,并系统地阐述了其研制方法。碳化硅镜体采用半封闭式结构,面板厚度为5 mm、加强筋仅厚3 mm,设置分散的凸台作为基准面,镜体设计质量为17.4 kg,获得了较高的镜体轻量化率。采用背部三点支撑形式的大长宽比平面镜具有优良的工作性能,经调整后的柔性支撑可以在提升平面镜热稳定性的同时卸载检测状态下大长宽比镜体自身的重力作用,镜体倾斜值仅为3.639″,各典型仿真工况中平面镜的面形精度变化RMS最大值为 5.044 nm,均充分满足设计指标要求。

    所有作者声明无利益冲突

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    DOI: 10.12086/oee.2025.250006
    Cite this Article
    Yuan Jian, Zhang Lei, Pei Siyu, Li Xiaotao, Zhang Guanchen. Structure design of flat mirror with large aspect ratio for space camera. Opto-Electronic Engineering 52, 250006 (2025). DOI: 10.12086/oee.2025.250006
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    Article History
    • Received Date January 07, 2025
    • Revised Date March 18, 2025
    • Accepted Date March 23, 2025
    • Published Date May 29, 2025
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  • No. Item Requirement
    1 Clear aperture 1220 mm×198 mm
    2 Testing attitude Optical axis horizontal
    3 Gravitational deformation Tilt: θM≤10″
    4 Working temperature (20±4) ℃
    5 Surface accuracy RMS≤1/50λ over sub-aperture of φ140 mm (λ=632.8 nm)
    6 Mass ≤40 kg
    7 Frequency ≥100 Hz
    View in article Downloads
  • Property SiC ULE Zerodur
    Density ρ/(kg·m−3) 3050 2210 2530
    Elastic modulus E/Gpa 340 67 91
    Specific stiffness E/ρ 111.5 30.3 36
    Thermal conductivity λ1/(W·K−1·m−1) 155 1.31 1.64
    Thermal expansion coefficient α/(10−6·K−1) 2.50 0.03 0.05
    Thermal stability λ1/α 62 43.7 32.8
    View in article Downloads
  • Parameter Main parts material
    Mirror Cone Flexure Base
    Material SiC Invar TC4 SiC/Al
    Density ρ/(kg·m−3) 3050 8100 4400 3000
    Elastic modulus E/Gpa 340 141 114 180
    Poisson ratio μ 0.27 0.25 0.34 0.18
    Thermal expansion coefficient α/(10−6·K−1) 2.5 2.5 9.1 8.4
    View in article Downloads
  • Typical condition RMS/nm θX/″
    Condition 1 Gravity/(1 G, −Y) 1.812 3.639
    Condition 2 Temperature change/4 ${}^ \circ {\mathrm{C}} $ 3.302 /
    Condition 3 Forced displacement/0.02 mm 0.948 /
    Condition 1+2+3 Compound 5.044 /
    Requirement ≤1/50λ (λ=632.8 nm) ≤10″
    View in article Downloads
  • No.Frequency/HzVibration mode
    1129.1Mirror rotation around Y-axis
    2134.6Mirror rotation around X-axis
    3174.9Mirror rotation around Z-axis
    4178.5Mirror translation along Y-axis
    5193.3Mirror translation along X-axis
    6201.5Mirror translation along Z-axis
    View in article Downloads
  • Zone RMS/λ
    Left Before 0.0203
    After 0.0213
    Middle Before 0.0197
    After 0.0204
    Right Before 0.0204
    After 0.0207
    View in article Downloads
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    Zhang Guanchen

    1. On this Site
    2. On Google Scholar
    3. On PubMed
    Structure design of flat mirror with large aspect ratio for space camera
    • Figure  1

      Flat mirror assembly in large off-axis TMA camera

    • Figure  2

      Lightweight structure of mirror blank

    • Figure  3

      Relative position between supports of mirror

    • Figure  4

      Influence of three-point back support position on gravitational deformation of mirror. (a) δy=50 mm; (b) δy=80 mm; (c) δy=110 mm

    • Figure  5

      Gravitational deformation of flat mirror under typical support positions. (a) Dx=610 mm; (b) Dx=650 mm; (c) Dx=690 mm

    • Figure  6

      Back three-point support structure for flat mirror. (a) Assembly relationship; (b) Component physical object

    • Figure  7

      Flexure support with biaxial orthogonal hinge. (a) Main flexure parameters; (b) Optimization of hinge structure parameters; (c) Relation between hinge position and mirror deformation

    • Figure  8

      Fitting nephograms of mirror deformation under typical conditions. (a) 1 G, -Y gravity; (b) 4 ℃ temperature change; (c) 0.02 mm forced displacement; (d) Compound

    • Figure  9

      First order vibration mode of flat mirror assembly

    • Figure  10

      Surface accuracy test of flat mirror. (a) Schematic of surface zoning; (b) Test scene using large aperture interferometer

    • Figure  11

      Zonal surface nephograms of flat mirror. (a) Left, RMS of 0.0203λ; (b) Middle, RMS of 0.0197λ; (c) Right, RMS of 0.0204λ

    • Figure  1
    • Figure  2
    • Figure  3
    • Figure  4
    • Figure  5
    • Figure  6
    • Figure  7
    • Figure  8
    • Figure  9
    • Figure  10
    • Figure  11
    Structure design of flat mirror with large aspect ratio for space camera
    • No. Item Requirement
      1 Clear aperture 1220 mm×198 mm
      2 Testing attitude Optical axis horizontal
      3 Gravitational deformation Tilt: θM≤10″
      4 Working temperature (20±4) ℃
      5 Surface accuracy RMS≤1/50λ over sub-aperture of φ140 mm (λ=632.8 nm)
      6 Mass ≤40 kg
      7 Frequency ≥100 Hz
    • Property SiC ULE Zerodur
      Density ρ/(kg·m−3) 3050 2210 2530
      Elastic modulus E/Gpa 340 67 91
      Specific stiffness E/ρ 111.5 30.3 36
      Thermal conductivity λ1/(W·K−1·m−1) 155 1.31 1.64
      Thermal expansion coefficient α/(10−6·K−1) 2.50 0.03 0.05
      Thermal stability λ1/α 62 43.7 32.8
    • Parameter Main parts material
      Mirror Cone Flexure Base
      Material SiC Invar TC4 SiC/Al
      Density ρ/(kg·m−3) 3050 8100 4400 3000
      Elastic modulus E/Gpa 340 141 114 180
      Poisson ratio μ 0.27 0.25 0.34 0.18
      Thermal expansion coefficient α/(10−6·K−1) 2.5 2.5 9.1 8.4
    • Typical condition RMS/nm θX/″
      Condition 1 Gravity/(1 G, −Y) 1.812 3.639
      Condition 2 Temperature change/4 ${}^ \circ {\mathrm{C}} $ 3.302 /
      Condition 3 Forced displacement/0.02 mm 0.948 /
      Condition 1+2+3 Compound 5.044 /
      Requirement ≤1/50λ (λ=632.8 nm) ≤10″
    • No.Frequency/HzVibration mode
      1129.1Mirror rotation around Y-axis
      2134.6Mirror rotation around X-axis
      3174.9Mirror rotation around Z-axis
      4178.5Mirror translation along Y-axis
      5193.3Mirror translation along X-axis
      6201.5Mirror translation along Z-axis
    • Zone RMS/λ
      Left Before 0.0203
      After 0.0213
      Middle Before 0.0197
      After 0.0204
      Right Before 0.0204
      After 0.0207
    • Table  1

      Main design metrics for flat mirror assembly

        1/6
    • Table  2

      Properties of spatial reflector materials in main visible light band

        2/6
    • Table  3

      Main parts materials and their physical properties

        3/6
    • Table  4

      Deformation data of the flat mirror assembly under typical conditions

        4/6
    • Table  5

      Modal analysis results of flat mirror assembly

        5/6
    • Table  6

      Surface accuracy data of flat mirror before and after overturn

        6/6