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如图1所示,文中提出的大口径快反镜面形测试系统由大口径前置离轴扩束系统、光源及光源扩束系统、偏摆补偿组件、波前测量组件、测试结果显示部分、机械支撑系统、电源构成[16-17]。如图2所示,光学系统主体采用离轴无焦卡塞格林系统光路结构,激光光源发射633 nm波长的光束,光束通过光源扩束系统将光束直径扩束为20 mm,经过第一个分束镜将光束反射到离轴扩束系统,直径20 mm的光束以1∶20的比例扩束到400 mm的光束,然后入射到待测快反镜的镜面上,通过待测快反镜镜面反射的光束携带待测快反镜镜面的面形变化的信息再次通过离轴扩束系统,光束被缩束为20 mm,经过第一个分束镜入射到衰减器进行光强衰减,再经过第二个分束镜将光束分成两部分,一部分入射到补偿反射镜,经过第三个分束镜将光束分成两部分,其中一束光入射CCD记录光斑变化,另外一束光入射到第一个PSD记录光斑质心变化。另一部分经过第四个分束镜将光束分成两部分,其中一束光到经反射镜反射进入到波前传感器进行波前分析,另一束光进入第二个PSD记录光斑质心变化。其中第一个PSD记录到的质心数据反馈给补偿反射镜,使得补偿反射镜的抖动频率与待测快反镜镜面抖动频率一致保证波前传感器稳定地进行波前分析。
文中采用的扩束系统为离轴无焦卡式系统。其优点为光路中无实际焦点,不会使得光能聚集而造成系统损伤,且结构紧凑,中心无遮挡,光能利用率高[18]。光学系统中的单色像差包括球差、彗差、像散、场曲和畸变,分别用
$ {S}_{1} $ 、$ {S}_{2} $ 、$ {S}_{3} $ 、$ {S}_{4} $ 、$ {S}_{5} $ 表示。在空气介质中,根据三级像差理论,对无穷远成像,可得到五种像差的求解结果为:$$ {S}_{1}=-\frac{2{h}_{1}^{4}}{{R}_{1}^{3}}\left(1-\frac{1}{{\varGamma }}-{e}_{1}^{2}+\frac{1}{{\varGamma }}{e}_{2}^{2}\right) $$ (1) $$ {S}_{2}=\frac{2{h}_{1}^{3}}{{R}_{1}^{3}}\left({y}_{1}{e}_{1}^{2}-{y}_{2}{e}_{2}^{2}-{y}_{1}+{y}_{2}\right) $$ (2) $$ {S}_{3}=-\frac{2{h}_{1}^{2}}{{R}_{1}}\left({y}_{1}^{2}{e}_{1}^{2}-{\varGamma }{y}_{2}^{2}{e}_{2}^{2}-{y}_{1}^{2}+{\varGamma }{y}_{2}^{2}\right) $$ (3) $$ {S}_{4}=\frac{2}{{R}_{1}}\left(1-{\varGamma }\right) $$ (4) $$ {S}_{5}=-\frac{2{h}_{1}}{{R}_{1}^{3}}\left({y}_{1}^{3}{e}_{1}^{2}-{{\varGamma }}^{2}{y}_{2}^{3}{e}_{2}^{2}-{y}_{1}^{3}+{\varGamma }{y}_{2}^{3}\right) $$ (5) 式中:
${\varGamma }$ 为系统的放大倍率;$ {e}_{1}^{2} $ 和$ {e}_{2}^{2} $ 为主、次镜面偏心率平方;$ {{h}}_{1} $ 为主镜边缘到光轴的距离;$ {y}_{1}^{2} $ 和$ {y}_{2}^{2} $ 为主、次镜面表达式。当且仅当$ {e}_{1}^{2}={e}_{2}^{2}=1 $ 时,${S}_{1}= {S}_{2}= {S}_{3}= {S}_{5}=0$ ,即若同时消除球差、彗差、像散及畸变,则主镜和次镜均需为抛物面镜。故前置扩束系统的主、次镜均使用抛物面镜,主、次镜的镀膜方式为金属铝膜同时加有保护膜,其工作波长为633 nm。无焦卡式系统是常用的扩束系统[19-21],其主镜的焦距和主镜直径的关系为:$$ {f}_{1}=\left(\frac{{f}_{1}}{\#}\right)\left({d}_{1}\right) $$ (6) 次镜的焦距为:
$$ {f}_{2}=\frac{{f}_{1}}{{\varGamma }} $$ (7) 主镜和次镜的间距为:
$$ s={f}_{1}-{f}_{2} $$ (8) 主镜的曲率半径R1、次镜的曲率半径R2和它们焦距的关系是:
$$ {R}_{1}=-2{f}_{1} $$ (9) $$ {R}_{2}=2{f}_{2} $$ (10) 主、次镜的面形参数取
$ {e}_{1}^{2}={e}_{2}^{2}=1 $ ,圆锥曲系数$ {k}_{1}=-{e}_{1}^{2}=-1,{k}_{2}={-e}_{2}^{2}=-1 $ 。主镜的离轴量与主、次镜口径的关系为:$$ b > \frac{{d}_{1}}{2}+\frac{{d}_{2}}{2}+\frac{b}{5}+p $$ (11) 式中:p为避免机械结构干扰光路所留余量。经上述公式计算,其中主镜的直径
$ {d}_{1} $ 为400 mm,曲率半径$ {R}_{1} $ 为3000 mm,离轴量$ b $ 为330 mm,次镜的直径$ {d}_{2} $ 为55 mm,曲率半径$ {R}_{2} $ 为150 mm,系统的扩束比为1∶20,主、次镜间距$ s $ 为1425 mm,视场为0.05°,前置扩束系统的参数如表1所示。为了实现光斑质心坐标变化、光斑变化和光斑波前的准确测量,需要在数据探测器即PSD、CCD和波前传感器前加入缩束系统。基于快反镜面形测试系统的参数指标要求,选择Imagine Optic公司的哈特曼波前传感器,表2为其具体参数。表 1 缩束系统参数表
Table 1. Parameters of shrink-beam system
Paraxial parameters $ {f}_{1} $/mm 1500 $ {R}_{2} $/mm 150 $ {f}_{2} $/mm 75 b/mm 330 $ s $/mm 1425 $ {k}_{1} $ −1 $ {R}_{1} $/mm −3000 $ {k}_{2} $ −1 表 2 波前传感器参数
Table 2. Parameters of wavefront sensors
Item Parameter Item Parameter Sensor type HASO3 FAST Repeatability/rms <λ/200 Wavelength range/nm 350-1100 Wavefront measurement accuracy in absolute/rms ~λ/100 Aperture/mm² 1.7×1.7 Wavefront measurement accuracy in absolute/rms ~λ/150 Number of microlenses 14×14 Spatial sampling/μm ~110 Tilt dynamic range >±3° Max acquisition frequency/Hz 900 Min measured curvature/m ±0.025 Processing frequency/Hz 800 将以上参数输入Zemax软件中实行系统优化从而得到光学系统的最佳设计,图3为光学系统的仿真结果。同时,考虑视场变化对快反镜面形测试系统的影响,在Zemax中设定工作波长为633 nm与视场角度0.05°。根据仿真结果可得,系统像差与视场角度增减成正比关系,当视场角为0.05°时系统的PV值为0.008λ,RMS值为0.006λ。
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考虑快反镜面形测试系统实际检测面形误差时外界环境温度会产生变化,由于光学镜片和机械结构的热膨胀系数不同,且温度变化对使得镜片和机械结构产生热应力和热变形而影响光束传播导致光学系统性能下降进而影响快反镜面形测试系统的测量精度。光机热集成分析方法(TSO)是一种通过结合光学、机械学和热力学等多个学科为一体的计算过程,于1981年由美国Honeywell公司的Miller等人[22]最早提出,其通过综合分析机械结构系统,光学设计,材料选择以及外界环境等多方面因素之间的关系,对光学系统施加热载荷以仿真分析系统性能的优劣,从而判断光学系统的温度稳定性[16-17, 23-25]。文中通过光机热集成分析对快反镜面形测试光学系统进行温度稳定性分析,光机热集成分析的流程图如图4所示[16-17, 26]。
快反镜面形测试系统检测状态时,其前置离轴无焦卡式扩束系统主要会受到外部工作环境温度变化的影响。根据光学系统结构设计采用SolidWorks软件建立系统的结构模型,依据系统部件材料的差异导入模型元件的对应参数,采用Patran软件创建有限元模型,其中网格划分的大小、疏密程度会影响分析结果的准确度。文中采用六面体网格对模型进行网格划分,使用手动划分网格方法,其中划分的网格模型单元总数为37671个,网格最小的尺寸为1 mm,最大的尺寸为33 mm,其有限元模型如图5所示。
划分网格后,对有限元模型添加约束条件,其中位移边界条件为限制支撑腿位移的自由度。基于温度变化对光学系统性能的影响,环境参考温度选取为20 ℃,温度分析范围为−10~50 ℃,以10 ℃温差为梯度计算光学系统的温度稳定性情况。通过对模型施加±30 ℃的热载荷,输入参数后即可生成分析计算所用的.bdf模型。采用Nastran软件打开.bdf模型进行分析计算获得.xdb结果文件,再采用Patran软件将其打开.xdb结果文件进行计算,得到系统的热变形云图如图6所示。
由于外界环境温度的变化会使得镜片面形和镜片间距产生变化,故完成光学系统机械热分析之后,需要分析温度变化对镜片面形产生的影响,故下一步将进行对镜片面形变化的数据拟合分析。其中数据拟合分析的方法有二次曲面拟合法,齐次坐标变换法, Zernike多项式拟合等[17, 27]。文中采用Zernike多项式拟合的方法在MATLAB软件中实现数据拟合分析,将获得的数据导入Zemax软件中得到像差数据(如图7所示),并且当温度为−10 ℃时,镜面面形RMS值为0.042λ(RMS,λ=633 nm),温度为50 ℃时,镜面面形RMS值为0.046λ(RMS,λ=633 nm)。
同时,如图8所示,外界环境温度变化后光学系统的光学传递函数(MTF)变化不大,当温度为−10 ℃和50 ℃时,截止频率为20 lp/mm处的光学系统各视场的MTF均高于0.2。图9表示系统在20°时,镜片无刚性位移,不会产生面形变化,截止频率为20 lp/mm处的光学系统各视场的MTF均为0。图10表明光学系统在−10 ~50 ℃的温度范围内,镜面面形虽然随外界环境温度变化也随之成线性变化,但在−10 ℃和50 ℃的极值情况下,镜面面形RMS值仍满足光学系统的性能指标,证明了快反镜面形测试系统具有温度稳定性。
Design of large aperture fast steering mirror surface figure test system
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摘要: 大口径快速反射镜(快反镜)常被应用于空间光通信和激光武器等领域。为实现工作状态下大口径快反镜面形误差的实时检测,设计了大口径快反镜面形测试系统。该系统的口径参数为400 mm,工作波长为633 mm,由离轴式前置扩束系统和焦面附件系统组成。对测试系统的设计参数及元件参数选择进行了阐述,设计和仿真了光学系统结构,并基于光机热集成分析获得温度变化对光学系统的影响。测试大口径快反镜面形测试系统后结果表明该系统可实现实时记录和高精度测量,且在温度变化的工作环境下也可实现稳定测量,其测量稳定性为0.048λ(RMS,λ=633 nm)。Abstract: The large aperture fast steering mirror(FSM) are often used in the fields of space optical communications and laser weapons. The large aperture fast steering mirror surface figure test system with an effective aperture of 400 mm has a working wavelength of 633 nm. The system is mainly composed of an off-axis beam expanding system and a focal plane system to achieve real-time detection of the mirror surface figure error when the large aperture FSM is working. In this paper, the design parameters of the optical system and the selection of optical element parameters were described. The optical system was designed and simulated, and the effect of temperature variation on the optical system was obtained based on the integrated optical-mechanical-thermal analysis. The test results show that the large aperture fast steering mirror surface figure test system can achieve real-time recording and high precision measurement, meanwhile, the system has stability in a working environment with temperature changes. The stability of the surface figure test system is 0.048λ (RMS, λ=633 nm).
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Key words:
- fast steering mirror /
- optical design /
- surface figure test system /
- effective aperture /
- stability
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表 1 缩束系统参数表
Table 1. Parameters of shrink-beam system
Paraxial parameters $ {f}_{1} $ /mm1500 $ {R}_{2} $ /mm150 $ {f}_{2} $ /mm75 b/mm 330 $ s $ /mm1425 $ {k}_{1} $ −1 $ {R}_{1} $ /mm−3000 $ {k}_{2} $ −1 表 2 波前传感器参数
Table 2. Parameters of wavefront sensors
Item Parameter Item Parameter Sensor type HASO3 FAST Repeatability/rms <λ/200 Wavelength range/nm 350-1100 Wavefront measurement accuracy in absolute/rms ~λ/100 Aperture/mm² 1.7×1.7 Wavefront measurement accuracy in absolute/rms ~λ/150 Number of microlenses 14×14 Spatial sampling/μm ~110 Tilt dynamic range >±3° Max acquisition frequency/Hz 900 Min measured curvature/m ±0.025 Processing frequency/Hz 800 -
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