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Wang Jing, Wang Xiaokun, Hu Haixiang, Li Lingzhong, Su Hang. Shack-Hartmann scanning and stiching detection plane mirror (Invited)[J]. Infrared and Laser Engineering, 2021, 50(10): 20210527. doi: 10.3788/IRLA20210527
Citation: Wang Jing, Wang Xiaokun, Hu Haixiang, Li Lingzhong, Su Hang. Shack-Hartmann scanning and stiching detection plane mirror (Invited)[J]. Infrared and Laser Engineering, 2021, 50(10): 20210527. doi: 10.3788/IRLA20210527

Shack-Hartmann scanning and stiching detection plane mirror (Invited)

doi: 10.3788/IRLA20210527
  • Received Date: 2021-07-30
  • Rev Recd Date: 2021-08-27
  • Publish Date: 2021-10-20
  • With the development of advanced optical system design and manufacturing, large aperture optical system has been widely used. However, the lack of high precision surface shape detection means limits the manufacture and application of large aperture plane mirrors. In order to detect the surface shape of large aperture planar mirror with high precision, a Shack-Hartmann scanning and stiching detection method was proposed. The scanning and stiching principle and wavefront reconstruction algorithm were studied, and the mathematical model of microlens array imaging was established to verify the feasibility of Shack-Hartmann scanning and stiching detection principle. A scanning and stiching test experiment was carried out for a 150 mm aperture plane mirror, the full aperture surface shape 0.019λ RMS(λ=635 nm) was obtained. Compared with the results of interference detection, the detection accuracy was 0.008λ RMS. The results show that the method can realize the high precision detection of large aperture planar mirror.
  • [1] Zhao Xianyu. Research on Hartmann principle based on sub-aperture slope scanning detection and error [J]. Infrared and Laser Engineering, 2019, 48(8): 0813003. (in Chinese) doi:  10.3788/IRLA201948.0813003
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    [3] Roland GEYL, Jacques PASERI. Optical polishing of the VLT 8.2 m primary mirrors–A report [C]//SPIE, 1996, 2775: 476-479.
    [4] 张林超. 大口径平面反射镜检测方法研究[D]. 长春: 中国科学院长春光学精密机械与物理研究所, 2010.
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    [7] An Qichang, Zhang Jingxu, Fei Yang, et al. Ritchey-Common sparse-aperture testing of the giant steerable science mirror [J]. Applied Optics, 2018, 57(27): 7764-7769. doi:  10.1364/AO.57.007764
    [8] Wang Xiaokun, Zheng Ligong, Zhang Binzhi, et al. Subaperture stitching interferometry for testing a large hyperboloid [J]. Infrared and Laser Engineering, 2009, 38(1): 114-119. (in Chinese) doi:  10.3969/j.issn.1007-2276.2009.01.026
    [9] Guo Fudong, Tang Feng, Lu Yunjun, et al. Rapid adjustment and measurement for subaperture stitching interferometry [J]. Opt. Precision Eng, 2017, 25(10): 2682-07. (in Chinese) doi:  10.3788/OPE.20172510.2682
    [10] Wang Xiaokun. Testing of a large rectangular mirror based on sub-aperture stitching method [J]. Chinese Optics Letter, 2015, 13(13): 40-43.
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    [12] Yan Lisong, Wang Xiaokun, Zheng Ligong, et al. Large-diameter reflector mirror stitching accuracy analysis based on selftest [J]. Infrared and Laser Engineering, 2014, 43(6): 1920-1924. (in Chinese) doi:  10.3969/j.issn.1007-2276.2014.06.040
    [13] Wang Xiaokun, Xue Donglin, Zhang Xuejun. Fabrication and testing of large aspheric system based on common reference [J]. Opt Precision Eng, 2018, 26(04): 743-748. (in Chinese) doi:  10.3788/OPE.20182604.0743
    [14] Mourad Idir, Konstantine Kaznatcheev, Guillaume Dovillaire, et al. A 2 D high accuracy slope measuring system based on a stitching shack hartmann optical head [J]. Optics Express, 2014, 22(3): 2770-2781. doi:  10.1364/OE.22.002770
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    [16] Wei H S, Yan F, Chen X D. Large aperture space optical system testing based on scanning hartmann [J]. Appl Opt, 2017, 56(8): 2078-2083. doi:  10.1364/AO.56.002078
    [17] Wang Xiaokun. Test convex aspheres by subaperture stitching interferometry [J]. Infrared and Laser Engineering, 2013, 42(3): 716-722. (in Chinese) doi:  10.3969/j.issn.1007-2276.2013.03.044
    [18] Wu Jing, Wang Jianli, Lin Xudong. Wave-front test by sub-aperture stitching technique based on Shack-Hartmann wave-front sensor [J]. Opto-Electronic Engineering, 2011, 38(1): 39-43. (in Chinese)
    [19] Burada D R, Pant K K , Bichra M, et al. Experimental investigations on characterization of freeform wavefront using Shack-Hartmann sensor [J]. Optical Engineering, 2017, 56(8): 084107.
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Shack-Hartmann scanning and stiching detection plane mirror (Invited)

doi: 10.3788/IRLA20210527
  • 1. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
  • 2. Univesity of Chinese Academy of Sciences, Beijing 100049, China

Abstract: With the development of advanced optical system design and manufacturing, large aperture optical system has been widely used. However, the lack of high precision surface shape detection means limits the manufacture and application of large aperture plane mirrors. In order to detect the surface shape of large aperture planar mirror with high precision, a Shack-Hartmann scanning and stiching detection method was proposed. The scanning and stiching principle and wavefront reconstruction algorithm were studied, and the mathematical model of microlens array imaging was established to verify the feasibility of Shack-Hartmann scanning and stiching detection principle. A scanning and stiching test experiment was carried out for a 150 mm aperture plane mirror, the full aperture surface shape 0.019λ RMS(λ=635 nm) was obtained. Compared with the results of interference detection, the detection accuracy was 0.008λ RMS. The results show that the method can realize the high precision detection of large aperture planar mirror.

  • 光学系统中,口径越大,则系统的角分辨能力和能量收集能力越强,意味着观测范围越大,观测物体越清晰,因此大口径光学系统是先进光学系统的必然发展趋势[1]。大口径光学望远镜系统检测时需要大口径平面反射镜作为标准反射镜,平面镜的精度直接决定了望远镜系统的精度。同时,大口径平面镜在很多大口径光学系统中担任着折镜的重要角色,例如LAMOST中反射施密特改正镜MA由24块对角线长为1 100 mm的六边形超薄平面镜组成[2];VLT中M3镜是长短轴分别为1 250 mm和800 mm的椭圆形大口径平面镜[3]。此外,大口径平面镜在大型高精度衍射光栅刻划系统中作为高精度平面导轨使用[4]。然而,大口径平面镜的高精度面形检测手段不足,一直是光学检测领域的难题。

    大口径平面镜的检测方法主要有:大口径干涉仪法[5]、Skip-Flat法[6]、Ritchey-Common法[7]、子孔径拼接法[8-10]、五棱镜扫描法[11]。大口径干涉仪检测方法简单,检测精度最高,但是需要大口径的平面标准镜头,制作难度大,周期长,成本高;Skip-Flat法优点在于通过斜入射减小了干涉仪和参考平面镜的口径,但是,随着入射角的增加,灵敏度会降低;Ritchey-Common法利用口径大于平面镜的球面反射镜替换平面参考镜,球面波斜入射平面镜,由于入射角分布的差异会影响波像差与面形差的转换关系,引入误差,随着入射角的增大,检测灵敏度减小;子孔径拼接法只需要小口径的干涉仪,在干涉仪口径与平面镜口径相差很大时,会引入相当大的拼接误差;五棱镜扫描法采用高精度自准直仪,五棱镜与大行程直线导轨相结合,扫描被测面上若干条轮廓线的法向角度变化,通过积分拼接出全口径面形,受直线导轨的误差影响大,检测精度较低。

    夏克哈特曼扫描拼接检测方法是基于夏克哈特曼传感器探测头(HASO)扫描的斜率检测方法,借鉴子孔径干涉检测[12-14]的拼接思想,将夏克哈特曼传感器采集到的各个子孔径信息拼接出整个口径的斜率信息,利用基于Zernike多项式的模式重构方法[15]恢复检测面形。检测方法简单,采样密度大,可实现高精度的面形检测。文中针对口径150 mm平面镜的检测进行了设计分析和测试,验证了夏克哈特曼扫描拼接检测大口径平面镜的适用性和高效性。

    • 检测光路示意图如图1所示,其主要装置为HASO(夏克哈特曼波前传感器检测头)。激光发出的点光源经过准直镜后产生的平行光被分束镜反射到待测平面镜,从平面镜反射回来的光束透过分束镜被微透镜阵列会聚到位于其焦面的CCD探测器上形成光斑阵列图。

      Figure 1.  Schematic diagram of Shack-Hartmann scanning and splicing plane mirror

    • 通过质心算法[15]提取出CCD上的离散光斑位置,比较实际光斑与理想光斑的位置偏离,求出检测区域在x方向与y方向的波前斜率SxSy,利用基于Zernike多项式的模式法波前重构进行波前恢复。

      夏克—哈特曼波前传感器采样测量得到的是离散点数据,依据波前斜率与波像差关系,建立如下所示的超定方程组[15]

      式中:k为Zernike多项式的项数;C为Zernike多项式的系数;n为离散数据的个数。

      利用极大范数下最小二乘法[15]求解模式系数,代入Zernike多项式中可以重构出波前。

    • 图2所示,选择待测平面镜的中心子孔径作为基准子孔径,子孔径间重叠区域的波前斜率满足:

      Figure 2.  Schematic diagram of sub-aperture center location planning

      式中:Txx方向倾斜修正量;Tyy方向倾斜修正量;D为离焦修正量。通过最小二乘算法拟合,使倾斜,离焦误差最小,进行误差解耦[16-20]

      由于夏克哈特曼传感器在扫描检测过程中产生机械移动定位误差,利用微孔径光阑定位装置,在测量前,采用迭代对准方法对偏移子孔径进行迭代对准,提高机械定位精度。

    • 夏克哈特曼波前传感器中的核心元件为微透镜阵列,利用傅里叶光学的方法可以描述微透镜阵列成像的物理过程。其物理过程如图3所示,已知紧靠微透镜的入射波前U0(x,y),经过微透镜调制后的波前U(x,y)传播到焦面CCD上,CCD对焦面上的波面Uf(x,y)的强度分布进行探测,CCD探测到的光斑和强度即为入射光经过微透镜阵列在焦面上的菲涅耳衍射图样及强度分布。

      Figure 3.  Fourier optical physics in the imaging of a single microlens

      单个微透镜的复振幅透过率Ts为:

      式中:j为虚数单位;n为微透镜的折射率,为微透镜的中心厚度;f为微透镜的焦距;${{k}} = \dfrac{{2{\rm{\pi }}}}{\lambda }$为波数。

      第一项位相因子仅表示透镜对于入射光波的常量位相延迟,并不影响位相的空间相对分布。即它不会改变光波波面的形状,故可以略去,不予考虑;第二项是透镜的位相调制因子。

      单个微透镜孔径为正方形,设其边长为a,则单个微透镜的孔径透过率函数Tk为:

      紧靠微透镜后的波前U(x,y)为:

      根据菲涅耳衍射公式,透镜后焦面上的光场分布正比于物体的傅里叶变换[21],则焦面上的强度分布为:

      利用MATLAB仿真上述过程,如图4所示,为被单个微透镜分割的波前区域会聚在焦面CCD上的光斑成像结果。

      Figure 4.  Simulation results of single microlens imaging

      整个微透镜阵列的成像相较于单个微透镜成像,在傅里叶光学上的区别在于孔径透过率函数,微透镜阵列的孔径透过率函数主要由三部分组成:(1)单个微透镜的孔径矩形函数rect(x/a) rect(y/a);(2)微透镜阵列中同形孔径构成的列阵,可视为梳状函数comb(x/a) comb(y/a);(3)将微透镜阵列整体整体示为边长为L的正方形孔径,rect(x/L) rect(y/L),a为单个微透镜孔径,同时也是相邻微透镜中心的间隔。

      则,整个微透镜阵列的孔径透过率函数T(x,y)为:

      依据微透镜阵列傅里叶光学成像原理,如图5所示,为平面波经过微透镜阵列会聚在焦面CCD上的光斑成像结果。

      Figure 5.  Simulation results of microlens array imaging

      全口径仿真中各项参数如表1所示;依据子孔径规划,仿真检测37个子孔径,将37个子孔径的光斑阵列图通过质心提取得到波前斜率矩阵,利用Zernike多项式的模式法波前重构和子孔径拼接得到全口径波前。在全口径上添加如图6(a)所示的波像差,RMS=0.182λ,PV=1.365λ,仿真得到的全口径波前与输入像差的误差如图6(c)所示,RMS=1.531e-06λ,PV=1.122e-05λ

      ParameterValue
      Microlens array diameter/mm 14.61
      Mirror radius /mm 25
      Number of subaperture 37
      Wave length/nm 635

      Table 1.  Simulation parameters

      Figure 6.  Full caliber simulation results. (a) Added wave aberrations; (b) Stitching simulation results; (c) Result error

    • 图7所示为由HASO,五维调节运动平台(xyz,偏转角度A,旋转角度C,其量程与精度如表2所示)和平面镜组成的夏克哈特曼扫描拼接检测系统。

      Figure 7.  Shack-Hartmann scanning and splicing detection system

      ParameterValueAccuracy
      x /mm1 0000.01
      y /mm5000.01
      z /mm8000.02
      A90 °4″
      C360 °10″

      Table 2.  Moving platform range and accuracy

    • 检测过程中需要使出射平行光中心垂直入射子孔径检测区域中心,即满足出射平行光的中心线,载物平台的法线和待测平面镜中心法线“三线合一”的对准调整。

      首先,利用电子水平仪调整平台水平;放置平面镜,找到其上下左右四个边缘位置,如图8所示,并计算平面镜中心位置;安装定心装置(孔径光阑),选择alignment模式,调整偏转角度A,完成精调对准,如图9所示。

      Figure 8.  Plane mirror edge position. (a) Uupper edge;(b) Lower edge;(c) Left edge; (d) Right edge

      由于HASO内部各元件存在客观的装调误差和制造误差,将检测标准平面镜的光斑位置作为标定结果,利用实际光斑位置对应减去标定光斑位置,可以去除掉系统误差。

      Figure 9.  Fine alignment process. (a) Misalignment;(b) Alignment

    • 实验中各项参数如表3所示,待检平面镜口径150 mm,子孔径检测口径为14.6 mm,17×17个子孔径可以实现覆盖全口径的检测。利用840D闭环控制系统对各子孔径进行了自动检测。

      ParameterValue
      Detection beam aperture /mm14.6
      Mirror diameter /mm150
      Sampling density17×17
      Scanning step /mm9.1
      Wave length/nm635

      Table 3.  Experiment parameters

      通过质心提取,求离散斜率矩阵,子孔径拼接,得到了全口径x方向斜率,y方向斜率,如图10所示。

      Figure 10.  Full caliber slope test results. (a) Slope in the x direction; (b) Slope in the y direction

      利用斜率模式法波前重构计算后得到的全口径面形RMS=0.019λ,PV=0.187λ,如图11(a)所示。与干涉仪检测结果图11(b)对比,残差分布如图12所示,PV=0.016λ,RMS=0.008λ。实验结果表明夏克哈特曼扫描拼接检测能够满足平面镜表面面形的高精度检测,验证了夏克哈特曼扫描拼接检测大口径平面镜的可行性。

      Figure 11.  (a) Full aperture surface; (b) Interferometer test results

      Figure 12.  Residual distribution

    • 为了实现大口径平面镜面形的高精度检测,文中提出了夏克哈特曼扫描拼接检测平面反射镜的方法。阐述了该检测方法原理,利用傅里叶光学建立了微透镜阵列成像的数学模型,规划了子孔径,完成了波前斜率重构算法,进行了原理仿真验证。并对一口径为150 mm的平面镜进行了夏克哈特曼扫描拼接检测的验证实验,检测精度为0.008λRMS,实验结果表明该检测方法在检测平面反射镜时,具有较好的可行性和实用性。另外,若将子孔径倾斜检测,可实现球面、非球面、自由曲面等更复杂曲面面形的检测,从而为先进光学系统的制造提供了依据与保障。

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