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凹非球面的非零位干涉检测技术

张旭 李世杰 刘丙才 田爱玲 梁海锋 蔡长龙

张旭, 李世杰, 刘丙才, 田爱玲, 梁海锋, 蔡长龙. 凹非球面的非零位干涉检测技术[J]. 中国光学(中英文). doi: 10.37188/CO.2023-0042
引用本文: 张旭, 李世杰, 刘丙才, 田爱玲, 梁海锋, 蔡长龙. 凹非球面的非零位干涉检测技术[J]. 中国光学(中英文). doi: 10.37188/CO.2023-0042
ZHANG Xu, LI Shi-jie, LIU Bing-cai, TIAN Ai-ling, LIANG Hai-feng, CAI Chang-long. A non-null interferometryfor concave aspheric surface[J]. Chinese Optics. doi: 10.37188/CO.2023-0042
Citation: ZHANG Xu, LI Shi-jie, LIU Bing-cai, TIAN Ai-ling, LIANG Hai-feng, CAI Chang-long. A non-null interferometryfor concave aspheric surface[J]. Chinese Optics. doi: 10.37188/CO.2023-0042

凹非球面的非零位干涉检测技术

doi: 10.37188/CO.2023-0042
基金项目: 陕西省科技厅项目(No. 2022GY-222,No. 2022GY-262);基础科研(No. JCKY2020426B009);“一带一路”外国专家创新人才交流项目(No. DL2022040006L)
详细信息
    作者简介:

    张旭(1998—),女,陕西渭南人,硕士研究生,2019年于西安工业大学获得学士学位,2021—至今于西安工大学就读硕士研究生,主要从事光学检测方面的研究。E-mail:zhangxu19982021@163.com

    李世杰(1988—),男,四川广安人,博士,副教授,硕士生导师,2014年于中国科学院光电技术研究所获得博士学位,主要从事先进光学制造技术及先进光学系统研发等方面的研究。E-mail:lishijie@xatu.edu.cn

  • 中图分类号: TN74

A non-null interferometryfor concave aspheric surface

Funds: Supported by Shaanxi Provincial Department of Science and Technology Project (No. 2022GY-222, No. 2022GY-262); Basic Scientific Research (No. JCKY2020426B009)、"The Belt and Road" Foreign Experts Innovative Talent Exchange Project (No. DL2022040006L)
More Information
  • 摘要:

    为了实现凹非球面的快速、高精度与通用化检测,文中提出了一种将非球面当做球面直接采用干涉仪检测的非零位干涉检测方法,并结合相应的数据处理方法,获得非球面的面形误差检测结果。首先介绍了该方法的检测原理,建立了回程误差、调整误差的计算与去除模型,研究了面形误差的数据处理方法。然后以两个不同非球面度的凹非球面为例,对其回程误差和调整误差进行了仿真计算,验证了该方法的有效性。最后搭建了凹非球面的非零位检测实验装置,成功测量得到其面形误差。通过与自准直零位检测法及LUPHOScan轮廓测量法检测结果的对比,发现两种方法测量得到的误差结果的面形分布和评价指标具有高度一致性,验证了该检测方法的正确性。该检测方法在保证高精度测量的同时兼备一定的通用性与便捷性,为凹非球面的通用化检测提供了一种有效手段。

     

  • 图 1  非零位干涉法直接检测非球面

    Figure 1.  Direct non-null interferometry of aspheric surfaces

    图 2  非零位检测光线追迹模型

    Figure 2.  Non-null testing of ray-tracing model

    图 3  调整误差的产生:(a)距离引起的离焦;(b)光轴倾斜引起的倾斜误差;(c)偏心引起的彗差

    Figure 3.  Generation of adjustment errors: (a) Distance induced defocusing; (b) Tilt error caused by optical axis tilt (c) Coma caused by eccentricity

    图 4  非零位检测凹非球面:(a)非零位检测凹非球面光路图;(b)非零位直接检测凹抛物面的数据; (c)非零位直接检测凹椭球面的数据;

    Figure 4.  Non-null testing concave aspheric: (a) The light path diagram of non-null testing concave aspheric; (b) Data of concave paraboloid by non-null direct non-null interferometry (c) Data of concave ellipsoid by non-null direct non-null interferometry

    图 5  非零位检测去除调整误差与回程误差:(a)凹抛物面处理后的面形结果;(b)凹椭球面处理后的面形结果;

    Figure 5.  Non-null testing removes adjustment error and retrace error: (a) Surface shape results after concave parabolic surface testing; (b) Surface shape results after concave ellipsoid surface testing

    图 6  凹非球面的对比实验

    Figure 6.  Comparative experiment on concave aspheric

    表  1  Zernike多项式的项数与像差的对应关系

    Table  1.   Correspondence between the number of terms of Zernike polynomials and aberrations

    TermPolynomialMeaning
    $ {Z_4} $$ - 1{\text{ + }}2\left( {{x^2} + {y^2}} \right) $Power
    $ {Z_7} $$ \left( { - 2 + 3{x^2} + 3{y^2}} \right)x $Coma X
    $ {Z_8} $$ \left( { - 2 + 3{x^2} + 3{y^2}} \right)y $Coma Y
    $ {Z_9} $$ 1 - 6\left( {{x^2} + {y^2}} \right) + 6{\left( {{x^2} + {y^2}} \right)^2} $Primary Spherical
    下载: 导出CSV

    表  2  凹抛物面参数

    Table  2.   Parameters of concave paraboloid

    Parameter Value Parameter Value
    Aspheric type Concave paraboloid Maximum sag 1.67 mm
    Diameter 90 mm Maximum slope 4.25°
    Radius curvature of the vertex 606 mm Maximum asphericity 0.575 μm
    Conic coefficient K −1 Best radius of the reference sphere 606.835 mm
    下载: 导出CSV

    表  3  凹椭球面参数

    Table  3.   Parameters of concave ellipsoid

    Parameter Value Parameter Value
    Aspheric type Concave ellipsoid Maximum sag 2.91 mm
    Diameter 90 mm Maximum slope 7.39°
    Radius curvature of the vertex 348 mm Maximum asphericity 2.0154 μm
    Conic coefficient K −0.66 Best radius of the reference sphere 348.9615 mm
    下载: 导出CSV

    表  4  凹抛物面回程误差的仿真计算

    Table  4.   Simulation calculation of retrace error of concave paraboloid

    OA/mm $ O P D $ Power item $ Z_{OPD(4)} $ Primary Spherical $Z_{\Delta{OPD(9)}}$ Retrace error
    605
    606
    606.835
    607
    608
    下载: 导出CSV

    表  5  凹椭球面回程误差的仿真计算

    Table  5.   Simulation calculation of retrace error of concave ellipsoid

    OA/mm $ O P D $ Power item $ Z_{OPD(4)} $ Primary Spherical $ Z_{\Delta{OPD(9)}}$ Retrace error
    347
    348
    348.9615
    349
    350
    下载: 导出CSV

    表  6  实验中距离误差引入的离焦误差与去除

    Table  6.   Defocusing error introduced by distance errors in experiments and its removal unit: nm

    Detection result Power is adjusted to a minimum Adjust the distance L1 Adjust the distance L2 Adjust the distance L3
    Fringe pattern
    Surface error before removing Power
    PV=639.7608
    RMS=135.4192

    PV=4283.4232
    RMS=1200.4216

    PV=1833.8544
    RMS=515.732

    PV=1999.0152
    RMS=523.3256
    Surface error after removing Power
    PV= 627.1048
    RMS=135.4192

    PV= 654.3152
    RMS=133.5208

    PV=721.392
    RMS=132.888

    PV=656.2136
    RMS=137.3176
    下载: 导出CSV

    表  7  实验中倾斜/偏心误差引入的彗差与去除

    Table  7.   Comet error introduced by tilt/eccentricity error in experiments and removal of the error unit:nm

    Detection result Coma is adjusted to a minimum Adjust the eccentric θ1 Adjust the eccentric θ2 Adjust the eccentric θ3
    Fringe pattern
    Surface error before removing Coma
    PV=722.6576
    RMS=137.3176

    PV=656.8464
    RMS=133.5208

    PV=641.6592
    RMS=134.7864

    PV=649.2528
    RMS=136.6848
    Surface error after removing Coma
    PV= 510.6696
    RMS=125.2944

    PV= 489.7872
    RMS=123.3960

    PV= 491.0528
    RMS=125.2944

    PV= 488.5216
    RMS=126.5600
    下载: 导出CSV
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