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空间引力波探测望远镜光学系统设计

李建聪 林宏安 罗佳雄 伍雁雄 王智

李建聪, 林宏安, 罗佳雄, 伍雁雄, 王智. 空间引力波探测望远镜光学系统设计[J]. 中国光学(中英文), 2022, 15(4): 761-769. doi: 10.37188/CO.2022-0018
引用本文: 李建聪, 林宏安, 罗佳雄, 伍雁雄, 王智. 空间引力波探测望远镜光学系统设计[J]. 中国光学(中英文), 2022, 15(4): 761-769. doi: 10.37188/CO.2022-0018
LI Jian-cong, LIN Hong-an, LUO Jia-xiong, WU Yan-xiong, WANG Zhi. Optical design of space gravitational wave detection telescope[J]. Chinese Optics, 2022, 15(4): 761-769. doi: 10.37188/CO.2022-0018
Citation: LI Jian-cong, LIN Hong-an, LUO Jia-xiong, WU Yan-xiong, WANG Zhi. Optical design of space gravitational wave detection telescope[J]. Chinese Optics, 2022, 15(4): 761-769. doi: 10.37188/CO.2022-0018

空间引力波探测望远镜光学系统设计

doi: 10.37188/CO.2022-0018
基金项目: 国家自然科学基金(No. 62075214);广东省科技计划项目(No. X190311UZ190);广东省重点领域研发计划项目(No. 2020B1111040001)
详细信息
    作者简介:

    李建聪(1997—),男,广东湛江人,硕士研究生,2020年于佛山科学技术学院获得学士学位,现于佛山科学技术学院攻读硕士学位,主要从事光学系统设计方面的研究。E-mail: 751934038@qq.com

    伍雁雄(1982—),男,湖南邵阳人,博士,教授,硕士生导师,2015年于中国科学院大学获得理学博士学位,主要研究方向为航空航天光学系统设计和光学仪器研制。E-mail:364477424@qq.com

    王 智(1978—),男,山东寿光人,博士,研究员,博士生导师,2006年于中国科学院长春光学精密机械与物理研究所获得工学博士学位,主要研究方向为空间引力波探测高精度精密测量技术。E-mail:wz070611@126.com

  • 中图分类号: O439

Optical design of space gravitational wave detection telescope

Funds: Supported by National Natural Science Foundation of China (No. 62075214); Science and Technology Plan Project of Guangdong Province (No. X190311UZ190); Research and Development Projects in Key Areas of Guangdong Province (No. 2020B1111040001)
More Information
  • 摘要:

    在空间引力波探测中,望远镜是空间激光干涉测量系统的重要组成部分,其出瞳处波前误差与抖动光程(Tilt-To-Length, TTL)噪声间的耦合,是影响空间引力波探测的主要噪声源。首先,基于平顶光束与高斯光束的干涉模型,采用Fringe Zernike多项式表征望远镜出瞳处的波前误差,运用LISA Pathfinder(LPF)信号分析出瞳处波前误差与TTL噪声的耦合机理。其次,采用蒙特卡洛分析方法,研究不同数值波前误差下低阶像差占比对TTL耦合噪声的影响,确定了不同数值波前误差下,望远镜光学系统出瞳处满足TTL耦合噪声控制要求的低阶像差设计比例。最后,基于上述理论分析结果与像差控制要求,完成了空间引力波探测望远镜光学系统设计,望远镜入瞳直径为200 mm,出瞳处波前误差RMS值为0.01908λ,低阶像差占比不高于50%。分析结果表明,当光束抖动在±300 μrad以内,TTL耦合噪声不超过8.25 pm/μrad;通过公差分析得知,TTL耦合噪声最大值为15.50 pm/μrad,满足空间引力波的探测要求。

     

  • 图 1  空间激光干涉仪望远镜光学系统

    Figure 1.  Telescope optical system of space laser interferometer

    图 2  干涉光束与四象限探测器的相对位置

    Figure 2.  The relative position of the interference beam and the four-quadrant detector

    图 3  倾斜像差余弦项与正弦项合并。(a)竖直倾斜项;(b)水平倾斜项;(c)合并后的倾斜项

    Figure 3.  Combined cosine and sine terms of the tilt aberration. (a) Vertical tilt aberration; (b) horizontal tilt aberration; (c) combined tilt aberration

    图 4  归一化的${{\boldsymbol{M}}_{\mathbf{1}}}$$ {{\boldsymbol{M}}_{\mathbf{2}}} $系数矩阵

    Figure 4.  Normalized coefficients of the $ {{\boldsymbol{M}}_{\mathbf{1}}} $ and $ {{\boldsymbol{M}}_{\mathbf{2}}} $ matrices

    图 5  ${{\boldsymbol{M}}_{\mathbf{2}}}$矩阵中不同像差对TTL噪声的影响

    Figure 5.  The influence of different aberrations on TTL noise in the $ {{\boldsymbol{M}}_{\mathbf{2}}} $ matrix

    图 6  低阶像差在不同占比下对TTL噪声的影响

    Figure 6.  The effect of low-order aberration on TTL noise under different proportions

    图 7  优化后的望远镜光学系统结构

    Figure 7.  Optimized structure of the telescope optical system

    图 8  (a)优化后望远镜出瞳处波前;(b)TTL耦合噪声计算结果

    Figure 8.  (a) Wavefront at the exit pupil of the telescope after optimization; (b) calculation results of TTL coupled noise

    图 9  蒙特卡洛公差分析下耦合系数统计结果

    Figure 9.  Statistical results of coupling coefficient with Monte Carlo tolerance analysis

    表  1  由Fringe Zernike多项式的前25项组成的14个Zernike像差

    Table  1.   The fourteen Zernike aberrations consist of the first 25 terms of Fringe Zernike polynomials

    in, mj${\textit{z}_j}\left( {\rho ,\theta } \right)$Aberration Name
    2,31,±11${\text{2} }\rho \cos (\theta - {\theta _{{\rm{TI}}} })$Tilt (TI)
    42,02$ \sqrt 3 \left( {2{\rho ^2} - 1} \right) $Defocus (DE)
    5,62,±23$\sqrt 6 {\rho ^2}\cos(2\theta - {\theta _{{\rm{PA}}} })$Primary astigmatism (PA)
    7,83,±14$\sqrt 8 \left( {3{\rho ^2} - 2\rho } \right)\cos (\theta - {\theta _{{\rm{PC}}} })$Primary coma (PC)
    94,05$ \sqrt 5 \left( {6{\rho ^4} - 6{\rho ^2} + 1} \right) $Primary spherical (PS)
    10,113,±36$\sqrt 8 {\rho ^3}\cos(3\theta - {\theta _{{\rm{PTR}}} })$Primary trefoil (PTR)
    12,134,±27$\sqrt {10} \left( {4{\rho ^4} - 3{\rho ^2} } \right)\cos (2\theta - {\theta _{{\rm{SA}}} })$Secondary astigmatism (SA)
    14,155,±18$\sqrt {12} \left( {10{\rho ^5} - 12{\rho ^3} + 3\rho } \right)\cos (\theta - {\theta _{{\rm{SC}}} })$Secondary coma (SC)
    166,09$ \sqrt 7 \left( {20{\rho ^6} - 30{\rho ^4} + 12{\rho ^2} - 1} \right) $Secondary spherical (SS)
    17,184,±410$\sqrt {10} {\rho ^4}\cos(4\theta - {\theta _{{\rm{PTE}}} })$Primary tetrafoil (PTE)
    19,205,±311$\sqrt {12} \left( {5{\rho ^5} - 4{\rho ^3} } \right)\cos (3\theta - {\theta _{{\rm{STR}}} })$Secondary trefoil (STR)
    21,226,±212$\sqrt {14} \left( {15{\rho ^6} - 20{\rho ^4} + 6{\rho ^2} } \right)\cos (2\theta - {\theta _{{\rm{TA}}} })$Tertiary astigmatism (TA)
    23,247,±113$4\left( {35{\rho ^7} - 60{\rho ^5} + 30{\rho ^3} - 3\rho } \right)\cos (2\theta - {\theta _{{\rm{TA}}} })$Tertiary coma (TC)
    258,014$ 3\left( {70{\rho ^8} - 140{\rho ^6} + 90{\rho ^4} - 20{\rho ^2} + 1} \right) $Tertiary spherical (TS)
    下载: 导出CSV

    表  2  不同占比低阶像差下TTL耦合噪声平均值及耦合噪声不超过25 pm/μrad的概率统计

    Table  2.   Average value of TTL coupling noise and probability statistics for TTL coupling noise not exceeding 25 pm/μrad under different proportions of low-order aberrations

    占比λ/60λ/50λ/40 λ/30λ/20
    平均值比例平均值比例平均值比例平均值比例平均值比例
    20%4.75100.00%5.85100.00%7.60100.00%10.76100.00%18.1988.10%
    30%6.42100.00%7.86100.00%10.11100.00%14.1598.92%23.0560.86%
    40%8.21100.00%10.07100.00%12.7099.96%17.6288.50%28.4036.12%
    50%10.07100.00%11.98100.00%15.4196.50%21.2368.92%34.2420.76%
    60%11.88100.00%14.5198.54%18.1584.20%25.1648.26%39.3814.84%
    70%13.8499.32%16.7890.80%21.1667.80%29.0334.62%45.2810.78%
    100%19.8574.20%24.3250.98%30.5029.94% 41.5214.30%64.155.36%
    下载: 导出CSV

    表  3  空间望远系统指标

    Table  3.   Indicators of space telescope system

    系统参数技术指标
    入瞳直径/mm200
    工作波长/nm1064
    科学视场/μrad±8
    系统放大倍率40
    系统波像差≤ 0.03λ@1064 nm
    TTL耦合噪声≤ 25 pm/μrad
    下载: 导出CSV

    表  6  Zernike多项式拟合望远镜出瞳处波前的幅值和方向

    Table  6.   Amplitude and orientation of the wavefront at the exit pupil of the telescope based on Zernike polynomials

    Mag/Ori$A_2^{{\rm{DE}}}$$A_3^{{\rm{PA}}}/{\theta _{ {\rm{PA} } } }$$A_4^{{\rm{PC}}}/{\theta _{ {\rm{PC} } } }$$ A_5^{{\rm{PS}}} $$ A_6^{{\rm{PTR}}}/{\theta _{{\rm{PTR}}}} $$ A_7^{{\rm{SA}}}/{\theta _{{\rm{SA}}}} $$ A_8^{{\rm{SC}}}/{\theta _{{\rm{SC}}}} $
    Value/(mm·rad−1)1.303.74/3.143.93/4.711.154.52/4.712.08/3.148.36/1.57
    Mag/Ori$ A_9^{{\rm{SS}}} $$ A_{10}^{{\rm{PTE}}}/{\theta _{{\rm{PTE}}}} $$ A_{11}^{{\rm{STR}}}/{\theta _{{\rm{STR}}}} $$ A_{12}^{{\rm{TA}}}/{\theta _{{\rm{TA}}}} $$ A_{13}^{{\rm{TC}}}/{\theta _{{\rm{TC}}}} $$ A_{14}^{{\rm{TS}}} $
    Value/(mm·rad−1)5.859.04/1.579.69/4.717.64/3.144.03/1.570.93
    下载: 导出CSV

    表  4  优化后望远镜光学系统的设计参数

    Table  4.   Optimized design parameters of the telescope optical system

    望远镜曲率半径空气间隔圆锥系数
    主镜−1212.526−573.883−1.00537
    次镜−68.658676.229−1.36538
    三镜−760.425−227.503
    四镜736.659223.794
    下载: 导出CSV

    表  5  次镜偶次非球面的高阶项系数

    Table  5.   High-order term coefficients of even-order aspheric surfaces of the secondary mirror

    项数4th6th8th10th12th
    系数2.9010×10−8−1.2858×10−107.6057×10−125.8855×10−14−4.5785×10−16
    下载: 导出CSV

    表  7  望远镜公差分配

    Table  7.   Tolerance allocation of the telescope

    类型公差项主镜次镜三镜四镜
    加工公差曲率半径(mm)0.10.020.10.1
    二次曲面系数0.00050.001
    面型精度(λ)1/1001/1001/2001/200
    装调公差X向位移(μm)152020
    Y向位移(μm)152020
    Z向位移(μm)152020
    X轴倾斜(″)202020
    Y轴倾斜(″)202020
    Z轴倾斜(″)406060
    下载: 导出CSV
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  • 收稿日期:  2022-01-22
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  • 网络出版日期:  2022-04-27

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