Acta Photonica Sinica, Volume. 50, Issue 7, 161(2021)

Micro-angle Measurement Method and Its Accuracy Evaluation Based on Fabry-Perot Etalon

Yuan LIU1... Xiaoyan SHEN1, Shinan ZHOU1, Xubo GUO2, Jing YU1, Dongsheng LI1 and Xuhui LAN1 |Show fewer author(s)
Author Affiliations
  • 1College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou3008, China
  • 2Department of Physics, Tsinghua University, Beijing100084, China
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    Figures & Tables(10)
    Micro-angle measurement optical path based on F-P etalon
    Basic process of lens focal length and center micro-displacement measurement
    Micro-angle measuring device
    Concentric interference ring at 546 nm wavelength
    Schematic diagram of circle data processing
    • Table 1. FWHM value under different focusing positions ()

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      Table 1. FWHM value under different focusing positions ()

      PositionFWHM x+FWHM x-FWHM y+FWHM y-FWHM¯
      010.2258.84311.42218.46712.239
      18.9457.62511.02611.6819.819
      27.6877.53810.42811.7299.345
      36.4956.4518.12913.5818.664
      45.6076.0806.6258.6686.745
      55.2686.2575.8235.4935.710
      65.3566.0016.0525.3165.681
      76.8166.5538.5307.0647.241
      87.6826.86611.66411.0389.313
      99.7887.51713.70413.16411.043
      108.7858.45920.34812.06812.415
    • Table 2. Calculated result of the standard deviationof the peak position coordinates in different directions and the average ()

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      Table 2. Calculated result of the standard deviationof the peak position coordinates in different directions and the average ()

      Serial number of the ring isx'+sx'-sy'+sy'-s¯
      10.0800.0880.0810.0900.085
      20.0560.0640.0560.0640.060
      30.0430.0610.0520.0560.053
      40.0340.0520.0430.0470.044
      50.0330.0460.0410.0380.039
      60.0240.0440.0380.0350.035
      70.0190.0460.0310.0270.031
      80.0160.0390.0260.0240.026
      90.0170.0300.0230.0190.022
      100.0150.0330.0150.0130.019
      110.0150.0290.0130.0120.017
      120.0150.0250.0120.0100.015
      130.0180.0210.0120.0110.016
      140.0190.0230.0150.0110.017
      150.0190.0190.0140.0140.017
      160.0210.0160.0140.0140.016
      170.0250.0170.0170.0140.018
    • Table 3. Experimental results of 600″ inner angle measurement

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      Table 3. Experimental results of 600″ inner angle measurement

      No.f/mmU'p(fw)fwδ/μmsδ/μmα/(″)Upα1/(″)
      0-178.180.0140.1570.0120.2070.041
      0-20.2690.0120.3540.041
      0-30.2630.0120.3480.041
      1-176.9910.014101.5670.056
      1-277.1690.013101.8020.056
      1-377.2370.012101.8910.056
      2-1153.6550.014202.7010.071
      2-2153.6990.013202.7590.071
      2-3153.8060.013202.9000.071
      3-1230.2240.012303.7100.087
      3-2230.2910.012303.8000.087
      3-3230.4340.013303.9880.087
      4-1306.9010.012404.8630.102
      4-2306.9580.012404.9370.102
      4-3307.0990.011405.1230.102
      5-1383.5630.012505.9930.117
      5-2383.6110.012506.0570.117
      5-3383.8190.012506.3300.117
      6-1460.2290.012607.1280.132
      6-2460.3230.012607.2520.132
      6-3460.2970.012607.2170.132
    • Table 4. Calculation instructions of measurement uncertainty

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      Table 4. Calculation instructions of measurement uncertainty

      Measurement uncertaintyUncertainty componentExpression

      Up(δw)

      (υeff1=39,p=0.95)

      u1relTake 15th sδwu1rel=s¯δw=0.0030w'
      u2relL±0.001w'u2rel=L3=5.8×10-4w'
      u3rel

      d=2015522.7 nm,Δn=±4.75×10-7

      Cosine of the cone angle of the optimal ring cosθ=0.9983

      u3rel=Δc3=dΔn/cosθ3=1.4×10-4w'

      u4rel

      β=3.5×10-6K-1,Optimal ring diameter l=2328.978w'

      Δt±0.5u4rel=Δl3=βlΔt3=0.0024w'

      Up(fw)

      (υeff2=21,p=0.95)

      u5relfw=19743.904w'sfw=0.13w'u5rel=sfw=0.13w'
      u6relufad=±2.466w'u6rel=ufad3=1.4w'
    • Table 5. Experimental results of 40″ inner angle measurement

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      Table 5. Experimental results of 40″ inner angle measurement

      No.f/mmU'p(fw)fwδ/μmsδ/μmα/(″)Up(α)2/(″)
      0-178.1570.0140. 1630.0100.2160.038
      0-20. 1620.0110.2140.038
      0-30. 1380.0120.1810.038
      1-17.6300.01210.0690.040
      1-27.6760.01110.1290.040
      1-37.5500.0119.9620.040
      2-115.7700.01120.8100.041
      2-215.9120.01120.9960.041
      2-315.9390.01121.0320.041
      3-124.0890.01231.7860.043
      3-224.1760.01131.9010.043
      3-324.1810.01231.9080.043
      4-132.4460.01242.8140.045
      4-232.6020.01243.0200.045
      4-332.5160.01242.9060.045
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    Yuan LIU, Xiaoyan SHEN, Shinan ZHOU, Xubo GUO, Jing YU, Dongsheng LI, Xuhui LAN. Micro-angle Measurement Method and Its Accuracy Evaluation Based on Fabry-Perot Etalon[J]. Acta Photonica Sinica, 2021, 50(7): 161

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    Paper Information

    Category: Instrumentation, Measurement and Metrology

    Received: Nov. 17, 2020

    Accepted: Jan. 11, 2021

    Published Online: Sep. 1, 2021

    The Author Email:

    DOI:10.3788/gzxb20215007.0712004

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