Opto-Electronic Engineering, Volume. 51, Issue 7, 240134(2024)

Spectral reduction algorithm for echelle grating spectrometer based on least-squares image coordinate correction

Yuxuan Ouyang1, Xiao Fu1、*, Fajie Duan1, Kuan Wang1, and Jingxin Wu2
Author Affiliations
  • 1The State Key Lab of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
  • 2China Aerospace Hunan Power Machinery Research Institute, Zhuzhou, Hunan 412002, China
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    Figures & Tables(19)
    Schematic diagram of the echelle grating spectrometer
    Two-dimensional spectrogram of the echelle grating spectrometer in the free spectrum region
    Spectral reduction flowchart
    Schematic diagram of the image plane spot
    Schematic of spectrogram reduction
    Schematic diagram of center of mass extraction. (a) Original image; (b) Addition of Gaussian noise; (c) Background noise reduction; (d) Edge extraction; (e) Connected domain analysis center of mass extraction; (f) OSTU dipolarization; (g) Gray scale weighted center of mass extraction
    Two-dimensional spectrogram of mercury-argon light source imaging
    Comparison of imaging spectrograms of mercury-argon light sources
    Common element wavelength coordinate correction residuals
    Two-dimensional spectrogram of mercury-argon light source imaging
    Common element wavelength coordinate correction residuals
    Final deviation after residual compensation of wavelength coordinates of common elements
    • Table 1. Echelle grating spectrometer design parameters

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      Table 1. Echelle grating spectrometer design parameters

      ParameterValue
      Raster etching density/(l·mm−1)79
      Grating flashing angle/°63
      Grating deflection angle/°7
      Prismatic peak angle/°18
      Curvature of a spherical mirror/mm300
      Cylindrical lens curvature/mm34.5
      Detector full resolution2048×2048
      Detector pixel size/μm211×11
    • Table 2. Center of mass extraction error

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      Table 2. Center of mass extraction error

      ErrorX/pixelY/pixelEuclidean distance/pixel
      MAE0.395110.379410.60333
      MSE0.184110.236830.42094
      RMSE0.429080.486650.64881
      MAE (OSTU)2.59281.37923.0394
      MSE (OSTU)7.04042.62169.662
      RMSE (OSTU)2.65341.61913.1084
    • Table 3. Simulation experiment optical path parameter error value

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      Table 3. Simulation experiment optical path parameter error value

      FactorTest1Test2Test3
      Collimated spherical mirror deflection angle difference/°0.10.2−0.2
      Grating flashing angle difference/°0.20.2−0.2
      Grating deflection angle difference/°0.2−0.20.2
      Prismatic peak angle difference/°0.050.05−0.05
      Focusing spherical mirror deflection angle/°−0.10.1−0.1
      Image plane X coordinate difference/mm0.5−0.10.1
      Image plane Y coordinate difference/mm−0.50.10.1
      Image plane Z coordinate difference/mm2.0−1.02
      Angle of rotation of image plane difference/°1.50−1.5
      Temperature difference/℃10.0−10.010.0
      Barometric pressure difference/ATM0.50−0.5
    • Table 4. Spectral information on characteristic wavelengths of mercury-argon lamps

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      Table 4. Spectral information on characteristic wavelengths of mercury-argon lamps

      Wavelength/nmOrder of diffractionX position/pixelY position/pixelWavelength/nmOrder of diffractionX position/pixelY position/pixel
      253.65288−1.0108287.6266727.29431−769.6398−229.8145
      296.72875−259.1705433.7794738.39830−768.3944653.3849
      302.15074−285.9167203.6792750.38730−778.3806−147.5455
      313.15572−324.6694−231.9005763.51129−774.8637674.6637
      334.14867−399.4394138.8264772.37629−787.3103113.8959
      365.01561−475.8133409.3228794.81828−790.2125433.5014
      404.65655−549.4312430.7239800.61628−794.603772.0627
      407.78355−557.119847.3395811.53128−775.0149−670.483
      435.83351−591.7942492.492826.45227−800.1515303.6997
      546.07441−694.7505136.294842.46527−778.8817−732.2836
      576.96039−710.6427−123.4383852.14426−798.1824645.4346
      579.06639−706.8637−320.3302866.79426−806.3448−207.1703
      696.54332−762.6245358.3138912.29725−783.509−894.4498
      706.72232−757.8462−397.779922.45024−811.9811681.0741
      714.70431−761.3504645.1947
    • Table 5. Spectral coordinate correction fitting factor

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      Table 5. Spectral coordinate correction fitting factor

      FactorTest1Test2Test3
      A10.99860.99390.9961
      B1−0.02790.00020.0261
      C1−33.6899−2.9814−15.0959
      A20.02900.0043−0.0262
      B20.98760.99490.9993
      C250.1140−15.79328.9989
    • Table 6. Spectral coordinates of common elements

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      Table 6. Spectral coordinates of common elements

      Wavelength/nmType of elementsX position/pixelY position/pixelWavelength/nmType of elementsX position/pixelY position/pixel
      328.0Ag−379.2747325.992281.6Mo−183.6679−186.0624
      308.2Al−308.3616−116.4983588.9Na−719.3371160.7838
      249.7B32.5311−56.4979221.6Ni341.3734153.1065
      230.4Ba227.3107226.7227213.6P464.37547.4839
      396.8Ca−534.824506.7872220.3Pb361.3903−50.9932
      226.5Cd275.575257.838251.6Si14.9795128.6809
      267.7Cr−102.4702−88.747283.9Sn−199.609747.3144
      324.7Cu−369.9202101.6626213.8Zn461.5029−0.894
      259.9Fe−49.8481220.8933334.9Ti−401.203223.8482
      285.2Mg−202.6585−192.7362310.2V−317.9437258.7749
      257.6Mn−32.798985.962
    • Table 7. Residual polynomial fitting coefficients

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      Table 7. Residual polynomial fitting coefficients

      FactorTest1Test2Test3
      A13.373×10−23.361×10−29.772×10−4
      B1−8.157×10−5−1.153×10−4−2.517×10−6
      C12.640×10−96.465×10−91.724×10−10
      A2−7.852×10−21.142×10−1−1.312×10−2
      B22.221×10−4−3.411×10−43.365×10−5
      C2−9.151×10−91.204×10−9−2.296×10−9
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    Yuxuan Ouyang, Xiao Fu, Fajie Duan, Kuan Wang, Jingxin Wu. Spectral reduction algorithm for echelle grating spectrometer based on least-squares image coordinate correction[J]. Opto-Electronic Engineering, 2024, 51(7): 240134

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    Paper Information

    Category: Article

    Received: Jun. 7, 2024

    Accepted: Aug. 2, 2024

    Published Online: Nov. 12, 2024

    The Author Email: Xiao Fu (傅骁)

    DOI:10.12086/oee.2024.240134

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