Journal of Atmospheric and Environmental Optics, Volume. 20, Issue 4, 423(2025)

Parametric analytical model of modulation transfer function in turbid atmosphere

GUO Mengxing1,2,3, WU Pengfei2,3、*, FAN Zizhao2,3,4, and RAO Ruizhong2,3
Author Affiliations
  • 1Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, China
  • 2Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, HFIPS,Chinese Academy of Sciences, Hefei 230031, China
  • 3Advanced Laser Technology Laboratory of Anhui Province, Hefei 230037, China
  • 4School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China,Hefei 230022, China
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    Figures & Tables(10)
    On the condition of certain ω and g, MTF of turbid atmosphere with differentτ. (a) ω=0.1,g=0.05; (b) ω=0.1,g=0.95; (c) ω=1.0,g=0.05; (d) ω=1.0,g=0.95
    On the condition of certain τ and g, MTF of turbid atmosphere with different ω. (a) τ=0.1,g=0.05; (b) τ=0.1,g=0.95; (c) τ=1.0,g=0.05; (d) τ=1.0,g=0.95
    On the condition of certain τ and ω, MTF of turbid atmosphere with different g. (a) τ=0.1,ω=0.1; (b) τ=0.1,ω=1.0; (c) τ=1.0,ω=0.1; (d) τ=1.0,ω=1.0
    Approximate results of SAAMTF, SAAMTF1, EQMTF and M-EQMTF (τ=0.5). (a) g=0.2; (b) g=0.5; (c) g=0.7; (d) g=0.9
    Approximate results of SAAMTF, SAAMTF1, EQMTF and M-EQMTF (τ=1.0). (a) g=0.2; (b) g=0.5; (c) g=0.7; (d) g=0.9
    • Table 1. High and low critical frequency

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      Table 1. High and low critical frequency

      NumberOptical thicknessSingle scattering albedoAsymmetric factorCritical frequency/rad-1
      Low(ΩC1)High(ΩC2)
      10.1 ≤ τ < 0.20.10 ≤ ω ≤ 0.550.05 ≤ g ≤ 0.801.030.0
      20.80 < g ≤ 0.951.035.0
      30.55 < ω ≤ 0.800.05 ≤ g ≤ 0.801.135.0
      40.80 < g ≤ 0.951.560.0
      5ω > 0.800.05 ≤ g ≤ 0.801.340.0
      60.80 < g ≤ 0.952.080.0
      70.2 ≤ τ < 0.30.10 ≤ ω ≤ 0.550.05 ≤ g ≤ 0.800.720.0
      80.80 < g ≤ 0.950.825.0
      90.55 < ω ≤ 0.800.05 ≤ g ≤ 0.801.025.0
      100.80 < g ≤ 0.951.240.0
      11ω > 0.800.05 ≤ g ≤ 0.801.130.0
      120.80 < g ≤ 0.951.650.0
      130.3 ≤ τ < 0.50.10 ≤ ω ≤ 0.550.05 ≤ g ≤ 0.800.714.0
      140.80 < g ≤ 0.950.718.0
      150.55 < ω ≤ 0.800.05 ≤ g ≤ 0.800.818.0
      160.80 < g ≤ 0.950.925.0
      17ω > 0.800.05 ≤ g ≤ 0.800.925.0
      180.80 < g ≤ 0.951.245.0
      190.5 ≤ τ ≤ 1.00.10 ≤ ω ≤ 0.550.05 ≤ g ≤ 0.800.57.0
      200.80 < g ≤ 0.950.59.0
      210.55 < ω ≤ 0.800.05 ≤ g ≤ 0.800.610.0
      220.80 < g ≤ 0.950.716.0
      23ω > 0.800.05 ≤ g ≤ 0.800.815.0
      240.80 < g ≤ 0.950.940.0
    • Table 2. Analytical model expression

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      Table 2. Analytical model expression

      Range of spatial frequencyExpression
      LowMTF,low=a1+b1τ+c1ω+d1g
      HighMTF,high=a2+b2τ+c2ω+d2g
      MiddleMTF,middle=MTF,low+lg(Ω/ΩC1)(MTF,high-MTF,low)/lg(ΩC2/ΩC1)
    • Table 3. Coefficient of low spatial frequency formula

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      Table 3. Coefficient of low spatial frequency formula

      Numbera1b1c1d1
      10.96742-0.859650.112310.01278
      20.93337-0.715170.119570.03180
      30.88282-0.517650.126730.06266
      40.83477-0.380150.169920.05097
      50.83250-0.346450.135000.08300
      60.75507-0.150700.186500.07695
      70.91617-0.680960.154880.04311
      80.88705-0.620020.215080.03186
      90.82174-0.494950.191080.09466
      100.75047-0.350010.255410.07616
      110.74266-0.329840.219220.12519
      120.63077-0.137780.291500.11070
      130.86731-0.609010.216570.05944
      140.82859-0.556410.300390.04841
      150.72828-0.445720.284630.13741
      160.63164-0.321330.372380.11448
      170.59340-0.295550.347780.18172
      180.45276-0.129900.435000.15879
      190.76169-0.455610.283290.08436
      200.70036-0.424570.417890.08107
      210.55902-0.371840.437290.20686
      220.38153-0.279620.592270.20510
      230.27944-0.258300.622170.28191
      240.04840-0.120720.746500.27905
    • Table 4. Coefficient of high spatial frequency formula

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      Table 4. Coefficient of high spatial frequency formula

      Numbera2b2c2d2
      10.04859-0.215860.31145-0.02776
      20.06488> 0.326730.37259-0.05879
      30.01168-0.440610.48880-0.02803
      40.28131-0.500020.50751-0.39133
      5-0.07412-0.417400.57395-0.00749
      6-0.01473-0.448940.73158-0.28450
      70.04926-0.199600.33824-0.02564
      80.04926-0.199000.33824-0.02380
      9-0.00377-0.309490.48157-0.02606
      100.25360-0.315870.50507-0.38885
      11-0.12259-0.301190.603870.00184
      12-0.15022-0.293490.82808-0.25113
      130.05200-0.125000.28420-0.02200
      140.18400-0.101000.19592-0.16100
      15-0.01774-0.225910.47076-0.02080
      160.21117-0.209250.49998-0.36115
      17-0.18916-0.220220.647560.01371
      18-0.23108-0.189720.88681-0.25434
      190.05080-0.060000.21158-0.01408
      200.13300-0.033000.14300-0.12000
      21-0.03853-0.144470.44583-0.00152
      220.14296-0.113020.46562-0.30009
      23-0.31024-0.145600.73448-0.04613
      24-0.38894-0.107800.99217-0.23086
    • Table 5. Root mean square error and average relative error of our analytical model

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      Table 5. Root mean square error and average relative error of our analytical model

      Optical thicknessNumberRMSERMSEEMR/%
      LowMiddleHigh
      0.1 ≤ τ < 0.210.0150.0510.0190.0373.25
      20.0130.0580.0210.0423.53
      30.0120.0390.0120.0282.30
      40.0130.0500.0150.0322.37
      50.0140.0320.0130.0231.97
      60.0110.0470.0180.0271.84
      0.2 ≤ τ < 0.370.0120.0440.0090.0343.77
      80.0120.0480.0350.0373.77
      90.0150.0340.0120.0262.54
      100.0140.0480.0160.0332.73
      110.0140.0310.0140.0232.12
      120.0110.0450.0230.0281.99
      0.3 ≤ τ < 0.5130.0170.0410.0110.0334.44
      140.0150.0540.0220.0425.22
      150.0160.0400.0140.0313.49
      160.0140.0490.0180.0363.45
      170.0150.0400.0150.0302.97
      180.0130.0510.0210.0352.71
      0.5 ≤ τ ≤ 1.0190.0160.0350.0170.0296.21
      200.0130.0460.0210.0377.24
      210.0180.0340.0170.0294.51
      220.0170.0530.0190.0415.16
      230.0210.0380.0480.0324.10
      240.0220.0610.0200.0474.33
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    Mengxing GUO, Pengfei WU, Zizhao FAN, Ruizhong RAO. Parametric analytical model of modulation transfer function in turbid atmosphere[J]. Journal of Atmospheric and Environmental Optics, 2025, 20(4): 423

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    Paper Information

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    Received: Oct. 20, 2022

    Accepted: --

    Published Online: Sep. 30, 2025

    The Author Email: Pengfei WU (wupengfei@aiofm.ac.cn)

    DOI:10.3969/j.issn.1673-6141.2025.04.001

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