• Opto-Electronic Engineering
  • Vol. 49, Issue 4, 210367 (2022)
Ziyi Zhang, Meng Chen*, Chunlei Wang, Hepeng Xiang, and Ruiqing Tao
Author Affiliations
  • Institute of Laser Engineering, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China
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    DOI: 10.12086/oee.2022.210367 Cite this Article
    Ziyi Zhang, Meng Chen, Chunlei Wang, Hepeng Xiang, Ruiqing Tao. Research on shaping characteristics of Gaussian beam aspheric shaping system[J]. Opto-Electronic Engineering, 2022, 49(4): 210367 Copy Citation Text show less
    Illustration for a uniform energy density distribution H(x) in one dimension
    Fig. 1. Illustration for a uniform energy density distribution H(x) in one dimension
    Structure of aspheric shaping system
    Fig. 2. Structure of aspheric shaping system
    Experimental device diagram
    Fig. 3. Experimental device diagram
    Laser power stability test
    Fig. 4. Laser power stability test
    Light intensity distribution maps corresponding to different incident beam diameters. (a) D=1.0 mm; (b) D=1.2 mm; (c) D=1.4 mm; (d) D=1.6 mm; (e) D=1.8 mm; (f) D=2.0 mm
    Fig. 5. Light intensity distribution maps corresponding to different incident beam diameters. (a) D=1.0 mm; (b) D=1.2 mm; (c) D=1.4 mm; (d) D=1.6 mm; (e) D=1.8 mm; (f) D=2.0 mm
    Fitting curves of incident beam diameter with optimal shaping position, flatness factor, beam uniformity and edge steepness. (a) D-L fitting curve; (b) D-FF fitting curve; (c) D-U fitting curve; (d) D-s fitting curve
    Fig. 6. Fitting curves of incident beam diameter with optimal shaping position, flatness factor, beam uniformity and edge steepness. (a) D-L fitting curve; (b) D-FF fitting curve; (c) D-U fitting curve; (d) D-s fitting curve
    Light intensity distributions corresponding to different incident divergence angles. (a) θ=3.7 mrad; (b) θ=6.5 mrad; (c) θ=9 mrad; (d) θ=11.5 mrad; (e) θ=13.5 mrad; (f) θ=18.4 mrad
    Fig. 7. Light intensity distributions corresponding to different incident divergence angles. (a) θ=3.7 mrad; (b) θ=6.5 mrad; (c) θ=9 mrad; (d) θ=11.5 mrad; (e) θ=13.5 mrad; (f) θ=18.4 mrad
    Fitting curve of incident divergence angle with optimal shaping position, flatness factor, beam uniformity and edge steepness. (a) θ-L fitting curve; (b) θ-FF fitting curve; (c) θ-U fitting curve; (d) θ-s fitting curve
    Fig. 8. Fitting curve of incident divergence angle with optimal shaping position, flatness factor, beam uniformity and edge steepness. (a) θ-L fitting curve; (b) θ-FF fitting curve; (c) θ-U fitting curve; (d) θ-s fitting curve
    RadiusThickness/mmGlassAsphere coefficients
    Infinity
    1−8.09020F_SILICA
    2−17.37980k=−4.74 A4=−2.81*10−4A6=8.42*10−7A8=−6*10−10
    3133.3848F_SILICAk=10 A4=−1.94*10−5A8=−3*10−9
    4Infinity
    Table 1. Design parameters of aspheric shaping mirror
    Beam diameter D/mm Optimal shaping position L/mm Flatness factor FF/% Beam uniformity U/% Edge steepness s/%
    1.085089.880320.079413.9002
    1.173086.749217.902211.9430
    1.269087.951116.607311.7702
    1.357085.264615.686211.2720
    1.445085.226315.220610.5791
    1.539086.339115.699311.6226
    1.634084.340515.429310.5575
    1.729086.562615.996711.7576
    1.822087.567417.696813.2841
    1.921085.629818.986313.8889
    2.017084.017718.051314.7741
    2.216085.631822.032419.0972
    2.413085.972924.160421.5402
    Table 2. Influence of incident beam diameter on aspheric shaping
    Beam divergence angle θ/mrad Optimal shaping position L/mm Flatness factor FF/% Beam uniformity U/% Edge steepness s/%
    3.746087.293617.039412.6779
    5.743085.486217.677212.8009
    6.545085.226315.220610.5791
    9.044086.326616.094211.6845
    11.538082.903315.143510.6089
    13.537084.433516.954812.6164
    18.423086.457021.692518.8504
    Table 3. Influence of incident divergence angle on aspheric surface shaping
    Factors−1−0.59200.5921
    Beam divergence angle/mrad3.75.78.611.513.5
    Beam diameter/mm1.01.21.51.82.0
    Table 4. Experimental influencing factors and experimental design level
    NumberBeam divergence angle θ/mrad Beam diameter D/mm Optimal shaping position L/mm
    13.71.01050
    23.72.0230
    35.71.5400
    48.61.2560
    58.61.5360
    68.61.8200
    711.51.5320
    813.51.0750
    913.52.0150
    Table 5. Experimental data table
    SourceSum of squaresdfMean squareF-valueP-value
    Model3.1421.57148.06< 0.0001significant
    Beam divergence angle0.170810.170816.100.0070
    Beam diameter2.9712.97280.03< 0.0001
    Residual0.063760.0106
    Cor total3.218
    R2=0.9801 Pre-R2=0.9395
    Adj-R2=0.9735 Adeq-precision=33.1476
    Table 6. Analysis of variance of the optimal shaping position
    NumberBeam divergence angle/mradBeam diameter/mmOptimal shaping position/mmError/%
    Experiment valuePredicted value
    13.71.3610620.53571.73
    23.71.6410385.11416.07
    33.71.75300303.38961.13
    45.71.1770789.03542.47
    55.71.7310303.90781.97
    65.72.0210188.609910.19
    76.51.2720652.41209.39
    86.51.5430404.89715.84
    96.51.75290272.08016.18
    109.01.2610591.95182.96
    119.01.5350367.37454.96
    129.01.85220210.57274.29
    1313.51.5280308.379010.14
    Table 7. Verification experiment of predictive function
    Ziyi Zhang, Meng Chen, Chunlei Wang, Hepeng Xiang, Ruiqing Tao. Research on shaping characteristics of Gaussian beam aspheric shaping system[J]. Opto-Electronic Engineering, 2022, 49(4): 210367
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