Opto-Electronic Engineering, Volume. 49, Issue 4, 210367(2022)
Research on shaping characteristics of Gaussian beam aspheric shaping system
Figures & Tables(15)
Fig. 1. Illustration for a uniform energy density distribution H(x) in one dimension
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
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
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
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
Table 1. Design parameters of aspheric shaping mirror
View tableView in ArticleTable 1. Design parameters of aspheric shaping mirror
Radius Thickness/mm Glass Asphere coefficients Infinity 1 −8.090 20 F_SILICA 2 −17.379 80 k=−4.74 A4=−2.81*10−4A6=8.42*10−7A8=−6*10−10 3 133.384 8 F_SILICA k=10 A4=−1.94*10−5A8=−3*10−9 4 Infinity
Table 2. Influence of incident beam diameter on aspheric shaping
View tableView in ArticleTable 2. Influence of incident beam diameter on aspheric shaping
Beam diameter D/mm Optimal shaping position L/mm Flatness factor FF/% Beam uniformity U/% Edge steepness s/% 1.0 850 89.8803 20.0794 13.9002 1.1 730 86.7492 17.9022 11.9430 1.2 690 87.9511 16.6073 11.7702 1.3 570 85.2646 15.6862 11.2720 1.4 450 85.2263 15.2206 10.5791 1.5 390 86.3391 15.6993 11.6226 1.6 340 84.3405 15.4293 10.5575 1.7 290 86.5626 15.9967 11.7576 1.8 220 87.5674 17.6968 13.2841 1.9 210 85.6298 18.9863 13.8889 2.0 170 84.0177 18.0513 14.7741 2.2 160 85.6318 22.0324 19.0972 2.4 130 85.9729 24.1604 21.5402
Table 3. Influence of incident divergence angle on aspheric surface shaping
View tableView in ArticleTable 3. Influence of incident divergence angle on aspheric surface shaping
Beam divergence angle θ/mrad Optimal shaping position L/mm Flatness factor FF/% Beam uniformity U/% Edge steepness s/% 3.7 460 87.2936 17.0394 12.6779 5.7 430 85.4862 17.6772 12.8009 6.5 450 85.2263 15.2206 10.5791 9.0 440 86.3266 16.0942 11.6845 11.5 380 82.9033 15.1435 10.6089 13.5 370 84.4335 16.9548 12.6164 18.4 230 86.4570 21.6925 18.8504
Table 4. Experimental influencing factors and experimental design level
View tableView in ArticleTable 4. Experimental influencing factors and experimental design level
Factors −1 −0.592 0 0.592 1 Beam divergence angle/mrad 3.7 5.7 8.6 11.5 13.5 Beam diameter/mm 1.0 1.2 1.5 1.8 2.0
Table 5. Experimental data table
View tableView in ArticleTable 5. Experimental data table
Number Beam divergence angle θ/mrad Beam diameter D/mm Optimal shaping position L/mm 1 3.7 1.0 1050 2 3.7 2.0 230 3 5.7 1.5 400 4 8.6 1.2 560 5 8.6 1.5 360 6 8.6 1.8 200 7 11.5 1.5 320 8 13.5 1.0 750 9 13.5 2.0 150
Table 6. Analysis of variance of the optimal shaping position
View tableView in ArticleTable 6. Analysis of variance of the optimal shaping position
Source Sum of squares df Mean square F-value P-value Model 3.14 2 1.57 148.06 < 0.0001 significant Beam divergence angle 0.1708 1 0.1708 16.10 0.0070 Beam diameter 2.97 1 2.97 280.03 < 0.0001 Residual 0.0637 6 0.0106 Cor total 3.21 8 R2=0.9801 Pre-R2=0.9395 Adj-R2=0.9735 Adeq-precision=33.1476
Table 7. Verification experiment of predictive function
View tableView in ArticleTable 7. Verification experiment of predictive function
Number Beam divergence angle/mrad Beam diameter/mm Optimal shaping position/mm Error/% Experiment value Predicted value 1 3.7 1.3 610 620.5357 1.73 2 3.7 1.6 410 385.1141 6.07 3 3.7 1.75 300 303.3896 1.13 4 5.7 1.1 770 789.0354 2.47 5 5.7 1.7 310 303.9078 1.97 6 5.7 2.0 210 188.6099 10.19 7 6.5 1.2 720 652.4120 9.39 8 6.5 1.5 430 404.8971 5.84 9 6.5 1.75 290 272.0801 6.18 10 9.0 1.2 610 591.9518 2.96 11 9.0 1.5 350 367.3745 4.96 12 9.0 1.85 220 210.5727 4.29 13 13.5 1.5 280 308.3790 10.14
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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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Received: Nov. 17, 2021
Accepted: --
Published Online: May. 24, 2022
The Author Email: Chen Meng (chenmeng@bjut.edu.cn)
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