Optics and Precision Engineering, Volume. 33, Issue 3, 389(2025)
Adaptive focusing evaluation algorithm for optical imaging of wafer positioning marks
Figures & Tables(18)
Fig. 1. Schematic diagram of single and double layer structure of wafer positioning marks
Fig. 2. Flowchart of multi-directional gradient variance adaptive focusing evaluation algorithm
Fig. 3. Schematic diagram of multi-directional gradient variance focusing evaluation algorithm
Fig. 5. Positive focus schematic and image sets of wafer location marker in four groups of experiments
Fig. 9. Normalized focus evaluation curves for sets of images with different noise levels
Table 1. Quantitative index of focusing evaluation function of single-layer square marks image set
View tableView in ArticleTable 1. Quantitative index of focusing evaluation function of single-layer square marks image set
聚焦评价函数 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen Brenner 15 0.105 6.168 0.022 0.552 Roberts 14 0.096 4.406 0.027 0.453 Tenengrad 14 0.123 15.844 0.023 0.626 DFT 13 0.034 1.467 0.042 0.048 Bre2d_Rob 12 0.030 1.616 0.061 0.083 Bre4d_var 6 0.305 27.263 0.015 3.784 Bre2d_Rob2d_var（ours） 3 0.664 39.521 0.012 16.511
Table 2. Quantitative index of focusing evaluation function of inner cross marks image set
View tableView in ArticleTable 2. Quantitative index of focusing evaluation function of inner cross marks image set
聚焦评价函数 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen Brenner 16 0.108 11.600 0.016 0.300 Roberts 16 0.101 6.796 0.015 0.330 Tenengrad 15 0.121 25.090 0.017 0.337 DFT 13 0.052 1.866 0.040 0.041 Bre2d_Rob 6 0.232 4.908 0.027 2.410 Bre4d_var 6 0.310 33.960 0.013 1.165 Bre2d_Rob2d_var（ours） 3 0.662 79.899 0.002 6.968
Table 3. Quantitative index of focusing evaluation function of outer cross marks image set
View tableView in ArticleTable 3. Quantitative index of focusing evaluation function of outer cross marks image set
聚焦评价函数 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen Brenner 13 0.118 5.437 0.019 0.630 Roberts 12 0.107 3.346 0.016 0.520 Tenengrad 11 0.153 11.575 0.020 0.800 DFT 11 0.049 1.568 0.033 0.099 Bre2d_Rob 7 0.155 2.418 0.022 0.877 Bre4d_var 5 0.374 60.772 0.012 4.880 Bre2d_Rob2d_var（ours） 4 0.493 84.563 0.003 6.712
Table 4. Quantitative index of focusing evaluation function of double-layer cross marks image set
View tableView in ArticleTable 4. Quantitative index of focusing evaluation function of double-layer cross marks image set
聚焦评价函数 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen Brenner 21 0.058 3.134 0.029 0.125 Roberts 20 0.046 2.135 0.025 0.118 Tenengrad 19 0.076 6.202 0.038 0.172 DFT 16 0.022 1.432 0.041 0.018 Bre2d_Rob 7 0.172 3.194 0.055 0.735 Bre4d_var 6 0.294 35.385 0.038 0.797 Bre2d_Rob2d_var（ours） 4 0.499 55.610 0.013 3.764
Table 5. Quantitative index of focusing evaluation function of image sets with different resolution
View tableView in ArticleTable 5. Quantitative index of focusing evaluation function of image sets with different resolution
分辨率 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen 160×128 7 0.286 28.935 0.017 2.116 320×256 6 0.283 31.865 0.021 2.451 640×512 4 0.496 32.852 0.012 2.827 1 280×1 024 4 0.499 55.610 0.013 3.764
Table 6. Number of pixels involved in calculation for a single image
View tableView in ArticleTable 6. Number of pixels involved in calculation for a single image
聚焦评价函数 图集1 图集2 图集3 图集4 Brenner 131 131 131 131 Roberts 131 131 131 131 Bre2d-Rob 131 131 131 131 Bre4d-var 131 131 131 131 Bre2d_Rob2d_Var 6.46 3.28 10.93 10.97
Table 7. Evaluation calculation time for a single image（ms）
View tableView in ArticleTable 7. Evaluation calculation time for a single image（ms）
聚焦评价函数 图集1 图集2 图集3 图集4 Brenner 75 74 70 93 Roberts 84 89 88 95 Bre2d-Rob 923 965 982 899 Bre4d-var 2 093 1 920 1 932 1 968 Bre2d_Rob2d_Var 161 183 214 268
Table 8. Quantitative index of focusing evaluation function of Gaussian white noise test validation set
View tableView in ArticleTable 8. Quantitative index of focusing evaluation function of Gaussian white noise test validation set
聚焦评价函数 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen Brenner 25 0.054 2.865 0.377 0.050 Roberts 22 0.043 1.995 0.325 0.047 Tenengrad 19 0.072 4.895 0.494 0.069 DFT 17 0.022 1.631 0.533 0.007 Bre2d_Rob 9 0.154 2.946 0.715 0.294 Bre4d_var 8 0.287 14.154 0.494 0.319 Bre2d_Rob2d_var（ours） 5 0.484 22.244 0.169 1.506
Table 9. Quantitative index of focusing evaluation function of salt-and-pepper noise test validation set
View tableView in ArticleTable 9. Quantitative index of focusing evaluation function of salt-and-pepper noise test validation set
聚焦评价函数 陡峭区宽度W 陡峭度Stp 清晰度比率R 平缓区域波动量Vf 灵敏度fsen Brenner 23 0.055 2.960 0.244 0.075 Roberts 19 0.044 2.017 0.138 0.071 Tenengrad 20 0.073 5.124 0.157 0.103 DFT 17 0.025 1.633 0.562 0.011 Bre2d_Rob 16 0.161 2.982 0.283 0.441 Bre4d_var 8 0.290 21.231 0.157 0.478 Bre2d_Rob2d_var（ours） 5 0.489 25.419 0.120 2.258
Tools
Get Citation
Copy Citation Text
Jin YANG, Hangying ZHANG, Kai MENG, Peihuang LOU. Adaptive focusing evaluation algorithm for optical imaging of wafer positioning marks[J]. Optics and Precision Engineering, 2025, 33(3): 389
Paper Information
Category:
Received: Nov. 25, 2024
Accepted: --
Published Online: Apr. 30, 2025
The Author Email: Hangying ZHANG (markzhang@nuaa.edu.cn)
© Copyright 2018-2021 | Chinese Laser Press.
All Rights Reserved 沪ICP备15018463号-20