• Acta Optica Sinica
  • Vol. 43, Issue 14, 1412002 (2023)
Xin Meng1, Hongjun Wang1,*, Dasen Wang2, Ailing Tian1..., Bingcai Liu1, Xueliang Zhu1 and Weiguo Liu1|Show fewer author(s)
Author Affiliations
  • 1Shaanxi Province Key Laboratory of Thin Films Technology and Optical Test, Xi'an Technological University, Xi'an 710021, Shaanxi, China
  • 2The Ningbo Branch of Ordnance Science Institute of China, Ningbo 310022, Zhejiang, China
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    DOI: 10.3788/AOS230499 Cite this Article Set citation alerts
    Xin Meng, Hongjun Wang, Dasen Wang, Ailing Tian, Bingcai Liu, Xueliang Zhu, Weiguo Liu. Application of TIE and Angular Spectrum Iteration to Scratch Depth Detection on the Surface of Optical Elements[J]. Acta Optica Sinica, 2023, 43(14): 1412002 Copy Citation Text show less
    Schematic of scattering method
    Fig. 1. Schematic of scattering method
    Flow chart of angular spectrum iterative algorithm
    Fig. 2. Flow chart of angular spectrum iterative algorithm
    Flow chart of TIE algorithm
    Fig. 3. Flow chart of TIE algorithm
    Scratch distribution on the surface of optical components. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Fig. 4. Scratch distribution on the surface of optical components. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Scattered light field distribution of different types of scratches. (a) Square scratch; (b) triangular scratch; (c) oval scratch
    Fig. 5. Scattered light field distribution of different types of scratches. (a) Square scratch; (b) triangular scratch; (c) oval scratch
    Reconstruction results of angular spectrum iterative algorithm. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Fig. 6. Reconstruction results of angular spectrum iterative algorithm. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Reconstruction results of TIE+angular spectrum iterative algorithm. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Fig. 7. Reconstruction results of TIE+angular spectrum iterative algorithm. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Intensity error curves of different types of scratches. (a) Square scratch; (b) triangular scratch; (c) oval scratch
    Fig. 8. Intensity error curves of different types of scratches. (a) Square scratch; (b) triangular scratch; (c) oval scratch
    Scratch scattered light field distribution acquisition optical path
    Fig. 9. Scratch scattered light field distribution acquisition optical path
    Detection result of white light interferometry
    Fig. 10. Detection result of white light interferometry
    Scattering distribution of scratches. (a) Scattering distribution; (b) scattering distribution after pretreatment
    Fig. 11. Scattering distribution of scratches. (a) Scattering distribution; (b) scattering distribution after pretreatment
    Scratch depth reconstruction results of two algorithms. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Fig. 12. Scratch depth reconstruction results of two algorithms. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution
    Scratch typeAngular spectrum iterative algorithmTIE+angular spectrum iterative algorithm
    Square scratch3321953
    Triangular scratch2645542
    Oval scratch3101876
    Table 1. Iterations when strength error is fixed
    Scratch typeAngular spectrum iterative algorithmTIE+ angular spectrum iterative algorithm
    Correlation coefficientRelevanceCorrelation coefficientRelevance
    Square scratch0.9926Highly relevant0.9953Highly relevant
    Triangular scratch0.9901Highly relevant0.9947Highly relevant
    Oval scratch0.9893Highly relevant0.9926Highly relevant
    Table 2. Calculation results of correlation coefficient
    Scratch typeAngular spectrum iterative algorithmTIE+angular spectrum iterative algorithm
    Square scratch5.85.3
    Triangular scratch6.25.2
    Oval scratch6.65.3
    Table 3. Calculation results of relative root mean square error
    Serial numberReconstruction value of 5 positions of scratch depthAverage value
    Position 1Position 2Position 3Position 4Position 5
    10.2340.2150.1940.2340.2180.219
    20.2190.1740.2200.2240.2070.209
    30.2390.2130.1850.1940.1930.205
    40.1560.1170.1310.1450.1360.137
    50.1340.1220.1270.1360.1160.127
    Table 4. Reconstruction results of scratches with different depths by angular spectrum iterative algorithm
    Serial numberReconstruction value of 5 positions of scratch depthAverage value
    Position 1Position 2Position 3Position 4Position 5
    10.2430.2070.2190.2150.2180.220
    20.2250.2140.1990.2050.2170.212
    30.2210.2340.2290.2120.2160.224
    40.1340.1330.1360.1520.1200.135
    50.1110.1390.1080.1340.1240.124
    Table 5. Reconstruction results of scratches with different depths by TIE+angular spectrum iterative algorithm
    Serial numberDepth by white light interferometry /μmAngular spectrum iterative algorithmTIE+angular spectrum iterative algorithm
    Depth /μmRelative error /%Depth /μmRelative error /%
    10.2220.2191.350.2200.90
    20.2180.2094.130.2122.75
    30.2140.2054.210.2223.73
    40.1320.1373.790.1352.27
    50.1250.1271.600.1231.60
    Table 6. Calculation results of relative error of two reconstruction algorithms
    Xin Meng, Hongjun Wang, Dasen Wang, Ailing Tian, Bingcai Liu, Xueliang Zhu, Weiguo Liu. Application of TIE and Angular Spectrum Iteration to Scratch Depth Detection on the Surface of Optical Elements[J]. Acta Optica Sinica, 2023, 43(14): 1412002
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