Application of TIE and Angular Spectrum Iteration to Scratch Depth Detection on the Surface of Optical Elements

Xin Meng; Hongjun Wang; Dasen Wang; Ailing Tian; Bingcai Liu; Xueliang Zhu; Weiguo Liu

doi:10.3788/AOS230499

Acta Optica Sinica, Volume. 43, Issue 14, 1412002(2023)

Application of TIE and Angular Spectrum Iteration to Scratch Depth Detection on the Surface of Optical Elements

Xin Meng¹, Hongjun Wang^1、*, Dasen Wang², Ailing Tian¹, Bingcai Liu¹, Xueliang Zhu¹, and Weiguo Liu¹

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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Figures & Tables(18)

Fig. 1. Schematic of scattering method

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Fig. 2. Flow chart of angular spectrum iterative algorithm

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Fig. 3. Flow chart of TIE algorithm

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Fig. 4. Scratch distribution on the surface of optical components. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution

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Fig. 5. Scattered light field distribution of different types of scratches. (a) Square scratch; (b) triangular scratch; (c) oval scratch

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Fig. 6. Reconstruction results of angular spectrum iterative algorithm. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution

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Fig. 7. Reconstruction results of TIE+angular spectrum iterative algorithm. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution

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Fig. 8. Intensity error curves of different types of scratches. (a) Square scratch; (b) triangular scratch; (c) oval scratch

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Fig. 9. Scratch scattered light field distribution acquisition optical path

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Fig. 10. Detection result of white light interferometry

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Fig. 11. Scattering distribution of scratches. (a) Scattering distribution; (b) scattering distribution after pretreatment

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Fig. 12. Scratch depth reconstruction results of two algorithms. (a) Transverse cross-section distribution; (b) three-dimensional distribution; (c) longitudinal cross-section distribution

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Table 1. Iterations when strength error is fixed
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Table 1. Iterations when strength error is fixed
Scratch type Angular spectrum iterative algorithm TIE+angular spectrum iterative algorithm
Square scratch 3321 953
Triangular scratch 2645 542
Oval scratch 3101 876

Table 2. Calculation results of correlation coefficient

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Table 2. Calculation results of correlation coefficient

Scratch type	Angular spectrum iterative algorithm		TIE+ angular spectrum iterative algorithm
Scratch type	Correlation coefficient	Relevance	Correlation coefficient	Relevance
Square scratch	0.9926	Highly relevant	0.9953	Highly relevant
Triangular scratch	0.9901	Highly relevant	0.9947	Highly relevant
Oval scratch	0.9893	Highly relevant	0.9926	Highly relevant

Table 3. Calculation results of relative root mean square error
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Table 3. Calculation results of relative root mean square error
Scratch type Angular spectrum iterative algorithm TIE+angular spectrum iterative algorithm
Square scratch 5.8 5.3
Triangular scratch 6.2 5.2
Oval scratch 6.6 5.3

Table 4. Reconstruction results of scratches with different depths by angular spectrum iterative algorithm

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Table 4. Reconstruction results of scratches with different depths by angular spectrum iterative algorithm

Serial number	Reconstruction value of 5 positions of scratch depth					Average value
Serial number	Position 1	Position 2	Position 3	Position 4	Position 5	Average value
1	0.234	0.215	0.194	0.234	0.218	0.219
2	0.219	0.174	0.220	0.224	0.207	0.209
3	0.239	0.213	0.185	0.194	0.193	0.205
4	0.156	0.117	0.131	0.145	0.136	0.137
5	0.134	0.122	0.127	0.136	0.116	0.127

Table 5. Reconstruction results of scratches with different depths by TIE+angular spectrum iterative algorithm

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Table 5. Reconstruction results of scratches with different depths by TIE+angular spectrum iterative algorithm

Serial number	Reconstruction value of 5 positions of scratch depth					Average value
Serial number	Position 1	Position 2	Position 3	Position 4	Position 5	Average value
1	0.243	0.207	0.219	0.215	0.218	0.220
2	0.225	0.214	0.199	0.205	0.217	0.212
3	0.221	0.234	0.229	0.212	0.216	0.224
4	0.134	0.133	0.136	0.152	0.120	0.135
5	0.111	0.139	0.108	0.134	0.124	0.124

Table 6. Calculation results of relative error of two reconstruction algorithms

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Table 6. Calculation results of relative error of two reconstruction algorithms

Serial number	Depth by white light interferometry / $μ m$	Angular spectrum iterative algorithm		TIE+angular spectrum iterative algorithm
Serial number	Depth by white light interferometry / $μ m$	Depth / $μ m$	Relative error /%	Depth / $μ m$	Relative error /%
1	0.222	0.219	1.35	0.220	0.90
2	0.218	0.209	4.13	0.212	2.75
3	0.214	0.205	4.21	0.222	3.73
4	0.132	0.137	3.79	0.135	2.27
5	0.125	0.127	1.60	0.123	1.60

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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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