MODELING THE TOPOGRAPHY OF MICROSCRATCHES ON MIRROR SURFACES
DOI:
https://doi.org/10.26906/SUNZ.2025.2.145Keywords:
modeling, topography, microscratches, algorithm, interpolationAbstract
The subject of the study is the modeling of the topography of a microscratch-type defect on a flat mirror surface using modern algorithmic approaches that ensure the reproduction of smooth defect profiles with high fidelity to real data. The aim of the work is to develop an algorithm for synthesizing topographic maps to model microscratches with smooth and realistic profiles, taking into account natural depth fluctuations and the defect’s area of influence. The tasks addressed include: 1) developing a mathematical model that accounts for the key characteristics of microscratches; 2) ensuring a smooth transition between discrete points of the microscratch profile; 3) modeling depth fluctuations and the defect’s area of influence. The methods used include: algorithmic modeling of digital height maps based on the synthesis of a scratch cross-section with specified parameters; cubic spline interpolation to ensure profile smoothness and accurate contour reproduction; sinusoidal depth modulation considering amplitude and oscillation frequency, as well as nonlinear attenuation functions (exponential and cosine) for a detailed description of the defect’s influence distribution in space. A batch mode for generating synthetic dat a was also employed, allowing variation of key model parameters (maximum depth, width of the influence area, modulation amplitude coefficient, oscillation frequency, and attenuation parameters), which enables the generation of a wide range of microscratch topography variants. Results: The synthetic height maps demonstrated high correspondence with experimental data, confirming the model’s effectiveness in real-world conditions and its advantages for automated optical surface inspection systems. Conclusions: The developed model holds significant potential for integration into defect analysis systems, contributes to improving the reliability of optical devices, and is promising for further research, particularly for integration with deep l earning methods and subsequent experimental validation.Downloads
References
1. Stover J. C. (2012), "Optical Scattering: Measurement and Analysis", SPIE Press, Bellingham, WA. https://doi.org/10.1117/3.975276
2. [Zhongkai Liu, Jincheng Wang, Rongkuan Leng, Xiaokun Wang, Min Zhang, Jing Wang, Mengxue Cai, Wenhan Li, Bin Liu, Lingzhong Li, Qiang Cheng, Longxiang Li, Xiao Luo, Xuejun Zhang. Impact of mirror local defects on system scattering in telescopes // Results in Physics. – 2024. – Vol. 56. – 107265. https://doi.org/10.1016/j.rinp.2023.107265
3. Cao H., Peng X., Shi F., Tian Y., Kong L., Chen M., Hao Q. Advances in Subsurface Defect Detection Techniques for Fused Silica Optical Components: A Literature Review // Journal of Materials Research and Technology. – 2025. – Vol. 35. – P. 809-835. https://doi.org/10.1016/j.jmrt.2025.01.045
4. Galuza A., Shkoda M., Tevyasheva O., Belyaeva A., Savchenko A., Kolenov I. Modeling and Synthesis of Monochrome Interference Patterns of Flat Optical Surfaces with Typical Defects for Automatic Surface Quality Control // 2020 10th International Conference on Advanced Computer Information Technologies (ACIT): Conference Proceedings, Deggendorf, Germany, 16-18 Sept. – 2020. - P. 344-347. https://doi.org/10.1109/ACIT49673.2020.9208908
5. Monnet J., Petrovic O., Herfs W. Investigating the generation of synthetic data for surface defect detection: A comparative analysis // Procedia CIRP. – 2024. – Vol. 130. – P. 767–773. https://doi.org/10.1016/j.procir.2024.10.162
6. [Mei L., Guan G. Profilometry and atomic force microscopy for surface characterization // Nano TransMed. – 2023. – Vol. 2, Issue 1. – e9130017. https://doi.org/10.26599/NTM.2023.9130017
7. Gutierrez P., Luschkova M., Cordier A., Shukor M., Schappert M., Dahmen T. Synthetic training data generation for deep learning based quality inspection // Proc. of SPIE. – 2021. – Vol. 11794. – 1179403. https://doi.org/10.1117/12.2586824
8. Discrete Geometry for Computer Imagery / Ed.: Couprie M., Cousty J., Kenmochi Y., Mustafa N. – Springer, Cham, 2019. – 496 p. https://doi.org/10.1007/978-3-030-14085-4
9. Bosch C., Pueyo X., Mérillou S., Ghazanfarpour D. A Physically-Based Model for Rendering Realistic Scratches // Computer Graphics Forum. – 2004. – Vol. 23, Issue 3. – P. 361-370. https://doi.org/10.1111/j.1467-8659.2004.00767.x
10. Shorten C., Khoshgoftaar T. M. A Survey on Image Data Augmentation for Deep Learning // Journal of Big Data. – 2019. - Vol. 6, No. 1. - P. 60. https://doi.org/10.1186/s40537-019-0197-0
11. H. Müser M. H., Nicola L. Modeling the surface topography dependence of friction, adhesion, and contact compliance // MRS Bulletin. – 2022. – Vol. 47. – P. 1221-1228. https://doi.org/10.1557/s43577-022-00468-2
12. Lagae A., Lefebvre S., Cook R., DeRose T., Drettakis G., Ebert D.S., Lewis J.P., Perlin K., Zwicker M. A Survey of Procedural Noise Functions // Computer Graphics Forum. – 2010. – Vol. 29, Issue 8. – P. 2579-2600. https://doi.org/10.1111/j.1467-8659.2010.01827.x
13. Lyche T., Manni C., Speleers H. Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement. In: Lyche, T., Manni, C., Speleers, H. (eds) Splines and PDEs: From Approximation Theory to Numerical Linear Algebra. Lecture Notes in Mathematics, vol 2219. Springer, Cham. https://doi.org/10.1007/978-3-319-94911-6_1
14. Pawlus P., Reizer R. Profilometric measurements of wear scars: A review // Wear. – 2023. - Vol. 534–535. – 205150. https://doi.org/10.1016/j.wear.2023.205150
15. Kwon T.-Y., Ramachandran M., Park J.-G. Scratch formation and its mechanism in chemical mechanical planarization (CMP) // Friction. – 2013. – Vol. 1, Issue 4. – P. 279–305. https://doi.org/10.1007/s40544-013-0026-y
16. Zhang J. Classification and Comparison of Data Augmentation Techniques // Transactions on Computer Science and Intelligent Systems Research. – 2024. – Vol. 6. – P. 180–187. https://doi.org/10.62051/7e91md96
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Copyright (c) 2025 Oleksandr Kravchenko, Oleksii Haluza, Alla Savchenko, Stanislav Pohorielov, Anton Rogovyi
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