Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation

doi:10.1007/s40436-024-00535-8

Advances in Manufacturing ›› 2025, Vol. 13 ›› Issue (4): 768-783.doi: 10.1007/s40436-024-00535-8

• • 上一篇

Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation

Yong-Hao Zhou¹, Bin Shen¹, Lin Chang², Sergiy Valyukh³, Ying-Jie Yu¹

1. Department of Precision Mechanical Engineering, Shanghai University, Shanghai, 200444, People's Republic of China;
2. School of Engineering, Huzhou University, Huzhou, 313000, Zhejiang, People's Republic of China;
3. Department of Physics, Chemistry, and Biology, Link?ping University, SE-58183, Link?ping, Sweden

收稿日期:2023-12-26 修回日期:2024-02-25 发布日期:2025-12-06
通讯作者: Ying-Jie Yu Email:E-mail:yingjieyu@staff.shu.edu.cn E-mail:yingjieyu@staff.shu.edu.cn
作者简介:Yong-Hao Zhou received the B.S. in information and computational science and the M.S. degree in technology for computer applications from the North China University of Water Resources and Electric Power, Zhengzhou, China, in 2018 and 2021, respectively. He is currently a Ph.D. candidate at Shanghai University. His research interests include optical interferometry and signal processing.
Bin Shen received the B.S. degree in mechanical and electrical engineering from the Nanjing Forest University, Nanjing, China, in 2019. He is currently pursuing the master’s degree with Shanghai University, Shanghai, China. His main research direction is wavelengtht uningphase-shifting interferometry.
Lin Chang received the M.S. degree in mechanical engineering from the Shandong University of Science and Technology, Qingdao, China, in 2019, and received the Ph.D. degree in mechanical engineering from Shanghai University, Shanghai, China, in 2022. He is currently working at Huzhou University, Huzhou, China. His main research direction is precision optical measurement.
Sergiy Valyukh received the Ph.D. degree in optics and laser physics from the Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, in 2003. He was a Post-Doctoral Researcher with Dalarna University, Falun, Sweden, and the Swedish LCD Center AB, Borl?nge, Sweden. Since 2010, he has been conducting research and teaching with Link?ping University, Link?ping, Sweden.
Ying-Jie Yu graduated from Harbin Institute of Technology in China with a doctoral degree. Now she is a professor at the School of Mechatronic Engineering and Automation of Shanghai University. Her research areas include optical interferometry, digital holography, computational imaging.
基金资助:
This research was supported by the Key Laboratory Project in the Anhui Province of China (Grant No.CGHBMWSJC10) and the Chengdu Tyggo Optoelectronic Technology Corporation.

Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation

Yong-Hao Zhou¹, Bin Shen¹, Lin Chang², Sergiy Valyukh³, Ying-Jie Yu¹

1. Department of Precision Mechanical Engineering, Shanghai University, Shanghai, 200444, People's Republic of China;
2. School of Engineering, Huzhou University, Huzhou, 313000, Zhejiang, People's Republic of China;
3. Department of Physics, Chemistry, and Biology, Link?ping University, SE-58183, Link?ping, Sweden

Received:2023-12-26 Revised:2024-02-25 Published:2025-12-06
Contact: Ying-Jie Yu Email:E-mail:yingjieyu@staff.shu.edu.cn E-mail:yingjieyu@staff.shu.edu.cn
Supported by:
This research was supported by the Key Laboratory Project in the Anhui Province of China (Grant No.CGHBMWSJC10) and the Chengdu Tyggo Optoelectronic Technology Corporation.

摘要/Abstract

摘要： Multiple-surface interferometry with nanoscale accuracy is important in the precise manufacturing of optically transparent parallel plates. To measure the surface profile and thickness variation of the plates simultaneously, the frequencies of the interferometric signal must be estimated from overlaid interferograms. Traditional algorithms typically suffer from issues such as spectrum leakage, reliance on initial iterative values, and the need for prior knowledge. In this study, the time-domain estimation algorithm for multiple-surface interferometry (MSI-TDe) is introduced based on a difference model to improve the accuracy of frequency estimation. The MSI-TDe algorithm is based on a normal equation that is insensitive to environmental noise. Using the algorithm, the frequencies of an interferometric signal can be estimated without prior knowledge and employed for wavefront reconstruction in multi-surface interferometry. Numerical simulation results indicate that the MSI-TDe algorithm has better frequency estimation performance than the discrete Fourier transform (DFT) algorithm. The relative error of the frequency estimation is on the order of 10^–4. Three-surface interferometry was first performed. The root-mean square repeatability standard deviations of 0.07, 0.12 and 0.11 nm for the thickness variation, front surface profile, and rear surface profile, respectively, indicate the stability of the MSI-TDe algorithm. Four-surface interferometry with six frequency components was then performed. The adaptability of the MSI-TDe algorithm is validated by the measurement results.

The full text can be downloaded at https://doi.org/10.1007/s40436-024-00535-8

关键词: Multiple-surface, Simultaneous measurement, Phase-shifting interferometry, Wavelength tuning, Parameter estimation

Abstract: Multiple-surface interferometry with nanoscale accuracy is important in the precise manufacturing of optically transparent parallel plates. To measure the surface profile and thickness variation of the plates simultaneously, the frequencies of the interferometric signal must be estimated from overlaid interferograms. Traditional algorithms typically suffer from issues such as spectrum leakage, reliance on initial iterative values, and the need for prior knowledge. In this study, the time-domain estimation algorithm for multiple-surface interferometry (MSI-TDe) is introduced based on a difference model to improve the accuracy of frequency estimation. The MSI-TDe algorithm is based on a normal equation that is insensitive to environmental noise. Using the algorithm, the frequencies of an interferometric signal can be estimated without prior knowledge and employed for wavefront reconstruction in multi-surface interferometry. Numerical simulation results indicate that the MSI-TDe algorithm has better frequency estimation performance than the discrete Fourier transform (DFT) algorithm. The relative error of the frequency estimation is on the order of 10^–4. Three-surface interferometry was first performed. The root-mean square repeatability standard deviations of 0.07, 0.12 and 0.11 nm for the thickness variation, front surface profile, and rear surface profile, respectively, indicate the stability of the MSI-TDe algorithm. Four-surface interferometry with six frequency components was then performed. The adaptability of the MSI-TDe algorithm is validated by the measurement results.

The full text can be downloaded at https://doi.org/10.1007/s40436-024-00535-8

Key words: Multiple-surface, Simultaneous measurement, Phase-shifting interferometry, Wavelength tuning, Parameter estimation

Yong-Hao Zhou, Bin Shen, Lin Chang, Sergiy Valyukh, Ying-Jie Yu. Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation[J]. Advances in Manufacturing, 2025, 13(4): 768-783.

参考文献

[1] Sun T, Zheng W, Yu Y et al (2019) Algorithm for surfaces profiles and thickness variation measurement of a transparent plate using a Fizeau interferometer with wavelength tuning. Appl Sci 9:2349. https://doi.org/10.3390/app9112349
[2] Seo YB, Joo KN, Ghim YS et al (2021) Subaperture stitching wavelength scanning interferometry for 3D surface measurement of complex-shaped optics. Meas Sci Technol 32:045201. https://doi.org/10.1088/1361-6501/abd056
[3] Hu Y, Chen Q, Liang Y et al (2019) Microscopic 3D measurement of shiny surfaces based on a multi-frequency phase-shifting scheme. Opt Lasers Eng 122:1-7
[4] Park J, Kim JA, Ahn H et al (2019) A review of thickness measurements of thick transparent layers using optical interferometry. Int J Precis Eng Manuf 20:463-477
[5] Guo H, Chen M (2005) Least-squares algorithm for phase-stepping interferometry with an unknown relative step. Appl Opt 44:4854-4859
[6] Chang L, He T, Wang C et al (2022) Multi-surface phase-shifting interferometry using harmonic frequency solution based on the total least squares. Opt Lasers Eng 150:106845. https://doi.org/10.1016/j.optlaseng.2021.106845
[7] Juarez-Salazar R, Robledo-Sánchez C, Meneses-Fabian C et al (2013) Generalized phase-shifting interferometry by parameter estimation with the least squares method. Opt Lasers Eng 51:626-632
[8] Kitagawa K (2014) Surface and thickness measurement of a transparent film using three-wavelength interferometry. In: Proceedings of the 14th international conference of the European society for precision engineering and nanotechnology, 1:4172-4175
[9] Wang Z, Han B (2004) Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms. Opt Lett 29:1671. https://doi.org/10.1364/ol.29.001671
[10] Xu X, Lu X, Tian J et al (2016) Random phase-shifting interferometry based on independent component analysis. Opt Commun 370:75-80
[11] Chen Y, Wang T, Kemao Q (2021) Parallel advanced iterative algorithm for phase extraction with unknown phase-shifts. Opt Lasers Eng 138:106408. https://doi.org/10.1016/j.optlaseng.2020.106408
[12] Chen Y, Kemao Q (2019) Advanced iterative algorithm for phase extraction: performance evaluation and enhancement. Opt Express 27:37634. https://doi.org/10.1364/oe.27.037634
[13] Hao Q, Zhu Q, Hu Y (2009) Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts. Opt Lett 34:1288. https://doi.org/10.1364/ol.34.001288
[14] Vargas J, Carazo JM, Sorzano COS (2014) Error analysis of the principal component analysis demodulation algorithm. Appl Phys B Lasers Opt 115:355-364
[15] Zhang W, Lu X, Luo C et al (2015) Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry. Opt Commun 341:276-283
[16] Deng J, Wang K, Wu D et al (2015) Advanced principal component analysis method for phase reconstruction. Opt Express 23:12222. https://doi.org/10.1364/oe.23.012222
[17] Xu JC, Jin WM, Chai LQ et al (2011) Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method. Opt Express 19:20483. https://doi.org/10.1364/oe.19.020483
[18] Deng J, Wu D, Wang K et al (2016) Precise phase retrieval under harsh conditions by constructing new connected interferograms. Sci Rep 6:1-10
[19] Bai Y, He Y, Bao H et al (2015) Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry. J Opt Soc Am A 32:1352. https://doi.org/10.1364/josaa.32.001352
[20] Huang T, Bai Y, Tan J et al (2021) Estimating the number of layers for precise wavelength scanning interferometry. Meas Sci Technol 32:115203. https://doi.org/10.1088/1361-6501/ac0ad0
[21] Das S, Liu CH, Singh M et al (2018) Modified wavelength scanning interferometry for simultaneous tomography and topography of the cornea with Fourier domain optical coherence tomography. Biomed Opt Express 9:4443. https://doi.org/10.1364/boe.9.004443
[22] Kim Y, Hibino K, Sugita N et al (2015) Absolute optical thickness measurement of transparent plate using excess fraction method and wavelength-tuning Fizeau interferometer. Opt Express 23:4065. https://doi.org/10.1364/oe.23.004065
[23] Lifshitz E, Arieli U, Katz S et al (2019) High-resolution multi-scan compact Fourier transform-infrared spectrometer. Opt Lett 44:3126. https://doi.org/10.1364/ol.44.003126
[24] Padilla M, Servin M, Garnica G et al (2019) Design of robust phase-shifting algorithms using N-step formulas as building blocks. Opt Lasers Eng 121:346-351
[25] Chang L, Yu Y (2022) Wavelength-tuning phase-shifting interferometry of transparent plates using sub-signal frequency correction. Measurement 205:112157. https://doi.org/10.1016/j.measurement.2022.112157
[26] Bai Y, Zhou Y, He Z et al (2018) Wavenumber synthesis approach to high-resolution wavenumber scanning interference using a mode-hoped laser. Opt Express 26:5441. https://doi.org/10.1364/oe.26.005441
[27] Guo R, Liao Z, Li J et al (2019) Optical homogeneity measurement of parallel plates by wavelength-tuning interferometry using nonuniform fast Fourier transform. Opt Express 27:13072. https://doi.org/10.1364/oe.27.013072
[28] Samir I, Sabry YM, Fathy A et al (2019) Autoregressive superresolution microelectromechanical systems Fourier transform spectrometer. Appl Opt 58:6784. https://doi.org/10.1364/ao.58.006784
[29] Duan S, Zheng H (2023) Model parameter estimations of the multi-channel turbulence response from flutter flight tests based on autoregressive spectra. J Low Freq Noise Vib Act Control 42:173-191
[30] Xiao X, Zhou R, Ma X et al (2023) Harmonic phasor estimation method considering dense interharmonic interference. Entropy 25:236. https://doi.org/10.3390/e25020236
[31] Zhai M, Locquet A, Roquelet C et al (2020) Terahertz time-of-flight tomography beyond the axial resolution limit: autoregressive spectral estimation based on the modified covariance method. J Infrared Millim TE 41:926-939
[32] Tan J, He Z, Bai Y et al (2023) High depth resolution wavelength scanning interferometry with narrow scanning bandwidth via sinewaves separation. Opt Lasers Eng 164:107519. https://doi.org/10.1016/j.optlaseng.2023.107519

Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation

Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价