Inspection of the accuracy of fringe projection profilometry by using hybrid methods

Year 2024, Volume: 13 Issue: 4, 1452 - 1467, 15.10.2024

Burak Özbay , Zehra Saraç

https://doi.org/10.28948/ngumuh.1458662

Abstract

Fringe Projection Profilometry- FPP system is widely used for three-dimensional(3D) imaging. This system is promising. However, for the changing environmental conditions, the measurement object, system noise, and strong backlighting changing, it is difficult to obtain 3D image accurately by fringe analyzing methods such as Traditional Fourier Transform Method-TFFT in FPP System. Therefore, in this paper, the TFFT method is combined with various method and hybrid methods are formed. The aim is to investigate how these methods affect the accuracy of FPP system. To make this determination, from simulated fringe pattern, phase is calculated. Then the error values are obtained using these phase values. Consequently, it is seen from error results that TFFT with two Dimensional Empirical Mode Decomposition method-2D-EMD-FFT which gives the lowest error, is the most insensitive to the disruptive effects mentioned above. Moreover, it is the most stability and least affected by the geometric of the object under test.

Keywords

Fringe Projection Profilometry, Hybrid Methods, Fringe Analysis, Accuracy

Hibrit metotlar kullanarak ızgara projeksiyon profilemetrisinin doğruluğunun incelenmesi

Abstract

Izgara Projeksiyon Profilometri-FPP sistemi, üç boyutlu (3D) görüntüleme için yaygın olarak kullanılmaktadır. Bu sistem umut vericidir. Ancak değişen çevre koşulları, ölçüm nesnesi, sistem gürültüsü ve güçlü arka ışık değişimi nedeniyle FPP Sisteminde Geleneksel Fourier Dönüşüm Yöntemi-TFFT gibi saçak analiz yöntemleriyle doğru 3 boyutlu görüntü elde etmek zordur. Bu nedenle bu bildiride TFFT yöntemi çeşitli yöntemlerle birleştirilerek hibrit yöntemler oluşturulmuştur. Amaç bu yöntemlerin FPP sisteminin doğruluğunu nasıl etkilediğini araştırmaktır. Bu belirlemeyi yapmak için simüle edilmiş saçak deseninden faz hesaplanır. Daha sonra bu faz değerleri kullanılarak hata değerleri elde edilir. Sonuç olarak, hata sonuçlarından, en düşük hatayı veren İki Boyutlu Ampirik Mod Ayrıştırma yöntemi olan 2D-EMD-FFT'ye sahip TFFT'nin yukarıda bahsedilen bozucu etkilere en duyarsız olduğu görülmektedir. Üstelik test edilen nesnenin geometrisinden en az etkilenen ve en kararlı olanıdır.

Keywords

Izgara Projeksiyon Profilometrisi, Hibrit Yöntemler, Izgara Analizi, Doğruluk

References

• K. E. Perry, J. McKelvie, A comparison of phase-shifting and Fourier methods in the analysis of discontinuous fringe patterns. Optics and Lasers in Engineering, 19, 269–284, 1993. https://doi.org/10. 1016/0143-8166(93)90068-V.
• L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry. Optics and Lasers in Engineering, 48, 141-148, 2010. https://doi.org/10.101 6/j.optlaseng.2009.04.003.
• P. S. Huang, C. Zhang, and F. P. Chiang, High-speed 3D shape measurement based on digital fringe projection. Optical Engineering, 42, 163-169, 2003. https://doi.org/10.1117/1.1525272.
• Z. H. Zhang, Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques, Optics and Lasers in Engineering, 50 106–1097, 2012. https://doi.org/10.10 16/j.optlaseng.2012.01.007
• P. Zhou, J. Zhu, X. Su, Z. You, H. Jing, C. Xiao, and M. Zhong, Experimental study of temporal-spatial binary pattern projection for 3D shape acquisition. Applied Optics, 56, 2995–3003, 2017. https://doi.org/ 10.1364/AO.56.002995.
• A. Martínez, J.A. Rayas, R.R. Cordero, D. Balieiro, and F. Labbe, Leaf cuticle topography retrieved by using fringe projection. Optics and Lasers in Engineering, 50, 231-235, 2012. https://doi.org/10.1016/j.optlaseng.201 1.08.011.
• X. Li, Z. Zhang, and C. Yang, Reconstruction method for fringe projection profilometry based on light beams. Applied Optics, 55(34), 9895-9906, 2016. https://doi .org/10.1364/AO.55.009895.
• H. Nguyen, J. Liang, Y. Wang, and A. Wang, Accuracy assessment of fringe projection profilometry and digital image correlation techniques for three-dimensional shape measurements. Journal of Physics: Photonics, 3 014004 2021. https://doi.org/10.1088/2515-7647/ab cbe4.
• C.V. Lopez, C.S. Salazar, K. Kells, J.C. Pedraza, and J.M. Ramos, Improving 3D reconstruction accuracy in wavelet transform profilometry by reducing shadow effects. IET Image Processing, 14, 310–317, 2020. https://doi.org/10.1049/iet-ipr.2019.0854.
• Y. Xu, H. Zhao, H. Jiang, and X. Li, High-accuracy 3D shape measurement of translucent objects by fringe projection profilometry. Optics Express, 27 (13), 18421-18434, 2019. https://doi.org/10.1364/OE.27.01 8421.
• C. Pérez, M. Chávez, F. C. Rivera, D. Sarocchi, C. Mares, and B. Barrientos, Fringe Projection Method for 3D High-Resolution Reconstruction of Oil Painting Surfaces. Heritage, 6 (4), 3461–3474, 2023. https://doi.org/10.3390/heritage6040184.
• Z. Yin, C. Liu, C. Zhang, X. He, and F. Yang, Point-Wise Phase Estimation Method in Fringe Projection Profilometry under Non-Sinusoidal Distortion. Sensors, 22 (12), 4478, 2022. https://doi.org/10.3390/ s22124478.
• S. Lv, D. Tang, X. Zhang, D. Yang, W. Deng, and K. Qian, Fringe projection profilometry method with high efficiency, precision, and convenience: theoretical analysis and development. Optics Express, 30(19), 33515-33537, 2022. https://doi.org/10.1364/OE.46750 2.
• H. Kaya, Z. Saraç, M. Özer, and H. Taşkın, Optical signal processing of interference fringes by Hartley transform method. 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 77461W, Liptovsky Jan, Slovakia, 14-16 December 2010.
• B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity. Optics and Lasers in Engineering, 78, 91–98, 2016. https://doi.org /10.1016/j.optlaseng.2015.10.007.
• A. Dursun, S. Özder, and F. N. Ecevit, Continuous wavelet transform analysis of projected fringe patterns. Measurement Science and Technology, 9(15), 0957-0233, 2004. 10.1088/0957-0233/15/9/013.
• J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, A state of the art in structured light patterns for surface profilometry. Pattern Recognition. 43. 2666-2680 2010. https://doi.org/10.1016/j.patcog.2010.03.004.
• R. W. Wygant, S. P. Almeida, and O. D. D. Soares, Surface inspection via projection interferometry. Applied Optics, 27 (22), 4626-4630, 1988. https://doi.org/10.1364/AO.27.004626.
• J. Zhong, and J. Weng, Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry. Applied Optics, 43 (26), 4993-4998, 2004. https://doi.org/10.1364/AO.43.004993.
• J. Zhou, Wavelet-aided spatial carrier fringe pattern analysis for 3-D shape measurement. Optical Engineering, 44 (11), 113602, 2005. https://doi.org/10 1117/1.2127887.
• Z. Saraç, H. G. Birkök, H. Taşkın, and E. Öztürk, Evaluation of thermal lens fringes using Hilbert and Fourier transform methods. IET Science, Measurement and Technology, 5 (3), 81 – 87, 2011. https://www. researchgate.net/publication/224238898.
• C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, Phase shifting algorithms for fringe projection profilometry: A review. Optics and Lasers in Engineering, 109, 23-59, 2018. https://doi.org/10.10 16/j.optlaseng.2018.04.019
• J. Geng, Structured-light 3D surface imaging: a tutorial. Advances in Optics and Photonics, 3 (2), 128–160, 2011. https://doi.org/10.1364/AOP.3.000128.
• H. A. Ali, M. A. Amer, and A. A. Omara, New Simple Large Depth of Field Fringe Projection Profilometry System Using Laser Projector. Journal of Measurement Science and Applications (JMSA), 2(2): 28-39, 2022.
• A. S. Segade, Fringe projection technique: New methods for shape measurement. Ph.D. Thesis, Centro de Investigaciones en Óptica A.C., Mexico, 2015.
• L. Mingzhou, Development of Fringe Analysis Techniques in white light interferometry for micro-component measurement. Ph.D. Thesis, National University of Singapore, Singapore, 2008.
• X. Su, and W. Chen, Fourier transform profilometry: a review. Optics and Lasers in Engineering, 35, 263–84, 2001.https://doi.org/10.1016/S0143-8166(01)00023-9.
• S. Zhang, and S-T. Yau, Generic nonsinusoidal phase error correction for three- dimensional shape measurement using a digital video projector. Applied Optics, 46 (1), 36–43, 2007. https://doi.org/10.1364/A O.46.000036.
• M. Takeda, and K. Mutoh, Fourier transform profilometry for the automatic measurement of 3D object shapes. Applied Optics, 22 (24), 3977–3982, 1983. https://doi.org/10.1364/AO.22.003977.
• A. Savitzky, M. J. E. Golay, Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36 (8), 1627–1639, 1964. https://pubs.acs.org/doi/10.1021/ac60214a047.
• P. A. Gorry, General lest-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Analytical Chemistry, 62, 570-573, 1990. https://pubs.acs.org/doi/abs/10.1021/ac00205a007.
• M. A. Awal, S. S. Mostafa, M. Ahmad, Performance analysis of Savitzky-Golay smoothing filter using ECG signal. International Journal of Computer and Information Technology, 1(02), 24, 2011. https://www. researchgate.net/publication/215628178.
• Q. Kemao, Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations. Optics and Lasers in Engineering, 45, 304-317, 2007. https://doi.org/10.101 6/j.optlaseng.2005.10.012.
• Q. Kemao, Windowed Fourier transform for fringe pattern analysis. Applied Optics, 43 (13), 2695-702, 2004. https://doi.org/10.1364/AO.43.002695.
• S. Zheng, and Y. Cao, Fringe-projection profilometry based on two-dimensional empirical mode decomposition. Applied Optics, 52(31), 7648–7653, 2013. https://doi.org/10.1364/AO.52.007648.
• N.E. Huang, Z. Shen, S.R. Long, et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454 (1971), pp. 903-995, Londra, England, 1998.
• W. Li, J. Huyan, S. L. Tighe, Q. Ren, and Z. Sun, Three-Dimensional Pavement Crack Detection Algorithm Based on Two-Dimensional Empirical Mode Decomposition. Journal of Transportation Engineering, Part B: Pavements, 143 (2), 04017005, 2017. https://doi.org/10.1061/JPEODX.0000006.
• X. Zhou, G. Adrian, Z. Yang, T. Yang, and H. Zhao, Morphological operation-based bi- dimensional empirical mode decomposition for automatic background removal of fringe patterns. Optics Express, 20 (22), 24247–24262, 2012. https://doi.org/10.1364 /OE.20.024247.
• S. Ertürk, Sayısal İşaret İşleme. 3rd ed., Birsen Yayınevi, Istanbul, 2016.