Abstract
Fringe projection profilometry is widely used in different areas; it has the benefit of retrieving full-field height information from a single or multiple fringe patterns with high precision and accuracy. Several algorithms are proposed on literature, most are techniques that base their analysis on the projection of sinusoidal fringe patterns, where the shape of an object is modulated into the pattern. In this paper, some algorithms have been reviewed and classified as spatial or temporal techniques, which make them suitable for the analysis of dynamic or static objects.
References
D. Malacara, Optical Shop Testing, 3rd edn. (Wiley, Hoboken, 2007), pp.547–791
K.J. Stout, L. Blunt, Three Dimensional Surface Topography, 2nd edn. (Penton Press, London, 2000), pp.50–68
D. Malacara, Z. Malacara, M. Servn, Interferogram Analysis for Optical Testing, 1st edn. (Marcel Dekker, New York, 1998), pp.113–332
P. Hariharan, Optical Interferometry, 2nd edn. (Academic Press, San Diego, 2003), pp.148–156
C. Jiang, B. Lim, S. Zhang, Three-dimensional shape measurement using a structured light system with dual projectors. Appl. Opt. 57, 3983 (2018). https://doi.org/10.1364/AO.57.003983
H. Yue, Y. Yu, W. Chen, X. Wu, Accurate three dimensional body scanning system based on structured light. Opt. Express 26, 28544 (2018). https://doi.org/10.1364/OE.26.028544
Y. Li, M. Kästner, E. Reithmeier, Triangulation-based edge measurement using polyview optics. Opt. Lasers Eng. 103, 71 (2018). https://doi.org/10.1016/J.OPTLASENG.2017.11.015
C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, Q. Chen, Phase shifting algorithms for fringe projection profilometry: a review. Opt. Lasers Eng. 109, 23 (2018). https://doi.org/10.1016/j.optlaseng.2018.04.019
X. Li, Z. Zhang, C. Yang, Reconstruction method for fringe projection profilometry based on light beams. Appl. Opt. 55, 9895 (2016). https://doi.org/10.1364/AO.55.009895
C. Faber, M. Strohmeier, H. Liang, How to exploit prior knowledge in industrial 3D-Metrology, in imaging Appl. Opt. 2019 (COSI, IS, MATH, PcAOP) (2019), Pap. CTh2A.6 (The Optical Society, 2019), p. CTh2A.6. https://doi.org/10.1364/cosi.2019.cth2a.6
M. Strohmeier, C. Faber, Harnessing inverse fringe patterns for actual industrial inspection applications, in Imaging Appl. Opt. 2019 (COSI, IS, MATH, pcAOP), OSA Technical Digest (Optica Publishing Group, 2019), paper IW1C.4. https://doi.org/10.1364/ISA.2019.IW1C.4
J.A.N. Buytaert, J.J.J. Dirckx, Study of the performance of 84 phase-shifting algorithms for interferometry. J. Opt. 40, 114 (2011). https://doi.org/10.1007/s12596-011-0044-y
C. Li, Y. Cao, C. Chen, Y. Wan, G. Fu, Y. Wang, Computer-generated Moiré profilometry. Opt. Express 25, 26815 (2017). https://doi.org/10.1364/oe.25.026815
S. Zhang, Active versus passive projector nonlinear gamma compensation method for high-quality fringe pattern generation, in Proc. SPIE 9110, Dimensional Optical Metrology and Inspection for Practical Applications III, 911002 (2014)) https://doi.org/10.1117/12.2050534
Z. Wang, D.A. Nguyen, J.C. Barnes, Some practical considerations in fringe projection profilometry. Opt. Lasers Eng. 48, 218 (2010). https://doi.org/10.1016/j.optlaseng.2009.06.005
X. Yu, Y. Liu, N. Liu, M. Fan, X. Su, Flexible gamma calculation algorithm based on probability distribution function in digital fringe projection system. Opt. Express 27, 32047 (2019). https://doi.org/10.1364/oe.27.032047
J. Geng, Structured-light 3D surface imaging: a tutorial. Adv. Opt. Photonics 3, 128 (2011). https://doi.org/10.1364/AOP.3.000128
J. Salvi, J. Pagès, J. Batlle, Pattern codification strategies in structured light systems. Pattern Recognit. 37, 827 (2004). https://doi.org/10.1016/J.PATCOG.2003.10.002
N. Tornero Martínez, G. Trujillo-Schiaffino, M. Anguiano-Morales, P. G. Mendoza-Villegas, D. P. Salas-Peimbert, L. F. Corral-Martínez, Color profilometry techniques: a review. Opt. Pura Apl. 51(4) 51001:1–26 (2018) https://doi.org/10.7149/OPA.51.4.51001
H. Zhao, C. Zhang, C. Zhou, K. Jiang, M. Fang, Circular fringe projection profilometry. Opt. Lett. 41, 4951 (2016). https://doi.org/10.1364/OL.41.004951
C. Zhang, H. Zhao, J. Qiao, C. Zhou, L. Zhang, G. Hu, H. Geng, Three-dimensional measurement based on optimized circular fringe projection technique. Opt. Express 27, 2465 (2019). https://doi.org/10.1364/OE.27.002465
W.-H. Su, C.-Y. Kuo, F.-J. Kao, Three-dimensional trace measurements for fast-moving objects using binary-encoded fringe projection techniques. Appl. Opt. 53, 5283 (2014). https://doi.org/10.1364/ao.53.005283
K. Chen, J. Xi, Y. Yu, S. Tong, Q. Guo, Three-dimensional measurement of object surfaces with complex shape and color distribution based on projection of color fringe patterns. Appl. Opt. 52, 7360 (2013). https://doi.org/10.1364/AO.52.007360
W.-H. Su, Color-encoded fringe projection for 3D shape measurements. Opt. Express 15, 13167 (2007). https://doi.org/10.1364/OE.15.013167
J.L. Flores, J.A. Ferrari, G. García Torales, R. Legarda-Saenz, A. Silva, Color-fringe pattern profilometry using a generalized phase-shifting algorithm. Appl. Opt. 54, 8827 (2015). https://doi.org/10.1364/AO.54.008827
L. Wang, Y. Ma, H. Zhang, Y. Xin, C. Yuan, T.-C. Poon, Accurate phase-shift estimation for fringe-pattern profilometry. Appl. Opt. 58, G358 (2019). https://doi.org/10.1364/ao.58.00g358
Y. Hu, J. Xi, E. Li, J. Chicharo, Z. Yang, Three-dimensional profilometry based on shift estimation of projected fringe patterns. Appl. Opt. 45, 678 (2006). https://doi.org/10.1364/AO.45.000678
S.S. Gorthi, Fringe projection techniques: Whither we are? Opt. Lasers Eng. 48, 133 (2010). https://doi.org/10.1016/J.OPTLASENG.2009.09.001
M. Takeda, H. Ina, S. Kobayashi, Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am. 72, 156 (1982). https://doi.org/10.1364/JOSA.72.000156
L. Huang, Q. Kemao, B. Pan, 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. Opt. Lasers Eng. 48, 141 (2010). https://doi.org/10.1016/j.optlaseng.2009.04.003
C. Quan, C.J. Tay, L.J. Chen, A study on carrier-removal techniques in fringe projection profilometry. Laser Technol. 39, 1155 (2007). https://doi.org/10.1016/J.OPTLASTEC.2006.09.003
M. Servin, J.A. Quiroga, M. Padilla, Fringe Pattern Analysis for Optical Metrology, 1st edn. (Wiley, Weinheim, 2014)
D.W. Phillion, General methods for generating phase-shifting interferometry algorithms. Opt. 36, 8098 (1997). https://doi.org/10.1364/AO.36.008098
Q. Kemao, L.T.H. Nam, L. Feng, S.H. Soon, Comparative analysis on some filters for wrapped phase maps. Appl. Opt. 46, 7412 (2007). https://doi.org/10.1364/AO.46.007412
L. Ying, Wiley Encycl. Biomed. Eng. (Wiley, Hoboken,2006).
K. Itoh, Analysis of the phase unwrapping algorithm. Opt. 21, 2470 (1982). https://doi.org/10.1364/AO.21.002470
D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping : Theory, Algorithms, and Software (Wile, Hoboken, 1998).
K.J. Gåsvik, Optical Metrology (Wiley, Hoboken, 2002)
M. Takeda, K. Mutoh, Fourier transform profilometry for the automatic measurement of 3-D object shapes. Appl. Opt. 22, 3977 (1983). https://doi.org/10.1364/AO.22.003977
Y. Wen, S. Li, H. Cheng, X. Su, Q. Zhang, Universal calculation formula and calibration method in Fourier transform profilometry. Appl. Opt. 49, 6563 (2010). https://doi.org/10.1364/AO.49.006563
C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, High-speed three-dimensional profilometry for multiple objects with complex shapes. Opt. Express 20, 19493 (2012). https://doi.org/10.1364/OE.20.019493
H. Jiang, H. Zhao, X. Li, High dynamic range fringe acquisition: a novel 3-D scanning technique for high-reflective surfaces. Opt. Lasers Eng. 50, 1484 (2012). https://doi.org/10.1016/J.OPTLASENG.2011.11.021
S.-T. Yau, High dynamic range scanning technique. Opt. Eng. 48, 033604 (2009). https://doi.org/10.1117/1.3099720
R. Zhang, H. Guo, A.K. Asundi, Geometric analysis of influence of fringe directions on phase sensitivities in fringe projection profilometry. Appl. Opt. 55, 7675 (2016). https://doi.org/10.1364/AO.55.007675
H. Sheng, J. Xu, S. Zhang, Dynamic projection theory for fringe projection profilometry. Appl. Opt. 56, 8452 (2017). https://doi.org/10.1364/ao.56.008452
M. Takeda, Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview. Ind. Metrol. 1, 79 (1990) https://doi.org/10.1016/0921-5956(90)80019-R
B. Li, Y. An, S. Zhang, Single-shot absolute 3D shape measurement with Fourier transform profilometry. Appl. Opt. 55, 5219 (2016). https://doi.org/10.1364/AO.55.005219
Q. Kemao, Windowed Fourier transform for fringe pattern analysis. Appl. Opt. 43, 2695 (2004). https://doi.org/10.1364/AO.43.002695
Q. Kemao, H. Wang, W. Gao, Windowed Fourier transform for fringe pattern analysis: theoretical analyses. Appl. Opt. 47, 5408 (2008). https://doi.org/10.1364/AO.47.005408
Q. Kemao, Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations. Opt. Lasers Eng. 45, 304 (2007). https://doi.org/10.1016/J.OPTLASENG.2005.10.012
J. Zhong, J. Weng, Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry. Appl. Opt. 43, 4993 (2004). https://doi.org/10.1364/AO.43.004993
M.A. Gdeisat, A. Abid, D.R. Burton, M.J. Lalor, F. Lilley, C. Moore, M. Qudeisat, Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: Recent progress, challenges, and suggested developments. Opt. Lasers Eng. 47, 1348 (2009). https://doi.org/10.1016/J.OPTLASENG.2009.07.009
S. Li, W. Chen, XSu. Appl, Reliability-guided phase unwrapping in wavelet-transform profilometry. Opt. 47, 3369 (2008). https://doi.org/10.1364/AO.47.003369
W. Zhaoyang, H. Ma, Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing. Opt. Eng. 45, 045601 (2006). https://doi.org/10.1117/1.2188399
R. Zou, S. Cui, F. Tian, Q. Li, M. Yao, Phase retrieval of optical fringe pattern using wavelet ridge section and adaptive bandpass filter. Opt. Eng. 55, 093103 (2016). https://doi.org/10.1117/1.OE.55.9.093103
Y. Tounsi, M. Kumar, A. Siari, F. Mendoza-Santoyo, A. Nassim, O. Matoba, Digital four-step phase-shifting technique from a single fringe pattern using Riesz transform. Opt. Lett. 44, 3434 (2019). https://doi.org/10.1364/OL.44.003434
Y. Tounsi, M. Kumar, A. Siari, F. Mendoza-Santoyo, O. Matoba, A. Nassim, Riesz transform for fringes pattern analysis: advantages and limitations, in Proc. SPIE 11551, Holography, Diffractive Optics, and Applications X, 115510P (2020) https://doi.org/10.1117/12.2574757
T. Yoshizawa, Handbook of optical metrology: principles and applications (CRC Press, Boca Raton, 2009)
K. Creath, Comparison Of Phase-Measurement Algorithms. Proc. SPIE 0680, Surface Characterization and Testing, (1987). https://doi.org/10.1117/12.939587
G. Cloud, Optical methods of engineering analysis (Cambridge University Press, Cambridge, 1995)
J.H. Bruning, D.R. Herriott, J.E. Gallagher, D.P. Rosenfeld, A.D. White, D.J. Brangaccio, Digital wavefront measuring interferometer for testing optical surfaces and lenses. Appl. Opt. 13, 2693 (1974). https://doi.org/10.1364/AO.13.002693
C.J. Morgan, Least-squares estimation in phase-measurement interferometry. Opt. Lett. 7, 368 (1982). https://doi.org/10.1364/OL.7.000368
V. Srinivasan, H.C. Liu, M. Halioua, Automated phase-measuring profilometry of 3-D diffuse objects. Appl. Opt. 23, 3105 (1984). https://doi.org/10.1364/AO.23.003105
K. Creath, V phase-measurement interferometry techniques. . Prog. Opt. 26, 349 (1988). https://doi.org/10.1016/S0079-6638(08)70178-1
P.S. Huang, Q.J. Hu, F.-P. Chiang, Double three-step phase-shifting algorithm. Appl. Opt. 41, 4503 (2002). https://doi.org/10.1364/AO.41.004503
P. Carré, Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures. Metrologia 2, 13 (1966). https://doi.org/10.1088/0026-1394/2/1/005
D. Li, C. Liu, J. Tian, Telecentric 3D profilometry based on phase-shifting fringe projection. Opt. Express 22, 31826 (2014). https://doi.org/10.1364/oe.22.031826
P. Hariharan, B.F. Oreb, T. Eiju, Digital phase-stepping interferometry: effects of multiply reflected beams. Appl. Opt. 26, 2504 (1987). https://doi.org/10.1364/AO.26.002506
J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, Digital wave-front measuring interferometry: some systematic error sources. Appl. Opt. 22, 3421 (1983). https://doi.org/10.1364/AO.22.003421
P.L. Wizinowich, Phase shifting interferometry in the presence of vibration: a new algorithm and system. Appl. Opt. 29, 3271 (1990). https://doi.org/10.1364/AO.29.003271
P. L. Wizinowich, System for phase shifting interferometry in the presence of vibration, in Proc. SPIE 1164, Surface Characterization and Testing II (1989) https://doi.org/10.1117/12.962804
S. Zhang, S.-T. Yau, High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm. Opt. Eng. 46, 113603 (2007). https://doi.org/10.1117/1.2802546
X.-Y. Su, J. Li, L.-R. Guo, W.-Y. Su, An improved fourier transform profilometry, in Proc. SPIE 0954, Optical Testing and Metrology II, (1989) https://doi.org/10.1117/12.947595
L. Guo, X. Su, L. Guo, Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes. Opt. Eng. 29, 1439 (Opt. Eng. 29(12), (1990) https://doi.org/10.1117/12.55746
Acknowledgements
The authors wish to thank the financial support of Tecnológico Nacional de México and Consejo Nacional de Ciencia y Tecnología (México).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zendejas-Hernández, E., Trujillo-Schiaffino, G., Anguiano-Morales, M. et al. Spatial and temporal methods for fringe pattern analysis: a review. J Opt 52, 888–899 (2023). https://doi.org/10.1007/s12596-023-01166-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12596-023-01166-1