Calibration is to transform the 2D phase information to the world coordinates in a fringe projection 3D measurement system. For the phase-to-height conversion, an equi-phase coordinate method based on two-reference-plane is proposed in this paper. The surface height is calculated by a linear interpolation using the coordinates where have the identical phase value of the object and the two reference planes. The conventional method, called equi-coordinate phase method in this paper, builds the function of the absolute phase and height by using the absolute phase obtained by subtracting the phase of object from that of the reference plane in the same coordinate. The proposed method can handle phase-to-height conversion and non-sinusoidal error caused by nonlinear response of the fringe projection system in one go. Theoretical and experimental analysis is given to prove the validity of the proposed method. Result indicates that the RMS error produced by equi-phase coordinate method is less half of equi-coordinate phase method when the primary error source is from the non-sinusoidal fringe patterns
Published in |
Optics (Volume 4, Issue 3-1)
This article belongs to the Special Issue Optical Techniques for Deformation, Structure and Shape Evaluation |
DOI | 10.11648/j.optics.s.2015040301.15 |
Page(s) | 18-23 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Three-Dimensional Shape Measurement, Calibration, Equi-Phase Coordinates, Non-Sinusoidal Error
[1] | J. Geng, “Structured-light 3d surface imaging: a tutorial,” Advances in Optics and Photonics, 3: 128–160, 2011. |
[2] | M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-d object shapes,” Applied Optics, 22(24): 3977–3982, 1983. |
[3] | V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-d diffuse objects,” Applied Optics, 23(18): 3105–3108, 1984. |
[4] | S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?,” Optics and Lasers in Engiering, 48(2): 133–140, 2010. |
[5] | W. S. Zhou and X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” Journal of Modern Optics, 41(1): 89–94, 1994. |
[6] | D. Q. Huynh, “Calibrating a structured light stripe system: A novel approach,” International Journal of Computer Vision, 33(1): 73–86, 1999. |
[7] | G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-d imaging sensor based on the projection of structured light,” IEEE Transactions on Instrumentation and Measurement, 49(3): 628–636, 2000. |
[8] | H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3d surface profile measurement,” Optics Communications, 216: 65–80, 2003. |
[9] | S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sensors and Actuators A, 115: 178–184, 2004. |
[10] | R. Legarda-S´aenz, T. Bothe, and W. P. J¨uptner, “Accurate procedure for the calibration of a structured light system,” Optical Engineering, 43(2): 464–471, 2004. |
[11] | L. C. Chen and C. C. Liao, “Calibration of 3d surface profilometry using digital fringe projection,” Measurement Science and Technology, 16: 1554–1566, 2005. |
[12] | X. Zhang, Y. Lin, M. Zhao, X. Niu, and Y. Huang, “Calibration of a fringe projection profilometry system using virtual phase calibrating model planes,” Journal of Optics A: Pure and Applied Optics, 7: 192–197, 2005. |
[13] | P. J. Tavares and M. A. Vaz, “Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry,” Optics Communications, 274: 307–314, 2007. |
[14] | X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a cameracprojector measurement system based on structured light projection,” Optics and Lasers in Engiering, 47: 310–319, 2009. |
[15] | R. Anchini, G. D. Leo, C. Liguori, and A. Paolillo, “A new calibration procedure for 3-d shape measurement system based on phase-shifting projected fringe profilometry,” IEEE Transactions on Instrumentation and Measurement, 58(5): 1291–1298, 2009. |
[16] | A. A. and C. S. Chan, “Phase shifting applied to non-sinusoidal intensity distribution–an error simulation,” Optics and Lasers in Engiering, 21: 3–30, 1994. |
[17] | H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Applied Optics, 43(14): 2906–2914, 2004. |
[18] | 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. |
[19] | B. Pan, K. Qian, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Optics Letters, 34(4): 416–418, 2009. |
[20] | V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Applied Optics, 24(2): 185–188, 1985. |
[21] | R. Hartley and A. Zisserman, eds., Multiple View Geometry in Computer Vision (Cambridge University, 2000). |
[22] | Wang Z Y, Nguyen D A, Barnes J C. “Some practical considerations in fringe projection profilometry,” Optics and Lasers in Engineering, 48(2): 218-225, 2010 |
APA Style
Dai Meiling, Yang Fujun, He Xiaoyuan. (2015). Calibration of a Fringe Projection 3D Measurement System Using an Equi-Phase Coordinate Method Based on Two-Reference-Plane. Optics, 4(3-1), 18-23. https://doi.org/10.11648/j.optics.s.2015040301.15
ACS Style
Dai Meiling; Yang Fujun; He Xiaoyuan. Calibration of a Fringe Projection 3D Measurement System Using an Equi-Phase Coordinate Method Based on Two-Reference-Plane. Optics. 2015, 4(3-1), 18-23. doi: 10.11648/j.optics.s.2015040301.15
AMA Style
Dai Meiling, Yang Fujun, He Xiaoyuan. Calibration of a Fringe Projection 3D Measurement System Using an Equi-Phase Coordinate Method Based on Two-Reference-Plane. Optics. 2015;4(3-1):18-23. doi: 10.11648/j.optics.s.2015040301.15
@article{10.11648/j.optics.s.2015040301.15, author = {Dai Meiling and Yang Fujun and He Xiaoyuan}, title = {Calibration of a Fringe Projection 3D Measurement System Using an Equi-Phase Coordinate Method Based on Two-Reference-Plane}, journal = {Optics}, volume = {4}, number = {3-1}, pages = {18-23}, doi = {10.11648/j.optics.s.2015040301.15}, url = {https://doi.org/10.11648/j.optics.s.2015040301.15}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.optics.s.2015040301.15}, abstract = {Calibration is to transform the 2D phase information to the world coordinates in a fringe projection 3D measurement system. For the phase-to-height conversion, an equi-phase coordinate method based on two-reference-plane is proposed in this paper. The surface height is calculated by a linear interpolation using the coordinates where have the identical phase value of the object and the two reference planes. The conventional method, called equi-coordinate phase method in this paper, builds the function of the absolute phase and height by using the absolute phase obtained by subtracting the phase of object from that of the reference plane in the same coordinate. The proposed method can handle phase-to-height conversion and non-sinusoidal error caused by nonlinear response of the fringe projection system in one go. Theoretical and experimental analysis is given to prove the validity of the proposed method. Result indicates that the RMS error produced by equi-phase coordinate method is less half of equi-coordinate phase method when the primary error source is from the non-sinusoidal fringe patterns}, year = {2015} }
TY - JOUR T1 - Calibration of a Fringe Projection 3D Measurement System Using an Equi-Phase Coordinate Method Based on Two-Reference-Plane AU - Dai Meiling AU - Yang Fujun AU - He Xiaoyuan Y1 - 2015/07/28 PY - 2015 N1 - https://doi.org/10.11648/j.optics.s.2015040301.15 DO - 10.11648/j.optics.s.2015040301.15 T2 - Optics JF - Optics JO - Optics SP - 18 EP - 23 PB - Science Publishing Group SN - 2328-7810 UR - https://doi.org/10.11648/j.optics.s.2015040301.15 AB - Calibration is to transform the 2D phase information to the world coordinates in a fringe projection 3D measurement system. For the phase-to-height conversion, an equi-phase coordinate method based on two-reference-plane is proposed in this paper. The surface height is calculated by a linear interpolation using the coordinates where have the identical phase value of the object and the two reference planes. The conventional method, called equi-coordinate phase method in this paper, builds the function of the absolute phase and height by using the absolute phase obtained by subtracting the phase of object from that of the reference plane in the same coordinate. The proposed method can handle phase-to-height conversion and non-sinusoidal error caused by nonlinear response of the fringe projection system in one go. Theoretical and experimental analysis is given to prove the validity of the proposed method. Result indicates that the RMS error produced by equi-phase coordinate method is less half of equi-coordinate phase method when the primary error source is from the non-sinusoidal fringe patterns VL - 4 IS - 3-1 ER -