## A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system |

Optics Express, Vol. 21, Issue 10, pp. 12218-12227 (2013)

http://dx.doi.org/10.1364/OE.21.012218

Acrobat PDF (1180 KB)

### Abstract

An important step of phase calculation-based fringe projection systems is 3D calibration, which builds up the relationship between an absolute phase map and 3D shape data. The existing 3D calibration methods are complicated and hard to implement in practical environments due to the requirement of a precise translating stage or gauge block. This paper presents a 3D calibration method which uses a white plate with discrete markers on the surface. Placing the plate at several random positions can determine the relationship of absolute phase and depth, as well as pixel position and X, Y coordinates. Experimental results and performance evaluations show that the proposed calibration method can easily build up the relationship between absolute phase map and 3D shape data in a simple, flexible and automatic way.

© 2013 OSA

## 1. Introduction

1. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. **39**(1), 10–22 (2000). [CrossRef]

3. Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. **50**(8), 1097–1106 (2012). [CrossRef]

4. Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng. **42**(3), 341–353 (2004). [CrossRef]

4. Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng. **42**(3), 341–353 (2004). [CrossRef]

5. Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. **42**(2), 487–493 (2003). [CrossRef]

6. P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. **46**(4), 043601 (2007). [CrossRef]

7. M. Vo, Z. Wang, T. Hoang, and D. Nguyen, “Flexible calibration technique for fringe-projection-based three-dimensional imaging,” Opt. Lett. **35**(19), 3192–3194 (2010). [CrossRef] [PubMed]

8. L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. **49**(9), 1539–1548 (2010). [CrossRef] [PubMed]

9. H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. **32**(16), 2438–2440 (2007). [CrossRef] [PubMed]

10. Z. H. Zhang, H. Y. Ma, S. X. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett. **36**(5), 627–629 (2011). [CrossRef] [PubMed]

11. Z. H. Zhang, H. Y. Ma, T. Guo, S. X. Zhang, and J. P. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett. **36**(7), 1257–1259 (2011). [CrossRef] [PubMed]

## 2. Principle and method

*F*and

_{u}*F*), two principal point coordinates (

_{v}*P*and

_{u}*P*), and four image radial and tangential distortion coefficients (

_{v}*K*,

_{1}*K*,

_{2}*K*, and

_{3}*K*), need to be determined by capturing the white plate from several random positions. The eight parameters can be calculated from the extracted location of all the hollow ring markers at different plate positions [12

_{4}12. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. **22**(11), 1330–1334 (2000). [CrossRef]

13. Jean-Yves Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/.

### 2.1 Marker locations

14. A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. **21**(5), 476–480 (1999). [CrossRef]

15. Z. H. Zhang, S. S. Meng, and S. J. Huang,D. J. Dorantes-Gonzalez, ed., “Simple and flexible calibration method of a 3D imaging system based on fringe projection technique” in *Proceedings of 16th International Conference on Mechatronics Technology*, Dante J. Dorantes-Gonzalez, ed. (Tianjin Foreign Language Electronic & Audio-Video Publishing House, Tianjin, China. 2012), pp. 101–105.

### 2.2 Depth calibration

11. Z. H. Zhang, H. Y. Ma, T. Guo, S. X. Zhang, and J. P. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett. **36**(7), 1257–1259 (2011). [CrossRef] [PubMed]

4. Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng. **42**(3), 341–353 (2004). [CrossRef]

### 2.3 Transverse calibration

## 3. Experiments and results

### 3.1 Experimental system

### 3.2 3D calibration

13. Jean-Yves Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/.

17. Z. H. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3-D shape and colour using optimum 3-frequency Selection,” Opt. Express **14**(14), 6444–6455 (2006). [CrossRef] [PubMed]

### 3.3 Quantitative evaluation

### 3.4 Qualitative evaluation

17. Z. H. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3-D shape and colour using optimum 3-frequency Selection,” Opt. Express **14**(14), 6444–6455 (2006). [CrossRef] [PubMed]

## 4. Conclusions

## Acknowledgments

## References and links

1. | F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. |

2. | F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging |

3. | Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. |

4. | Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng. |

5. | Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. |

6. | P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. |

7. | M. Vo, Z. Wang, T. Hoang, and D. Nguyen, “Flexible calibration technique for fringe-projection-based three-dimensional imaging,” Opt. Lett. |

8. | L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. |

9. | H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. |

10. | Z. H. Zhang, H. Y. Ma, S. X. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett. |

11. | Z. H. Zhang, H. Y. Ma, T. Guo, S. X. Zhang, and J. P. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett. |

12. | Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. |

13. | Jean-Yves Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/. |

14. | A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. |

15. | Z. H. Zhang, S. S. Meng, and S. J. Huang,D. J. Dorantes-Gonzalez, ed., “Simple and flexible calibration method of a 3D imaging system based on fringe projection technique” in |

16. | |

17. | Z. H. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3-D shape and colour using optimum 3-frequency Selection,” Opt. Express |

**OCIS Codes**

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.2830) Instrumentation, measurement, and metrology : Height measurements

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(150.1488) Machine vision : Calibration

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: December 13, 2012

Revised Manuscript: April 30, 2013

Manuscript Accepted: May 1, 2013

Published: May 10, 2013

**Citation**

Zonghua Zhang, Shujun Huang, Shasha Meng, Feng Gao, and Xiangqian Jiang, "A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system," Opt. Express **21**, 12218-12227 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12218

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### References

- F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000). [CrossRef]
- F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–240 (2004). [CrossRef]
- Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng.50(8), 1097–1106 (2012). [CrossRef]
- Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng.42(3), 341–353 (2004). [CrossRef]
- Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003). [CrossRef]
- P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007). [CrossRef]
- M. Vo, Z. Wang, T. Hoang, and D. Nguyen, “Flexible calibration technique for fringe-projection-based three-dimensional imaging,” Opt. Lett.35(19), 3192–3194 (2010). [CrossRef] [PubMed]
- L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt.49(9), 1539–1548 (2010). [CrossRef] [PubMed]
- H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett.32(16), 2438–2440 (2007). [CrossRef] [PubMed]
- Z. H. Zhang, H. Y. Ma, S. X. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett.36(5), 627–629 (2011). [CrossRef] [PubMed]
- Z. H. Zhang, H. Y. Ma, T. Guo, S. X. Zhang, and J. P. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett.36(7), 1257–1259 (2011). [CrossRef] [PubMed]
- Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal.22(11), 1330–1334 (2000). [CrossRef]
- Jean-Yves Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .
- A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999). [CrossRef]
- Z. H. Zhang, S. S. Meng, and S. J. Huang,D. J. Dorantes-Gonzalez, ed., “Simple and flexible calibration method of a 3D imaging system based on fringe projection technique” in Proceedings of 16th International Conference on Mechatronics Technology, Dante J. Dorantes-Gonzalez, ed. (Tianjin Foreign Language Electronic & Audio-Video Publishing House, Tianjin, China. 2012), pp. 101–105.
- http://www.ti-times.com/
- Z. H. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3-D shape and colour using optimum 3-frequency Selection,” Opt. Express14(14), 6444–6455 (2006). [CrossRef] [PubMed]

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