## Fringe projection profilometry based on a novel phase shift method |

Optics Express, Vol. 19, Issue 22, pp. 21739-21747 (2011)

http://dx.doi.org/10.1364/OE.19.021739

Acrobat PDF (1144 KB)

### Abstract

Fringe projection profilometry is generally used to measure the 3D shape of an object. In oblique-angle projection, the grating fringe cycle is broadened on the reference surface. A well-fitted, convenient, and quick cycle correction method is proposed in this study. Based on the proposed method, an accurate four-step phase shift method is developed. Comparative experiments show that the fringe projection profilometry based on the novel phase shift method can eliminate cycle error and significantly improve measurement accuracy. The relative error of the measurement is less than 1.5%. This method can be widely employed for measuring large objects.

© 2011 OSA

## 1. Introduction

1. H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express **17**(17), 15118–15127 (2009). [CrossRef] [PubMed]

2. E. Stoykova, G. Minchev, and V. Sainov, “Fringe projection with a sinusoidal phase grating,” Appl. Opt. **48**(24), 4774–4784 (2009). [CrossRef] [PubMed]

3. M. Sasso, G. Chiappini, G. Palmieri, and D. Amodio, “Superimposed fringe projection for three-dimensional shape acquisition by image analysis,” Appl. Opt. **48**(13), 2410–2420 (2009). [CrossRef] [PubMed]

4. B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. **34**(4), 416–418 (2009). [CrossRef] [PubMed]

## 2. Principle

### 2.1 Theoretical model for cycle correction of grating fringe

*O*′ is the optical center of the projector.

*X*is the reference surface,

*X*′is the virtual reference surface, and

*X*′′is the surface of the projector.

*L*is the distance between the camera and the reference plane, and

*d*is the distance between the camera and the projector. The projector and the camera have the same distance in relation to the reference surface. The grating fringe is on an oblique angle projected to the surface

*X*. The fringe cycle is broadeningon the reference surface.

*X*′ is perpendicular to the central axis of the projector.

*OA = x*and

*OA′*=

*x′*are assumed. Consequently,

*X*; hence, the fringe cycle is certainly non-uniform on the surface

*X*′ and on the projector surface. Given that the fringe phase is

*X*, where

*X*, the phases of points

*A*and

*A*′ are shown to be the same. Subsequently, the phase on the surface

*X*′ is described as

*M*is the magnification of the projector, and

### 2.2 Simulation experiment of cycle correction

*M*is set to 2,

*L*to 119 cm,

*d*to 33 cm, and

### 2.3 A novel phase shift method

*T*/4,

*T*/2, and 3

*T*/4, where

*T*is the grating cycle, the corresponding phase shifts are 0°, 90°, 180°, and 270°, respectively. Thus, if the grating fringe on the reference surface is moved by

*T*/4, the coordinate on the projection surface must be obtained. The coordinate on the projection surface is obtained using Eq. (2):

## 3. Experiments

*L*and

*d*.

*L*is 159.004 ± 0.022 cm and

*d*is 74.002 ± 0.017 cm.

*M*is obtained through a simple experiment, and

*M*is 3.442 ± 0.008.

*L*,

*d*,

*M,*and

*N*= 0,

^{−1}. Based on Eq. (5),

21. L. Huang, P. S. 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]

## 4. Discussion

*X*′

*.*The fringe cycle is calculated using Eq. (1):

*T*is the fringe cycle of the surface

*X*′, it has a value of 2.860 cm, and

*T*is the fringe cycle of the surface

_{x}*X*. The relationship curve of

*T*and

_{x}*x*is shown in Fig. 10 .

*X*.

^{−1}.

*x*.

*x*increases. When

*x*increases, the height of the object measured through the ordinary four-step phase shift method becomes smaller than the actual height. Moreover, the error also increases. At 1000 pixels, the error is approximately 0.1 cm, and the relative error is 15.2%. These results are not acceptable in high-precision measurements. Therefore, the ordinary fringe projection profilometry is suitable only for measuring small objects.

## 5. Conclusion

## Acknowledgments

## References and links

1. | H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express |

2. | E. Stoykova, G. Minchev, and V. Sainov, “Fringe projection with a sinusoidal phase grating,” Appl. Opt. |

3. | M. Sasso, G. Chiappini, G. Palmieri, and D. Amodio, “Superimposed fringe projection for three-dimensional shape acquisition by image analysis,” Appl. Opt. |

4. | B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. |

5. | S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. |

6. | Z. Wang, H. Du, and H. Bi, “Out-of-plane shape determination in generalized fringe projection profilometry,” Opt. Express |

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 Trans. Instrum. Meas. |

8. | Z. Zhang, C. E. Towers, and D. P. Towers, “Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology,” Appl. Opt. |

9. | Z. Zhang, H. Ma, S. 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. |

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

11. | L. Chen and C. Quan, “Fringe projection profilometry with nonparallel illumination: a least-squares approach,” Opt. Lett. |

12. | L. Chen and C. Quan, “Reply to comment on ‘Fringe projection profilometry with nonparallel illumination: a least-squares approach’,” Opt. Lett. |

13. | Z. Wang and H. Bi, “Comment on ‘Fringe projection profilometry with nonparallel illumination: a least-squares approach’,” Opt. Lett. |

14. | V. S. Cheng, R. Yang, C. Hui, and Y. Chen, “Optimal layout of fringe projection for three-dimensional measurement,” Opt. Eng. |

15. | A. Maurel, P. Cobelli, V. Pagneux, and P. Petitjeans, “Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry,” Appl. Opt. |

16. | B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimatedfringe-pattern Projections,” J. Opt. A, Pure Appl. Opt. |

17. | L. Salas, E. Luna, J. Salinas, V. Garcı́a, and M. Servı́n, “Profilometry by fringe projection,” Opt. Eng. |

18. | H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. |

19. | M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole space tabulation method,” Proc. SPIE |

20. | V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. |

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

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

23. | Q. Xu, Y. Zhong, and Z. You, “System calibration technique of profilometry by projected grating,” Opt. Technol. |

**OCIS Codes**

(050.5080) Diffraction and gratings : Phase shift

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(150.6910) Machine vision : Three-dimensional sensing

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: September 7, 2011

Revised Manuscript: October 5, 2011

Manuscript Accepted: October 14, 2011

Published: October 19, 2011

**Citation**

Yanjun Fu and Qian Luo, "Fringe projection profilometry based on a novel phase shift method," Opt. Express **19**, 21739-21747 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21739

Sort: Year | Journal | Reset

### References

- H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express17(17), 15118–15127 (2009). [CrossRef] [PubMed]
- E. Stoykova, G. Minchev, and V. Sainov, “Fringe projection with a sinusoidal phase grating,” Appl. Opt.48(24), 4774–4784 (2009). [CrossRef] [PubMed]
- M. Sasso, G. Chiappini, G. Palmieri, and D. Amodio, “Superimposed fringe projection for three-dimensional shape acquisition by image analysis,” Appl. Opt.48(13), 2410–2420 (2009). [CrossRef] [PubMed]
- B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett.34(4), 416–418 (2009). [CrossRef] [PubMed]
- S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng.48(2), 133–140 (2010). [CrossRef]
- Z. Wang, H. Du, and H. Bi, “Out-of-plane shape determination in generalized fringe projection profilometry,” Opt. Express14(25), 12122–12133 (2006). [CrossRef] [PubMed]
- 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 Trans. Instrum. Meas.49(3), 628–636 (2000). [CrossRef]
- Z. Zhang, C. E. Towers, and D. P. Towers, “Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology,” Appl. Opt.46(24), 6113–6119 (2007). [CrossRef] [PubMed]
- Z. Zhang, H. Ma, S. 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. Zhang, H. Ma, T. Guo, S. Zhang, and J. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett.36(7), 1257–1259 (2011). [CrossRef] [PubMed]
- L. Chen and C. Quan, “Fringe projection profilometry with nonparallel illumination: a least-squares approach,” Opt. Lett.30(16), 2101–2103 (2005). [CrossRef] [PubMed]
- L. Chen and C. Quan, “Reply to comment on ‘Fringe projection profilometry with nonparallel illumination: a least-squares approach’,” Opt. Lett.31(13), 1974–1975 (2006). [CrossRef]
- Z. Wang and H. Bi, “Comment on ‘Fringe projection profilometry with nonparallel illumination: a least-squares approach’,” Opt. Lett.31(13), 1972–1973 (2006). [CrossRef] [PubMed]
- V. S. Cheng, R. Yang, C. Hui, and Y. Chen, “Optimal layout of fringe projection for three-dimensional measurement,” Opt. Eng.47(5), 050503 (2008). [CrossRef]
- A. Maurel, P. Cobelli, V. Pagneux, and P. Petitjeans, “Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry,” Appl. Opt.48(2), 380–392 (2009). [CrossRef] [PubMed]
- B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimatedfringe-pattern Projections,” J. Opt. A, Pure Appl. Opt.9(6), S66–S75 (2007). [CrossRef]
- L. Salas, E. Luna, J. Salinas, V. Garcı́a, and M. Servı́n, “Profilometry by fringe projection,” Opt. Eng.42(11), 3307–3314 (2003). [CrossRef]
- H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun.216(1–3), 65–80 (2003). [CrossRef]
- M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole space tabulation method,” Proc. SPIE7066, 61–68 (2008).
- V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt.24(2), 185–188 (1985). [CrossRef] [PubMed]
- L. Huang, P. S. 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]
- 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]
- Q. Xu, Y. Zhong, and Z. You, “System calibration technique of profilometry by projected grating,” Opt. Technol.26(2), 126–133 (2000).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.