## Phase coding method for absolute phase retrieval with a large number of codewords |

Optics Express, Vol. 20, Issue 22, pp. 24139-24150 (2012)

http://dx.doi.org/10.1364/OE.20.024139

Acrobat PDF (1199 KB)

### Abstract

A recently proposed phase coding method for absolute phase retrieval performs well because its codeword is embedded into phase domain rather than intensity. Then, the codeword can determine the fringe order for the phase unwrapping. However, for absolute phase retrieval with a large number of codewords, the traditional phase coding method becomes not so reliable. In this paper, we present a novel phase coding method to tackle this problem. Six additional fringe images can generate more than

© 2012 OSA

## 1. Introduction

1. S. Zhang, “High-resolution 3-D profilometry with binary phase-shifting methods,” Appl. Opt. **50**(12), 1753–1757 (2011). [CrossRef] [PubMed]

5. E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express **17**(10), 7818–7830 (2009). [CrossRef] [PubMed]

6. C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. **48**(2), 235–243 (2010). [CrossRef]

7. T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. **35**(12), 1992–1994 (2010). [CrossRef] [PubMed]

8. Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. **48**(2), 218–225 (2010). [CrossRef]

11. Y. Ding, J. Xi, Y. Yu, W. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express **20**(12), 13238–13251 (2012). [CrossRef] [PubMed]

12. J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. **32**(17), 3047–3052 (1993). [CrossRef] [PubMed]

13. J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng. **46**(4), 336–342 (2008). [CrossRef]

14. G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of Gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. **38**(31), 6565–6573 (2005). [CrossRef] [PubMed]

16. Y. Liu, X. Su, and Q. Zhang, “A novel encoded-phase technique for phase measuring profilometry,” Opt. Express **19**(15), 14137–14144 (2011). [CrossRef] [PubMed]

17. Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. **50**(4), 574–579 (2012). [CrossRef]

18. D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. **50**(8), 1130–1139 (2012). [CrossRef]

19. Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett. **37**(11), 2067–2069 (2012). [CrossRef] [PubMed]

20. S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. **48**(10), 105601 (2009). [CrossRef]

21. Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. **36**(13), 2518–2520 (2011). [CrossRef] [PubMed]

17. Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. **50**(4), 574–579 (2012). [CrossRef]

20. S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. **48**(10), 105601 (2009). [CrossRef]

21. Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. **36**(13), 2518–2520 (2011). [CrossRef] [PubMed]

22. 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]

23. S. Zhang and S. T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. **46**(1), 36–43 (2007). [CrossRef] [PubMed]

## 2. Principle of the novel phase coding method

### 2.1 The problem of a large number of codewords phase retrieval

23. S. Zhang and S. T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. **46**(1), 36–43 (2007). [CrossRef] [PubMed]

### 2.2 The novel phase coding method for a large number of codewords

18. D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. **50**(8), 1130–1139 (2012). [CrossRef]

## 3. Experiment

19. Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett. **37**(11), 2067–2069 (2012). [CrossRef] [PubMed]

23. S. Zhang and S. T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. **46**(1), 36–43 (2007). [CrossRef] [PubMed]

18. D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. **50**(8), 1130–1139 (2012). [CrossRef]

19. Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett. **37**(11), 2067–2069 (2012). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | S. Zhang, “High-resolution 3-D profilometry with binary phase-shifting methods,” Appl. Opt. |

2. | J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. |

3. | S. Li, X. Su, and W. Chen, “Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet,” Appl. Opt. |

4. | S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express |

5. | E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express |

6. | C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. |

7. | T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. |

8. | Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. |

9. | Y. Wang, S. Zhang, and J. H. Oliver, “3-D shape measurement technique for multiple rapidly moving objects,” Opt. Express |

10. | W. H. Su, “Projected fringe profilometry using the area-encoded algorithm for spatially isolated and dynamic objects,” Opt. Express |

11. | Y. Ding, J. Xi, Y. Yu, W. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express |

12. | J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. |

13. | J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng. |

14. | G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of Gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. |

15. | J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng. |

16. | Y. Liu, X. Su, and Q. Zhang, “A novel encoded-phase technique for phase measuring profilometry,” Opt. Express |

17. | Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. |

18. | D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. |

19. | Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett. |

20. | S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. |

21. | Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. |

22. | 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. |

23. | S. Zhang and S. T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. |

**OCIS Codes**

(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

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

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

(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

(100.5088) Image processing : Phase unwrapping

**ToC Category:**

Image Processing

**History**

Original Manuscript: July 30, 2012

Revised Manuscript: September 5, 2012

Manuscript Accepted: September 26, 2012

Published: October 8, 2012

**Citation**

Dongliang Zheng and Feipeng Da, "Phase coding method for absolute phase retrieval with a large number of codewords," Opt. Express **20**, 24139-24150 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24139

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### References

- S. Zhang, “High-resolution 3-D profilometry with binary phase-shifting methods,” Appl. Opt.50(12), 1753–1757 (2011). [CrossRef] [PubMed]
- J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt.43(26), 4993–4998 (2004). [CrossRef] [PubMed]
- S. Li, X. Su, and W. Chen, “Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet,” Appl. Opt.48(36), 6893–6906 (2009). [CrossRef] [PubMed]
- S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express18(9), 9684–9689 (2010). [CrossRef] [PubMed]
- E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express17(10), 7818–7830 (2009). [CrossRef] [PubMed]
- C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng.48(2), 235–243 (2010). [CrossRef]
- T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett.35(12), 1992–1994 (2010). [CrossRef] [PubMed]
- Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng.48(2), 218–225 (2010). [CrossRef]
- Y. Wang, S. Zhang, and J. H. Oliver, “3-D shape measurement technique for multiple rapidly moving objects,” Opt. Express19(9), 8539–8545 (2011). [CrossRef] [PubMed]
- W. H. Su, “Projected fringe profilometry using the area-encoded algorithm for spatially isolated and dynamic objects,” Opt. Express16(4), 2590–2596 (2008). [CrossRef] [PubMed]
- Y. Ding, J. Xi, Y. Yu, W. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express20(12), 13238–13251 (2012). [CrossRef] [PubMed]
- J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt.32(17), 3047–3052 (1993). [CrossRef] [PubMed]
- J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng.46(4), 336–342 (2008). [CrossRef]
- G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of Gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt.38(31), 6565–6573 (2005). [CrossRef] [PubMed]
- J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng.44(2), 023606 (1999). [CrossRef]
- Y. Liu, X. Su, and Q. Zhang, “A novel encoded-phase technique for phase measuring profilometry,” Opt. Express19(15), 14137–14144 (2011). [CrossRef] [PubMed]
- Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng.50(4), 574–579 (2012). [CrossRef]
- D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng.50(8), 1130–1139 (2012). [CrossRef]
- Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett.37(11), 2067–2069 (2012). [CrossRef] [PubMed]
- S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng.48(10), 105601 (2009). [CrossRef]
- Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett.36(13), 2518–2520 (2011). [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. Zhang and S. T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt.46(1), 36–43 (2007). [CrossRef] [PubMed]

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