An improved method is proposed to perform calibration-based fringe projected profilometry using a two-frequency fringe pattern for the 3D shape measurements of objects with large discontinuous height steps. A fabrication scheme for the two-frequency pattern is described as well. The proposed method offers following major advantages: (1) only one phase measurement needed for operation, (2) easiness for calibration, (3) robust performance, especially for automatic phase unwrapping, and (4) more flexible data acquisition for complex objects. This makes it possible for a single-shot measurement of dynamic objects with discontinuities. Both theoretical descriptions and experimental demonstrations are provided.

© 2006 Optical Society of America

1. G. Indebetouw, "Profile measurement using projection of running fringes," Appl. Opt. 17, 2930-2933 (1978). [CrossRef] [PubMed]
2. V. Srinivasan, H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-D diffuse objects," Appl. Opt. 23, 3105-3108 (1984). [CrossRef] [PubMed]
3. M. Takeda and K. Motoh, "Fourier transform profilometry for the automatic measurement of 3-D object shaped," Appl. Opt. 22, 3977-3982 (1983). [CrossRef] [PubMed]
4. X. Su, and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001). [CrossRef]
5. K. G. Larkin and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms," J. Opt. Soc. Am. A 9, 1740-1748 (1992). [CrossRef]
6. V. Y. Su, G von Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993). [CrossRef]
7. Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35, 51-60 (1996). [CrossRef] [PubMed]
8. F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000). [CrossRef]
9. W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003). [CrossRef]
10. D. C. Ghiglia and L. A. Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am. A 11, 107 (1994). [CrossRef]
11. K. A. Stetson, J. Wahid, and P. Gauthier, "Noise-immune phase unwrapping by use of calculated wrap regions," Appl. Opt. 36, 4830-4838 (1997). [CrossRef] [PubMed]
12. A. Collaro, G. Franceschetti, F. Palmieri, and M. S. Ferreiro, "Phase unwrapping by means of genetic algorithms," J. Opt. Soc. Am. A 15, 407-418 (1998). [CrossRef]
13. J.-J. Chyou, S.-J. Chen, and Y.-K. Chen, "Two-dimensional phase unwrapping with a multichannel least-mean-square algorithm," Appl. Opt. 43, 5655-5661 (2004). [CrossRef] [PubMed]
14. J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated inteferogram analysis," Appl. Opt. 32, 3047-3052 (1993). [CrossRef] [PubMed]
15. H. O. Saldner and J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector," Opt. Eng. 36, 610-615 (1997). [CrossRef]
16. K. Creath, "Step height measurement using two-wavelength phase-shifting interferometry," Appl. Opt. 26, 2810-2816 (1987). [CrossRef] [PubMed]
17. H. Zhao, W. Chen, and Y. Tan, "Phase-unwrapping algorithm for the measurement of three-dimensional object shapes," Appl. Opt. 33, 4497-4500 (1994). [CrossRef] [PubMed]
18. D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994) [CrossRef] [PubMed]
19. Y. Hao, Y. Zhao, and D. Li, "Multifrequency grating projection profilometry based on the nonlinear excess fraction method," Appl. Opt. 38, 4106-4110 (1999). [CrossRef]
20. E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D.W. Zhang, "Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry," Opt. Express 13, 1561-1569 (2005). [CrossRef] [PubMed]
21. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, "Frequency-multiplex Fourier-transform profilomery: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," Appl. Opt. 36, 5347-5354 (1997). [CrossRef] [PubMed]
22. J. L. Li, H. J. Su, and X. Y. Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36, 277-280 (1997). [CrossRef] [PubMed]
23. H. Liu, W. H. Su, K. R., and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Opt. Commun. 216, 65-80 (2003). [CrossRef]
24. L. B. Jackson, Digital Filters and Signal Processing (Toppan, 1996), Chap. 6.

Appl. Opt.

• G. Indebetouw, "Profile measurement using projection of running fringes," Appl. Opt. 17, 2930-2933 (1978). [CrossRef] [PubMed]
• V. Srinivasan, H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-D diffuse objects," Appl. Opt. 23, 3105-3108 (1984). [CrossRef] [PubMed]
• M. Takeda and K. Motoh, "Fourier transform profilometry for the automatic measurement of 3-D object shaped," Appl. Opt. 22, 3977-3982 (1983). [CrossRef] [PubMed]
• Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35, 51-60 (1996). [CrossRef] [PubMed]
• K. A. Stetson, J. Wahid, and P. Gauthier, "Noise-immune phase unwrapping by use of calculated wrap regions," Appl. Opt. 36, 4830-4838 (1997). [CrossRef] [PubMed]
• J.-J. Chyou, S.-J. Chen, and Y.-K. Chen, "Two-dimensional phase unwrapping with a multichannel least-mean-square algorithm," Appl. Opt. 43, 5655-5661 (2004). [CrossRef] [PubMed]
• J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated inteferogram analysis," Appl. Opt. 32, 3047-3052 (1993). [CrossRef] [PubMed]
• K. Creath, "Step height measurement using two-wavelength phase-shifting interferometry," Appl. Opt. 26, 2810-2816 (1987). [CrossRef] [PubMed]
• H. Zhao, W. Chen, and Y. Tan, "Phase-unwrapping algorithm for the measurement of three-dimensional object shapes," Appl. Opt. 33, 4497-4500 (1994). [CrossRef] [PubMed]
• D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994) [CrossRef] [PubMed]
• Y. Hao, Y. Zhao, and D. Li, "Multifrequency grating projection profilometry based on the nonlinear excess fraction method," Appl. Opt. 38, 4106-4110 (1999). [CrossRef]
• M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, "Frequency-multiplex Fourier-transform profilomery: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," Appl. Opt. 36, 5347-5354 (1997). [CrossRef] [PubMed]
• J. L. Li, H. J. Su, and X. Y. Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36, 277-280 (1997). [CrossRef] [PubMed]

J. Opt. Soc. Am. A

• D. C. Ghiglia and L. A. Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am. A 11, 107 (1994). [CrossRef]
• A. Collaro, G. Franceschetti, F. Palmieri, and M. S. Ferreiro, "Phase unwrapping by means of genetic algorithms," J. Opt. Soc. Am. A 15, 407-418 (1998). [CrossRef]
• K. G. Larkin and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms," J. Opt. Soc. Am. A 9, 1740-1748 (1992). [CrossRef]

Opt. Commun.

• V. Y. Su, G von Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993). [CrossRef]
• H. Liu, W. H. Su, K. R., and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Opt. Commun. 216, 65-80 (2003). [CrossRef]

Opt. Eng.

• F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000). [CrossRef]
• W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003). [CrossRef]
• H. O. Saldner and J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector," Opt. Eng. 36, 610-615 (1997). [CrossRef]

Opt. Express

• E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D.W. Zhang, "Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry," Opt. Express 13, 1561-1569 (2005). [CrossRef] [PubMed]

Opt. Lasers Eng.

• X. Su, and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001). [CrossRef]

Other

• L. B. Jackson, Digital Filters and Signal Processing (Toppan, 1996), Chap. 6.

Click here to see a list of articles that cite this paper

Related Journal Articles

• Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths (JOSAA)
• A large-depth-of-field projected fringe profilometry using supercontinuum light illumination (OE)
• Color-encoded fringe projection for 3D shape measurements (OE)
• Comparison of three-dimensional optical coherence tomography and high resolution photography for art conservation studies (OE)
• Projected fringe profilometry using the area-encoded algorithm for spatially isolated and dynamic objects (OE)

Related Conference Papers

• Security and Non Destructive Evaluation Application of High Speed Time Domain Terahertz Imaging
• Application of a 2W/nm All-Fiber Supercontinuum Source to the Characterization of Nonlinear Crystals
• Application of a 2W/nm All-Fiber Supercontinuum Source to the Characterization of Nonlinear Crystals
• Chirped AM Ladar for 3D Imaging and Range-Doppler Tracking at 1550 nm Wavelength: Update
• Three-Dimensional Shape Measurement Using Binary Spatio-Temporal Encoded Illumination