OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 6 — Jun. 1, 2012
  • pp: 1047–1058

Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

Xu Zhang, Limin Zhu, Youfu Li, and Dawei Tu  »View Author Affiliations

JOSA A, Vol. 29, Issue 6, pp. 1047-1058 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (966 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Gamma distortion is a dominant error source of phase measuring profilometry. It makes a single frequency for the ideal sinusoidal waveform an infinite width of spectrum. Besides, the defocus of the projector-camera system, like a spatial low-pass filter, attenuates the amplitudes of the high-frequency harmonics. In this paper, a generic distorted fringe model is proposed, which is expressed as a Fourier series. The mathematical model of the harmonic coefficients is derived. Based on the proposed model, a robust gamma calibration method is introduced. It employs the multifrequency phase-shifting method to eliminate the effect of defocus and preserve the influence of gamma distortion. Then, a gamma correction method is proposed to correct the gamma distortion with the calibrated gamma value. The proposed correction method has the advantage of high signal-to-noise ratio. The proposed model is verified through experiments. The results confirm that the phase error is dependent on the defocus and the pitch. The proposed gamma calibration method is compared with the state of the art and proves to be more robust to pitch and defocus variations. After adopting the proposed gamma correction method, the phase precision is much enhanced with higher quality in the measured surfaces.

© 2012 Optical Society of America

OCIS Codes
(000.3110) General : Instruments, apparatus, and components common to the sciences
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(150.6910) Machine vision : Three-dimensional sensing
(330.1400) Vision, color, and visual optics : Vision - binocular and stereopsis

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 28, 2011
Revised Manuscript: February 11, 2012
Manuscript Accepted: March 14, 2012
Published: May 29, 2012

Xu Zhang, Limin Zhu, Youfu Li, and Dawei Tu, "Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry," J. Opt. Soc. Am. A 29, 1047-1058 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?,” Opt. Lasers Eng. 48, 133–140 (2010). [CrossRef]
  2. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010). [CrossRef]
  3. J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010). [CrossRef]
  4. X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. Lasers Eng. 48, 191–204 (2010). [CrossRef]
  5. T. Judge and P. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994). [CrossRef]
  6. A. Baldi, F. Bertolino, and F. Ginesu, “On the performance of some unwrapping algorithms,” Opt. Lasers Eng. 37, 313–330 (2002). [CrossRef]
  7. D. Malacara, Optical Shop Testing (Wiley-Blackwell, 2007).
  8. P. Huang, Q. Hu, and F. Chiang, “Double three-step phase-shifting algorithm,” Appl. Opt. 41, 4503–4509 (2002). [CrossRef]
  9. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. A 12, 1997–2008 (1995). [CrossRef]
  10. J. Li, L. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20, 106–115 (2003). [CrossRef]
  11. S. Zhang and S. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46, 36–43 (2007). [CrossRef]
  12. T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35, 1992–1994 (2010). [CrossRef]
  13. K. Freischlad and C. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7, 542–551 (1990). [CrossRef]
  14. K. Liu, Y. Wang, D. Lau, Q. Hao, and L. Hassebrook, “Gamma model and its analysis for phase measuring profilometry,” J. Opt. Soc. Am. A 27, 553–562 (2010). [CrossRef]
  15. K. Hibino, B. Oreb, D. Farrant, and K. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12, 761–768 (1995). [CrossRef]
  16. S. Kakunai, T. Sakamoto, and K. Iwata, “Profile measurement taken with liquid-crystal gratings,” Appl. Opt. 38, 2824–2828 (1999). [CrossRef]
  17. P. Huang, C. Zhang, and F. Chiang, “High-speed 3-d shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003). [CrossRef]
  18. M. Baker, J. Xi, and J. Chicharo, “Neural network digital fringe calibration technique for structured light profilometers,” Appl. Opt. 46, 1233–1243 (2007). [CrossRef]
  19. H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43, 2906–2914 (2004). [CrossRef]
  20. Z. Li and Y. Li, “Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry,” Opt. Lett. 36, 154–156 (2011). [CrossRef]
  21. C. Poynton, “Gamma and its disguises: The nonlinear mappings of intensity in perception, crts, film, and video,” SMPTE J. 102, 1099–1108 (1993). [CrossRef]
  22. S. Zhang and P. Huang, “Phase error compensation for a 3-d shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007). [CrossRef]
  23. P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular-pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–3158 (2007). [CrossRef]
  24. 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, 416–418 (2009). [CrossRef]
  25. X. Su, W. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94, 561–573 (1992). [CrossRef]
  26. Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50, 2572–2581 (2011). [CrossRef]
  27. M. J. Baker, J. Xi, and J. F. Chicharo, “Elimination of gamma non-linear luminance effects for digital video projection phase measuring profilometers,” in 4th IEEE International Symposium on Electronic Design, Test and Applications, 2008. DELTA 2008. (IEEE, 2008), pp. 496–501.
  28. Y. Hu, J. Xi, J. Chicharo, and Z. Yang, “Improved three-step phase shifting profilometry using digital fringe pattern projection,” in 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 161–167.
  29. Y. Hu, J. Xi, E. Li, J. Chicharo, and Z. Yang, “Three-dimensional profilometry based on shift estimation of projected fringe patterns,” Appl. Opt. 45, 678–687 (2006). [CrossRef]
  30. C. Claxton and R. Staunton, “Measurement of the point-spread function of a noisy imaging system,” J. Opt. Soc. Am. A 25, 159–170 (2008). [CrossRef]
  31. D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  32. G. H. Notni and G. Notni, “Digital fringe projection in 3d shape measurement: an error analysis,” Proc. SPIE 5144, 372–380 (2003). [CrossRef]
  33. T. Peng, “Algorithms and models for 3-d shape measurement using digital fringe projections,” (University of Maryland, 2006), pp. 221–223.
  34. X. Zhang, L. Zhu, and Y. Li, “Indirect decoding edges for one-shot shape acquisition,” J. Opt. Soc. Am. A 28, 651–661(2011). [CrossRef]
  35. C. Coggrave and J. Huntley, “Optimization of a shape measurement system based on spatial light modulators,” Opt. Eng. 39, 91–98 (2000). [CrossRef]
  36. L. Kinell and M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40, 2297–2303 (2001). [CrossRef]

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.

CrossCheck Deposited