OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: 3150–3158

Intensity-ratio error compensation for triangular-pattern phase-shifting profilometry

Peirong Jia, Jonathan Kofman, and Chad English  »View Author Affiliations

JOSA A, Vol. 24, Issue 10, pp. 3150-3158 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (346 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present an intensity-ratio error-compensation method to decrease the measurement error caused by projector gamma nonlinearity and image defocus in triangular-pattern phase-shifting profilometry. The intensity-ratio measurement error is first determined by simulating the measurement with the triangular-pattern phase-shifting method with ideal and real captured triangular-pattern images based on the ideal and real gamma nonlinearity functions. A lookup table that stores the intensity-ratio measurement error corresponding to the measured intensity ratio is constructed and used for intensity-ratio error compensation. Experiments demonstrated that the intensity-ratio error compensation method significantly reduced the measurement error in the triangular-pattern phase-shifting method by 28.5%.

© 2007 Optical Society of America

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
(150.6910) Machine vision : Three-dimensional sensing

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 14, 2006
Revised Manuscript: May 28, 2007
Manuscript Accepted: June 26, 2007
Published: September 13, 2007

Peirong Jia, Jonathan Kofman, and Chad English, "Intensity-ratio error compensation for triangular-pattern phase-shifting profilometry," J. Opt. Soc. Am. A 24, 3150-3158 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, Vol. XXVI, E.Wolf, ed. (Elsevier Science, 1988), pp. 349-393. [CrossRef]
  2. M. Halioua and H. C. Liu, "Optical three-dimensional sensing by phase measuring profilometry," Opt. Lasers Eng. 11, 185-215 (1989). [CrossRef]
  3. J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometry," in Optical Shop Testing (Wiley, 1992), pp. 501-598.
  4. X. Y. He, D. Q. Zou, S. Liu, and Y. F. Guo, "Phase-shifting analysis in moiré interferometry and its application in electronic packaging," Opt. Eng. (Bellingham) 37, 1410-1419 (1998). [CrossRef]
  5. Y. B. Choi and S. W. Kim, "Phase-shifting grating projection moiré topography," Opt. Eng. (Bellingham) 37, 1005-1010 (1998). [CrossRef]
  6. G. Frankowski, M. Chen, and T. Huth, "Real-time 3D shape measurement with digital strip projection by Texas Instruments Micromirror Devices DMDtrade," Proc. SPIE 3958, 90-105 (2000). [CrossRef]
  7. H. Guo, H. He, and M. Chen, "Gamma correction for digital fringe projection profilometry," Appl. Opt. 43, 2906-2914 (2004). [CrossRef] [PubMed]
  8. B. Carrihill and R. Hummel, "Experiments with the intensity ratio depth sensor," in Computer Vision, Graphics and Image Processing (Academic, 1985), pp. 337-358. [CrossRef]
  9. T. Miyasaka and K. Araki, "Development of real time 3-D measurement system using intensity ratio method," in Photogrammetric Computer Vision (PCV02), Proceedings of the ISPRS Commission III (ISPRS, 2002), Vol. XXXIV, Part 3B, pp. 181-185.
  10. G. Chazan and N. Kiryati, "Pyramidal intensity-ratio depth sensor," Tech. Rep. 121, Department of Electrical Engineering (Center for Communication and Information Technologies, Technion, Haifa, Israel, 1995).
  11. P. Jia, J. Kofman, and C. English, "Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement," Opt. Eng. (Bellingham) 46, 083201 (2007). [CrossRef]
  12. P. Jia, J. Kofman, and C. English, "Multiple-step triangular-pattern phase-shifting and the influence of number of steps and pitch on measurement accuracy," Appl. Opt. 46, 3253-3262 (2007). [CrossRef] [PubMed]
  13. P. S. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for the three-dimensional shape measurement," Opt. Eng. (Bellingham) 44, 123601 (2005). [CrossRef]
  14. Q. Fang, "Linearly coded profilometry with a coding light that has isosceles triangle teeth: even-number-sample decoding method," Appl. Opt. 36, 1615-1620 (1997). [CrossRef] [PubMed]
  15. Q. Fang and S. Zheng, "Linearly coded profilometry," Appl. Opt. 36, 2401-2407 (1997). [CrossRef] [PubMed]
  16. J. Pan, P. S. Huang, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed 3D shape measurement--color coupling and imbalance compensation," Proc. SPIE 5265, 205-212 (2004). [CrossRef]
  17. S. Zhang and P. S. Huang, "Phase error compensation for a 3-D shape measurement system based on the phase-shifting method," Proc. SPIE 6000, E1-E10 (2005). [CrossRef]
  18. P. S. Huang, Q. J. Hu, and F. P. Chiang, "Double three-step phase-shifting algorithm," Appl. Opt. 41, 4503-4509 (2002). [CrossRef] [PubMed]
  19. P. Jia, J. Kofman, and C. English, "Repeated phase-offset measurement for error compensation in two-step triangular phase-shifting profilometry," Proc. SPIE 6375, 63750D (2006). [CrossRef]
  20. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley-Interscience, 1998).
  21. P. Jia, J. Kofman, and C. English, "Comparison of linear and non-linear calibration methods for phase-measuring profilometry," Opt. Eng. (Bellingham) 46, 043601 (2007). [CrossRef]
  22. C. Zhang, P. S. Huang, and F. P. Chiang, "Microscopic phase-shifting profilometry based on digital micromirror device technology," Appl. Opt. 41, 5896-5904 (2002). [CrossRef] [PubMed]

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