OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 36, Iss. 1 — Jan. 1, 1997
  • pp: 277–280

Two-frequency grating used in phase-measuring profilometry

Jie-Lin Li, Hong-Jun Su, and Xian-Yu Su  »View Author Affiliations

Applied Optics, Vol. 36, Issue 1, pp. 277-280 (1997)

View Full Text Article

Enhanced HTML    Acrobat PDF (420 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a method that uses two groups of fringe patterns on one grating for phase-measuring profilometry. A two-frequency grating is projected onto the object. The high frequency is N(N = 3, 4, 5, …) times greater than the low frequency. Using a proper phase shift, we calculated the wrapped phases of the two frequencies. When the linearity of the two phases are considered, an accurate phase of the high frequency can be unwrapped. Because the low frequency is N times more insensitive to height discontinuity, the system is more tolerable to height discontinuity.

© 1997 Optical Society of America

Original Manuscript: April 15, 1996
Revised Manuscript: June 3, 1996
Published: January 1, 1997

Jie-Lin Li, Hong-Jun Su, and Xian-Yu Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36, 277-280 (1997)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984). [CrossRef] [PubMed]
  2. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185–188 (1985). [CrossRef] [PubMed]
  3. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983). [CrossRef] [PubMed]
  4. J. Li, X.-Y. Su, L.-R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990). [CrossRef]
  5. X.-Y. Su, G. von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993). [CrossRef]
  6. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991). [CrossRef] [PubMed]
  7. D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987). [CrossRef]
  8. D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991). [CrossRef]
  9. M. Takeda, K. Natome, Y. Watanabe, “Phase unwrapping by neural network,” in Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns. W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 136–141.
  10. J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993). [CrossRef] [PubMed]
  11. M. Takeda, M. Kitoh, “Spatiotemporal frequency multiplex heterodyne interferometry,” J. Opt. Soc. Am. A 9, 1607–1614 (1992). [CrossRef]
  12. D. R. Burton, M. J. Lalor, “Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping,” Appl. Opt. 33, 2939–2948 (1994). [CrossRef] [PubMed]
  13. H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497–4500 (1994). [CrossRef] [PubMed]
  14. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited