OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 33, Iss. 14 — May. 10, 1994
  • pp: 2939–2948

Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping

David R. Burton and Michael J. Lalor  »View Author Affiliations

Applied Optics, Vol. 33, Issue 14, pp. 2939-2948 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (1530 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We describe a technique termed multichannel Fourier fringe analysis and its application to the problem of automatic phase unwrapping in the presence of surface discontinuities. The technique is especially useful for the analysis of fringe projection contour maps in order to measure surface height distributions. Use is made of multiple fringe patterns that are separated in the frequency space of the Fourier transform by means of a set of bandpass filters. We also describe the design of a special fiber-optic interferometer with features particularly important in the case of this technique: easily adjustable fringe spacing and rotation. Fringe production by the interferometer is analyzed, and the relationship between the fringe phase and the height distribution of an illuminated surface is derived. A method for measuring phase in the case of multichannel Fourier fringe analysis is presented. The application of the technique to automatic phase unwrapping is shown. An example of the technique in operation is given, and a discussion of implementation of the technique is included.

© 1994 Optical Society of America

Original Manuscript: June 18, 1993
Revised Manuscript: November 16, 1993
Published: May 10, 1994

David R. Burton and Michael J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. H. Bruning, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, J. Brangaccio, “Digital wave-front measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  2. K. Creath, “Phase shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985). [CrossRef] [PubMed]
  3. C. T. Farrell, M. A. Player, “Phase step measurement and variable step algorithms in phase-shifting interferometry,” J. Meas. Sci. Technol. 3, 953–958 (1992). [CrossRef]
  4. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3981 (1983). [CrossRef] [PubMed]
  5. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer based tomography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  6. T. M. Kreis, “Digital holographic interference phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–856 (1986). [CrossRef]
  7. A. A. Malcolm, D. R. Burton, “The relationship between Fourier fringe analysis and the FFT,” in Lase’r Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 286–297 (1991).
  8. T. M. Kreis, W. P. O. Juptner, “Fourier transform evaluation of interference patterns: the role of filtering in the spatial frequency domain,” in Laser Interferometry: Quantitative Analysis of Interferograms, R. V. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 116–125 (1990).
  9. D. R. Burton, M. J. Lalor, “Managing some of the problems of Fourier fringe analysis,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 149–160 (1989).
  10. D. R. Burton, M. J. Lalor, “Precision measurement of engineering form by computer analysis of optically generated contours,” in Industrial Inspection, D. W. Braggins, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1010, 17–24 (1989).
  11. J. T. Atkinson, D. R. Burton, M. J. Lalor, P. C. O’Donovan, “Opto-computer methods applied to the evaluation of a range of acetabular cups,” Eng. Med. 17, 105–110 (1988). [CrossRef] [PubMed]
  12. W. Macy, “Two-dimensional fringe pattern analysis,” Appl. Opt. 22, 3898–3901 (1984). [CrossRef]
  13. W. H. Carter, “On unwrapping two-dimensional phase data in contour maps,” Opt. Commun. 94, 1–7 (1992). [CrossRef]
  14. N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spacing tree algorithm,” IEEE Trans. Image Proc. 1, 355–365 (1992). [CrossRef]
  15. M. Hedley, D. Rosenfeld, “A new two-dimensional phase unwrapping algorithm for MRI images,” J. Magn. Reson. 24, 177–181 (1992). [CrossRef]
  16. T. R. Judge, C. Quan, P. J. Bryanston-Cross, “Holographic deformation measurements by Fourier transform technique with automatic unwrapping,” Opt. Eng. 31, 533–543(1992). [CrossRef]
  17. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991). [CrossRef] [PubMed]
  18. J. M. Huntley, H. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993). [CrossRef] [PubMed]
  19. M. Takeda, M. Kitoh, “Spatiotemporal frequency multiplex heterodyne interferometry,” J. Opt. Soc. Am. A 9, 1607–1614(1992). [CrossRef]
  20. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), pp. 260–261.
  21. E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice-Hall, Englewood Cliffs, N.J., 1988), pp. 30–31.
  22. R. J. Schalkoff, Digital Image Processing and Computer Vision, 1st ed. (Wiley, New York, 1989), pp. 149–150.
  23. M. Takeda, H. Iijima, “Spatio-temporal heterodyne interferometry,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 210–216 (1990).

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited