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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 6 — Jun. 1, 1999
  • pp: 1484–1495

Speckle-induced phase error in laser-based phase-shifting projected fringe profilometry

Hongyu Liu, Guowen Lu, Shudong Wu, Shizhuo Yin, and Francis T. S. Yu  »View Author Affiliations

JOSA A, Vol. 16, Issue 6, pp. 1484-1495 (1999)

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Laser sources offer advantages over white-light sources in some phase-shifting projected fringe profilometry applications. These benefits, however, are gained at the cost of incurring speckle noise. Some basic statistics of speckle-induced phase-measurement errors are investigated based on the multiplicative noise model for image-plane speckles. First, the dependence of phase-error distribution and measurement uncertainty on speckle size and grating pitch is numerically studied, based on the Karhunen–Loève expansion method. Then an analytical expression that relates phase-error distributions to optical system parameters is derived as a direct extension of the simulation results. This expression is useful for system design and optimization. Analysis shows that phase noise caused by speckles can be modeled as additive white Gaussian noise. Optical system design and noise-reduction algorithms are also briefly discussed, based on the simulation results.

© 1999 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: August 13, 1998
Revised Manuscript: January 19, 1999
Manuscript Accepted: February 1, 1999
Published: June 1, 1999

Hongyu Liu, Guowen Lu, Shudong Wu, Shizhuo Yin, and Francis T. S. Yu, "Speckle-induced phase error in laser-based phase-shifting projected fringe profilometry," J. Opt. Soc. Am. A 16, 1484-1495 (1999)

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  1. R. E. Brooks, L. O. Heflinger, “Moiré gauging using optical interference patterns,” Appl. Opt. 8, 935–939 (1969). [CrossRef] [PubMed]
  2. D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9, 942–947 (1970). [CrossRef] [PubMed]
  3. H. Takasaki, “Moiré topography,” Appl. Opt. 9, 1467–1472 (1970). [CrossRef] [PubMed]
  4. G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurement of three-dimensional shape by phase measuring moiré topography,” Opt. Laser Technol. 16, 315–319 (1984). [CrossRef]
  5. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984). [CrossRef] [PubMed]
  6. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185–188 (1985). [CrossRef] [PubMed]
  7. M. Halioua, R. S. Krishnamurthy, H. C. Liu, F. P. Chiang, “Automated 360° profilometry of 3-D diffuse objects,” Appl. Opt. 24, 2193–2196 (1985). [CrossRef]
  8. B. W. Bell, “Digital heterodyne topography,” in Photomechanics and Speckle Metrology, F. Chiang, ed., Proc. SPIE814, 754–768 (1987).
  9. O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley Interscience, New York, 1990).
  10. B. F. Oreb, K. G. Larkin, P. Fairman, M. Ghaffari, “Moiré based optical surface profiler for the minting industry,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 48–57 (1992).
  11. 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]
  12. B. F. Oreb, R. G. Dorsch, “Profilometry by phase-shifted Talbot images,” Appl. Opt. 33, 7955–7962 (1994). [CrossRef] [PubMed]
  13. T. Matsumoto, Y. Kitagawa, T. Minemoto, “Sensitivity-variable moiré topography with a phase shift method,” Opt. Eng. (Bellingham) 35, 1754–1760 (1996). [CrossRef]
  14. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 350–393.
  15. J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. XXVIII, pp. 271–359.
  16. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976). [CrossRef]
  17. J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).
  18. S. Lowenthal, H. H. Arsenault, “Image formation for coherent diffuse objects: statistical properties,” J. Opt. Soc. Am. 60, 1478–1483 (1970). [CrossRef]
  19. G. Häusler, J. M. Herrmann, “Range sensing by shearing interferometry: influence of speckle,” Appl. Opt. 27, 4631–4637 (1988). [CrossRef] [PubMed]
  20. R. Baribeau, M. Rioux, “Influence of speckle on laser range finders,” Appl. Opt. 30, 2873–2878 (1991). [CrossRef] [PubMed]
  21. A. Papoulis, Probability, Random Variables, and Stochastic Progress, 2nd ed. (McGraw-Hill, New York, 1984).
  22. A. W. Lohmann, D. P. Paris, “Space-variant image formation,” J. Opt. Soc. Am. 55, 1007–1013 (1965).
  23. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  24. J. C. Dainty, “Detection of images immersed in speckle noise,” Opt. Acta 18, 327–339 (1971). [CrossRef]
  25. R. Barakat, “First-order probability densities of laser speckle patterns observed through finite-size scanning apertures,” Opt. Acta 20, 729–740 (1973). [CrossRef]
  26. R. P. Kanwal, Linear Integral Equations (Academic, New York, 1971).
  27. L. M. Delves, J. L. Mohamed, Computational Methods for Integral Equations (Cambridge U. Press, Cambridge, UK, 1985).
  28. D. Slepian, E. Sonnenblick, “Eigenvalues associated with prolate spheroidal wave functions of zero order,” Bell Syst. Tech. J. 44, 1745–1759 (1966).
  29. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  30. T. S. McKechnie, Opt. Quantum Electron. 8, 61–67 (1976). [CrossRef]
  31. A. Lohmann, “Grating diffraction spectra as coherent light sources for two or three beam interferometry,” Opt. Acta 9, 1–12 (1962). [CrossRef]
  32. J. C. Dainty, W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971). [CrossRef]
  33. F. T. S. Yu, E. Y. Wang, “Speckle reduction in holography by means of random spatial sampling,” Appl. Opt. 12, 1656–1659 (1973). [CrossRef] [PubMed]
  34. D. Donoho, “Denoising by soft thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995). [CrossRef]
  35. D. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. 57, 301–369 (1995).

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