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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 35 — Dec. 10, 2012
  • pp: 8433–8439

Separation of complex fringe patterns using two-dimensional continuous wavelet transform

Krzysztof Pokorski and Krzysztof Patorski  »View Author Affiliations

Applied Optics, Vol. 51, Issue 35, pp. 8433-8439 (2012)

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A method for processing fringe patterns containing additively superimposed multiple fringe sets is presented. It enables to analyze different fringe families present in a single image separately. The proposed method is based on a two-dimensional continuous wavelet transform. A robust ridge extraction algorithm for a single fringe set extraction is presented. The method is fully automatic and requires no user interference. Spectral separation of fringe families is not required. Simulations are presented to verify performance and advantage of the proposed method over the Fourier transform based technique. Method validity has been confirmed using experimental images.

© 2012 Optical Society of America

OCIS Codes
(100.7410) Image processing : Wavelets
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: September 21, 2012
Revised Manuscript: November 8, 2012
Manuscript Accepted: November 9, 2012
Published: December 7, 2012

Krzysztof Pokorski and Krzysztof Patorski, "Separation of complex fringe patterns using two-dimensional continuous wavelet transform," Appl. Opt. 51, 8433-8439 (2012)

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  1. J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1990).
  2. D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics Publishing, 1993).
  3. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis For Optical Testing (Marcel Dekker, 1998).
  4. K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001). [CrossRef]
  5. K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. ii. stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1871–1881 (2001). [CrossRef]
  6. M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt. 50, 5513–5523 (2011). [CrossRef]
  7. Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006). [CrossRef]
  8. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006). [CrossRef]
  9. A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, and F. Lilley, “Spatial fringe pattern analysis using the two-dimensional continuous wavelet transform employing a cost function,” Appl. Opt. 46, 6120–6126 (2007). [CrossRef]
  10. K. Pokorski and K. Patorski, “Visualization of additive-type Moiré and time-average fringe patterns using the continuous wavelet transform,” Appl. Opt. 49, 3640–3651 (2010). [CrossRef]
  11. K. Patorski and K. Pokorski, “Examination of singular scalar light fields using wavelet processing of fork fringes,” Appl. Opt. 50, 773–781 (2011). [CrossRef]
  12. K. Patorski, K. Pokorski, and M. Trusiak, “Fourier domain interpretation of real and pseudo-Moiré phenomena,” Opt. Express 19, 26065–26078 (2011). [CrossRef]
  13. P. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, 1969).
  14. D. Post, “The Moiré grid-analyzer method for strain analysis,” Exp. Mech. 5, 368–377 (1965). [CrossRef]
  15. J. M. Burch and C. Forno, “High resolution Moire photography,” Opt. Eng. 21, 214602 (1982). [CrossRef]
  16. J. M. Huntley and J. E. Field, “High resolution Moire photography: application to dynamic stress analysis,” Opt. Eng. 28, 288926 (1989). [CrossRef]
  17. T. Bertin-Mourot, C. Denoual, G. Deshors, P. F. Louvigné, and T. Thomas, “High speed photography of Moire fringes. Application to ceramics under impact,” J. Phys. IV 07, C3-311–C3-316 (1997). [CrossRef]
  18. M. Dadkhah, F. Wang, and A. Kobayashi, “Simultaneous on-line measurement of orthogonal displacement fields by Moiré interferometry,” Exp. Tech. 12, 28–30 (1988). [CrossRef]
  19. A. S. Kobayashi and Z. K. Guo, “Simultaneous measurement of u- and v-displacement fields by Moiré interferometry,” Exp. Tech. 17, 21–24 (1993). [CrossRef]
  20. L. Salbut, “Multichannel system for automatic analysis of u, v, w displacements in grating interferometry,” in Physical Research, W. Juptner and W. Osten, eds. 19 (Akademie Verlag, 1993), pp. 282–287.
  21. J. Schmit, K. Patorski, and K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997). [CrossRef]
  22. N. Demoli and D. Vukicevic, “Detection of hidden stationary deformations of vibrating surfaces by use of time-averaged digital holographic interferometry,” Opt. Lett. 29, 2423–2425 (2004). [CrossRef]
  23. G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic Moiré,” Appl. Opt. 50, 4189–4197 (2011). [CrossRef]
  24. G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Express 20, 1281–1291 (2012). [CrossRef]
  25. J. Vargas, J. A. Quiroga, and T. Belenguer, “Direct demodulation of closed-fringe interferograms based on active contours,” Opt. Lett. 35, 3550–3552 (2010). [CrossRef]
  26. K. Pokorski and K. Patorski, “Continuous wavelet transform processing of fringe patterns containing multiple fringe sets,” Proc. SPIE, 8697-29.
  27. J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge University, 2008).
  28. J. Kirby, “Which wavelet best reproduces the Fourier power spectrum,” Comput. Geosci. 31, 846–864 (2005). [CrossRef]
  29. S. Li, X. Wang, X. Su, and F. Tang, “Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis,” Appl. Opt. 51, 2026–2034 (2012). [CrossRef]
  30. J. Ma, Z. Wang, M. Vo, and L. Luu, “Parameter discretization in two-dimensional continuous wavelet transform for fast fringe pattern analysis,” Appl. Opt. 50, 6399–6408 (2011). [CrossRef]
  31. J. Ma, Z. Wang, B. Pan, T. Hoang, M. Vo, and L. Luu, “Two-dimensional continuous wavelet transform for phase determination of complex interferograms,” Appl. Opt. 50, 2425–2430 (2011). [CrossRef]
  32. S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008). [CrossRef]
  33. J. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Trans. Image Process. 16, 698–709 (2007). [CrossRef]
  34. K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993).
  35. L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010). [CrossRef]
  36. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  37. R. Czarnek, “Three-mirror, four-beam Moiré interferometer and its capabilities,” Opt. Lasers Eng. 15, 93–101 (1991). [CrossRef]
  38. P. Post, B. Han, and P. Ifju, High Sensitivity Moiré (Springer Verlag, 1994).

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