Abstract

An application of the continuous wavelet transform to modulation extraction of additive moiré fringes and time-average patterns is proposed. We present numerical studies of the influence of various param eters of the wavelet transformation itself and a fringe pattern under study on the demodulation results. To facilitate the task of demodulating a signal with zero crossing values, a two-frame approach for wavelet ridge extraction is proposed. Experimental studies of vibration mode patterns by time-average interferometry provide excellent verification of numerical findings. They compare very well with the results of our previous investigations using the temporal phase-shifting method widely considered as the most accurate one. No need of performing phase shifting represents significant simplification of the experimental procedure.

© 2010 Optical Society of America

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  1. A. S. Kobayashi, Handbook on Experimental Mechanics, 2nd ed. (SEM, 1993).
  2. K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993).
  3. O. Bryngdahl, “Characteristics of superposed patterns in optics,” J. Opt. Soc. Am. 66, 87–94 (1976).
    [CrossRef]
  4. C. Forno and M. Whelan, “Digital moiré subtraction in optical engineering,” Opt. Eng. 40, 2199–2208 (2001).
    [CrossRef]
  5. J. Wasowski, “Moiré topographic maps,” Opt. Commun. 2, 321–323 (1970).
    [CrossRef]
  6. J. D. Hovanesian and Y. Hung, “Moiré contour-sum, contour-difference and vibration analysis of arbitrary objects,” Appl. Opt. 10, 2734–2738 (1971).
    [CrossRef] [PubMed]
  7. M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
    [CrossRef]
  8. G. Rosvold, “Video-based vibration analysis using projected fringes,” Appl. Opt. 33, 775–786 (1994).
    [CrossRef] [PubMed]
  9. M. Ragulskis and Z. Navickas, “Interpretation of fringes produced by time-averaged projection moiré,” Strain 45, doi: 10.1111/j.1475–1305.2009.00625x (2009) and references therein.
    [CrossRef]
  10. S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
    [CrossRef]
  11. A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).
    [CrossRef]
  12. L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
    [CrossRef]
  13. K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).
    [CrossRef]
  14. K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).
    [CrossRef]
  15. A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624 (2007).
    [CrossRef] [PubMed]
  16. H. Osterberg, “An interferometer method of studying the vibrations of an oscillating quartz plate,” J. Opt. Soc. Am. 22, 19–35 (1932).
    [CrossRef]
  17. J. Lim, J. Kim, and M. Chung, “Additive type moiré with computer image processing,” Appl. Opt. 28, 2677–2680 (1989).
    [CrossRef] [PubMed]
  18. R. Eschbach, “Generation of moiré of nonlinear transfer characteristics,” J. Opt. Soc. Am. A 5, 1828–1835 (1988).
    [CrossRef]
  19. L. Saunoriene and M. Ragulskis, “Visualization of fringes in time averaged moiré patterns,” Inf. Technol. Control 35, 249–254 (2006).
  20. M. Ragulskis, A. Aleksa, and R. Maskeliunas, “Contrast enhancement of time-averaged fringes based on moving average mapping functions,” Opt. Lasers Eng. 47, 768–773 (2009).
    [CrossRef]
  21. S. Malat, A Wavelet Tour of Signal Processing (Academic, 1999).
  22. J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge U. Press, 2008).
  23. Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
    [CrossRef]
  24. 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] [PubMed]
  25. B. Chen and C. Basaran, “Automatic full strain field moiré interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).
    [CrossRef]
  26. M. Li, C. Quan, and C. Tai, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929 (2008).
    [CrossRef]
  27. S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
    [CrossRef] [PubMed]
  28. C. J. Tay, C. Quan, Y. Fu, and Y. Huang, “Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis,” Appl. Opt. 43, 4164–4171 (2004).
    [CrossRef] [PubMed]
  29. C. Quan, Y. Fu, C. J. Tay, and J. M. Tan, “Profiling of objects with height steps by wavelet analysis of shadow moiré fringes,” Appl. Opt. 44, 3284–3290 (2005).
    [CrossRef] [PubMed]
  30. R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
    [CrossRef]
  31. C.-M. Liu, L.-W. Chen, and C.-C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17, 4359–4366 (2006).
    [CrossRef]
  32. K. Qian, H. Seah, and A. Asundi, “Instantaneous frequency and its application to strain extraction in moiré interferometry,” Appl. Opt. 42, 6504–6513 (2003).
    [CrossRef]
  33. K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
    [CrossRef]
  34. H. Liu, A. N. Cartwright, and C. Basaran, “Moiré interferogram phase extraction: a ridge detection algorithm for continous wavelet transforms,” Appl. Opt. 43, 850–857 (2004).
    [CrossRef] [PubMed]
  35. L. Debnath, Wavelets and Signal Processing (Birkhauser, 2003).
    [CrossRef]
  36. M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
    [CrossRef]
  37. J. Kirby, “Which wavelet best reproduces the Fourier power spectrum?” Comput. Geosci. 31, 846–864 (2005).
    [CrossRef]
  38. A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
    [CrossRef]
  39. M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
    [CrossRef]
  40. A. Z. Abid, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Ridge extraction algorithms for one-dimensional continuous wavelet transform: a comparison,” J. Phys. Conf. Ser. 76, 012045(2007).
    [CrossRef]
  41. 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] [PubMed]
  42. Z. Wang and H. Ma, “Automatic analysis of photomechanics interferogram using wavelet transform,” in Proceedings of 2005 SEM Annual Conference and Exposition on Experimental and Applied Mechanics (Society of Experimental Mechanics, 2005).
  43. B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
    [CrossRef]
  44. K. Patorski, A. Styk, and Z. Sienicki, “Time-average interference microscopy for vibration testing of silicon microelements,” Proc. SPIE 6158, 615806 (2006).
    [CrossRef]
  45. K. Patorski, D. Post, R. Czarnek, and Y. Guo, “Real-time optical differentiation for moire interferometry,” Appl. Opt. 26, 1977–1982 (1987).
    [CrossRef] [PubMed]
  46. M. Nisida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376 (1964).
    [CrossRef]
  47. R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).
    [CrossRef]
  48. B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).
    [CrossRef]
  49. YAWTb: Yet Another Wavelet Toolbox, http://rhea.tele.ucl.ac.be/yawtb/ (accessed 4 March 2009).

2009 (3)

M. Ragulskis and Z. Navickas, “Interpretation of fringes produced by time-averaged projection moiré,” Strain 45, doi: 10.1111/j.1475–1305.2009.00625x (2009) and references therein.
[CrossRef]

M. Ragulskis, A. Aleksa, and R. Maskeliunas, “Contrast enhancement of time-averaged fringes based on moving average mapping functions,” Opt. Lasers Eng. 47, 768–773 (2009).
[CrossRef]

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

2008 (4)

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

B. Chen and C. Basaran, “Automatic full strain field moiré interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).
[CrossRef]

M. Li, C. Quan, and C. Tai, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929 (2008).
[CrossRef]

S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (6)

K. Patorski, A. Styk, and Z. Sienicki, “Time-average interference microscopy for vibration testing of silicon microelements,” Proc. SPIE 6158, 615806 (2006).
[CrossRef]

C.-M. Liu, L.-W. Chen, and C.-C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17, 4359–4366 (2006).
[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).
[CrossRef]

L. Saunoriene and M. Ragulskis, “Visualization of fringes in time averaged moiré patterns,” Inf. Technol. Control 35, 249–254 (2006).

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] [PubMed]

2005 (4)

C. Quan, Y. Fu, C. J. Tay, and J. M. Tan, “Profiling of objects with height steps by wavelet analysis of shadow moiré fringes,” Appl. Opt. 44, 3284–3290 (2005).
[CrossRef] [PubMed]

M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).
[CrossRef]

J. Kirby, “Which wavelet best reproduces the Fourier power spectrum?” Comput. Geosci. 31, 846–864 (2005).
[CrossRef]

2004 (2)

2003 (5)

K. Qian, H. Seah, and A. Asundi, “Instantaneous frequency and its application to strain extraction in moiré interferometry,” Appl. Opt. 42, 6504–6513 (2003).
[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).
[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
[CrossRef]

2002 (1)

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

2001 (2)

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
[CrossRef]

C. Forno and M. Whelan, “Digital moiré subtraction in optical engineering,” Opt. Eng. 40, 2199–2208 (2001).
[CrossRef]

1994 (1)

1992 (1)

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[CrossRef]

1989 (1)

1988 (1)

1987 (1)

1976 (1)

1973 (1)

B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).
[CrossRef]

1971 (2)

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).
[CrossRef]

J. D. Hovanesian and Y. Hung, “Moiré contour-sum, contour-difference and vibration analysis of arbitrary objects,” Appl. Opt. 10, 2734–2738 (1971).
[CrossRef] [PubMed]

1970 (1)

J. Wasowski, “Moiré topographic maps,” Opt. Commun. 2, 321–323 (1970).
[CrossRef]

1964 (1)

M. Nisida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376 (1964).
[CrossRef]

1932 (1)

Abdul-Rahman, H. S.

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

Abid, A.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Abid, A. Z.

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Ridge extraction algorithms for one-dimensional continuous wavelet transform: a comparison,” J. Phys. Conf. Ser. 76, 012045(2007).
[CrossRef]

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] [PubMed]

Afifi, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Aleksa, A.

M. Ragulskis, A. Aleksa, and R. Maskeliunas, “Contrast enhancement of time-averaged fringes based on moving average mapping functions,” Opt. Lasers Eng. 47, 768–773 (2009).
[CrossRef]

Ali, S. T.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge U. Press, 2008).

Antoine, J.-P.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge U. Press, 2008).

Asundi, A.

Basaran, C.

B. Chen and C. Basaran, “Automatic full strain field moiré interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).
[CrossRef]

H. Liu, A. N. Cartwright, and C. Basaran, “Moiré interferogram phase extraction: a ridge detection algorithm for continous wavelet transforms,” Appl. Opt. 43, 850–857 (2004).
[CrossRef] [PubMed]

Bosseboeuf, A.

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).
[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
[CrossRef]

Bryngdahl, O.

Burton, D. R.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Ridge extraction algorithms for one-dimensional continuous wavelet transform: a comparison,” J. Phys. Conf. Ser. 76, 012045(2007).
[CrossRef]

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] [PubMed]

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] [PubMed]

Cartwright, A. N.

Chang, R.-S.

R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
[CrossRef]

Chatelain, B.

B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).
[CrossRef]

Chen, B.

B. Chen and C. Basaran, “Automatic full strain field moiré interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).
[CrossRef]

Chen, L.-W.

C.-M. Liu, L.-W. Chen, and C.-C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17, 4359–4366 (2006).
[CrossRef]

Chen, W.

Chung, M.

Czarnek, R.

Danaie, K.

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
[CrossRef]

Dean, T.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Debnath, L.

L. Debnath, Wavelets and Signal Processing (Birkhauser, 2003).
[CrossRef]

Durelli, A. J.

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).
[CrossRef]

Eschbach, R.

Fassi-Fihri, A.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Forno, C.

C. Forno and M. Whelan, “Digital moiré subtraction in optical engineering,” Opt. Eng. 40, 2199–2208 (2001).
[CrossRef]

Fu, Y.

Gdeisat, M. A.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Ridge extraction algorithms for one-dimensional continuous wavelet transform: a comparison,” J. Phys. Conf. Ser. 76, 012045(2007).
[CrossRef]

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] [PubMed]

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] [PubMed]

Gorecki, C.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Guo, Y.

Hovanesian, J. D.

Huang, Y.

Hung, Y.

Jacobelli, A.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Jozwik, M.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Kacperski, J.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Kadooka, K.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

Kim, J.

Kirby, J.

J. Kirby, “Which wavelet best reproduces the Fourier power spectrum?” Comput. Geosci. 31, 846–864 (2005).
[CrossRef]

Kobayashi, A. S.

A. S. Kobayashi, Handbook on Experimental Mechanics, 2nd ed. (SEM, 1993).

Kunoo, K.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

Lalor, M. J.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Ridge extraction algorithms for one-dimensional continuous wavelet transform: a comparison,” J. Phys. Conf. Ser. 76, 012045(2007).
[CrossRef]

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] [PubMed]

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] [PubMed]

Li, M.

M. Li, C. Quan, and C. Tai, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929 (2008).
[CrossRef]

Li, S.

Lilley, F.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

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] [PubMed]

Lim, J.

Lin, C.-H.

R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
[CrossRef]

Liu, C.-M.

C.-M. Liu, L.-W. Chen, and C.-C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17, 4359–4366 (2006).
[CrossRef]

Liu, H.

Liu, H.-C.

R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
[CrossRef]

Ma, H.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Z. Wang and H. Ma, “Automatic analysis of photomechanics interferogram using wavelet transform,” in Proceedings of 2005 SEM Annual Conference and Exposition on Experimental and Applied Mechanics (Society of Experimental Mechanics, 2005).

Malat, S.

S. Malat, A Wavelet Tour of Signal Processing (Academic, 1999).

Marjane, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Maskeliunas, R.

M. Ragulskis, A. Aleksa, and R. Maskeliunas, “Contrast enhancement of time-averaged fringes based on moving average mapping functions,” Opt. Lasers Eng. 47, 768–773 (2009).
[CrossRef]

M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
[CrossRef]

Moore, C.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Murenzi, R.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge U. Press, 2008).

Nagayasu, T.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

Nassim, K.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Navickas, Z.

M. Ragulskis and Z. Navickas, “Interpretation of fringes produced by time-averaged projection moiré,” Strain 45, doi: 10.1111/j.1475–1305.2009.00625x (2009) and references therein.
[CrossRef]

Nisida, M.

M. Nisida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376 (1964).
[CrossRef]

Ono, K.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

Osterberg, H.

Patorski, K.

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624 (2007).
[CrossRef] [PubMed]

K. Patorski, A. Styk, and Z. Sienicki, “Time-average interference microscopy for vibration testing of silicon microelements,” Proc. SPIE 6158, 615806 (2006).
[CrossRef]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).
[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).
[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

K. Patorski, D. Post, R. Czarnek, and Y. Guo, “Real-time optical differentiation for moire interferometry,” Appl. Opt. 26, 1977–1982 (1987).
[CrossRef] [PubMed]

K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993).

Petitgrand, S.

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).
[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
[CrossRef]

Post, D.

Qian, K.

Quan, C.

Qudeisat, M.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Rachafi, S.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Ragulskis, L.

M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
[CrossRef]

Ragulskis, M.

M. Ragulskis and Z. Navickas, “Interpretation of fringes produced by time-averaged projection moiré,” Strain 45, doi: 10.1111/j.1475–1305.2009.00625x (2009) and references therein.
[CrossRef]

M. Ragulskis, A. Aleksa, and R. Maskeliunas, “Contrast enhancement of time-averaged fringes based on moving average mapping functions,” Opt. Lasers Eng. 47, 768–773 (2009).
[CrossRef]

L. Saunoriene and M. Ragulskis, “Visualization of fringes in time averaged moiré patterns,” Inf. Technol. Control 35, 249–254 (2006).

M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
[CrossRef]

Rosvold, G.

Saito, H.

M. Nisida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376 (1964).
[CrossRef]

Salbut, L.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Sanford, R. J.

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).
[CrossRef]

Saunoriene, L.

L. Saunoriene and M. Ragulskis, “Visualization of fringes in time averaged moiré patterns,” Inf. Technol. Control 35, 249–254 (2006).

Seah, H.

Sheu, J.-Y.

R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
[CrossRef]

Sidki, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Sienicki, Z.

K. Patorski, A. Styk, and Z. Sienicki, “Time-average interference microscopy for vibration testing of silicon microelements,” Proc. SPIE 6158, 615806 (2006).
[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).
[CrossRef]

Styk, A.

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624 (2007).
[CrossRef] [PubMed]

K. Patorski, A. Styk, and Z. Sienicki, “Time-average interference microscopy for vibration testing of silicon microelements,” Proc. SPIE 6158, 615806 (2006).
[CrossRef]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).
[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).
[CrossRef]

Su, X.

Szu, H. H.

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[CrossRef]

Tai, C.

M. Li, C. Quan, and C. Tai, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929 (2008).
[CrossRef]

Tan, J. M.

Tay, C. J.

Telfer, B.

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[CrossRef]

Turla, V.

M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
[CrossRef]

Uda, N.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

Vandergheynst, P.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge U. Press, 2008).

Wang, C.-C.

C.-M. Liu, L.-W. Chen, and C.-C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17, 4359–4366 (2006).
[CrossRef]

Wang, Z.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Z. Wang and H. Ma, “Automatic analysis of photomechanics interferogram using wavelet transform,” in Proceedings of 2005 SEM Annual Conference and Exposition on Experimental and Applied Mechanics (Society of Experimental Mechanics, 2005).

Wasowski, J.

J. Wasowski, “Moiré topographic maps,” Opt. Commun. 2, 321–323 (1970).
[CrossRef]

Whelan, M.

C. Forno and M. Whelan, “Digital moiré subtraction in optical engineering,” Opt. Eng. 40, 2199–2208 (2001).
[CrossRef]

Yahiaoui, R.

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
[CrossRef]

Appl. Opt. (12)

J. D. Hovanesian and Y. Hung, “Moiré contour-sum, contour-difference and vibration analysis of arbitrary objects,” Appl. Opt. 10, 2734–2738 (1971).
[CrossRef] [PubMed]

K. Qian, H. Seah, and A. Asundi, “Instantaneous frequency and its application to strain extraction in moiré interferometry,” Appl. Opt. 42, 6504–6513 (2003).
[CrossRef]

H. Liu, A. N. Cartwright, and C. Basaran, “Moiré interferogram phase extraction: a ridge detection algorithm for continous wavelet transforms,” Appl. Opt. 43, 850–857 (2004).
[CrossRef] [PubMed]

C. J. Tay, C. Quan, Y. Fu, and Y. Huang, “Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis,” Appl. Opt. 43, 4164–4171 (2004).
[CrossRef] [PubMed]

C. Quan, Y. Fu, C. J. Tay, and J. M. Tan, “Profiling of objects with height steps by wavelet analysis of shadow moiré fringes,” Appl. Opt. 44, 3284–3290 (2005).
[CrossRef] [PubMed]

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] [PubMed]

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624 (2007).
[CrossRef] [PubMed]

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] [PubMed]

S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
[CrossRef] [PubMed]

K. Patorski, D. Post, R. Czarnek, and Y. Guo, “Real-time optical differentiation for moire interferometry,” Appl. Opt. 26, 1977–1982 (1987).
[CrossRef] [PubMed]

J. Lim, J. Kim, and M. Chung, “Additive type moiré with computer image processing,” Appl. Opt. 28, 2677–2680 (1989).
[CrossRef] [PubMed]

G. Rosvold, “Video-based vibration analysis using projected fringes,” Appl. Opt. 33, 775–786 (1994).
[CrossRef] [PubMed]

Comput. Geosci. (1)

J. Kirby, “Which wavelet best reproduces the Fourier power spectrum?” Comput. Geosci. 31, 846–864 (2005).
[CrossRef]

Exp. Mech. (4)

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003).
[CrossRef]

M. Nisida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376 (1964).
[CrossRef]

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).
[CrossRef]

B. Chen and C. Basaran, “Automatic full strain field moiré interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).
[CrossRef]

Inf. Technol. Control (1)

L. Saunoriene and M. Ragulskis, “Visualization of fringes in time averaged moiré patterns,” Inf. Technol. Control 35, 249–254 (2006).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Phys. Conf. Ser. (1)

A. Z. Abid, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Ridge extraction algorithms for one-dimensional continuous wavelet transform: a comparison,” J. Phys. Conf. Ser. 76, 012045(2007).
[CrossRef]

Nanotechnology (1)

C.-M. Liu, L.-W. Chen, and C.-C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17, 4359–4366 (2006).
[CrossRef]

Opt. Commun. (2)

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

J. Wasowski, “Moiré topographic maps,” Opt. Commun. 2, 321–323 (1970).
[CrossRef]

Opt. Eng. (5)

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).
[CrossRef]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).
[CrossRef]

C. Forno and M. Whelan, “Digital moiré subtraction in optical engineering,” Opt. Eng. 40, 2199–2208 (2001).
[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[CrossRef]

Opt. Laser Technol. (3)

B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).
[CrossRef]

M. Li, C. Quan, and C. Tai, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929 (2008).
[CrossRef]

R.-S. Chang, J.-Y. Sheu, C.-H. Lin, and H.-C. Liu, “Analysis of CCD moire pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35, 43–47 (2003).
[CrossRef]

Opt. Lasers Eng. (3)

M. Ragulskis, A. Aleksa, and R. Maskeliunas, “Contrast enhancement of time-averaged fringes based on moving average mapping functions,” Opt. Lasers Eng. 47, 768–773 (2009).
[CrossRef]

M. Ragulskis, R. Maskeliunas, L. Ragulskis, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962 (2005).
[CrossRef]

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Proc. SPIE (5)

K. Patorski, A. Styk, and Z. Sienicki, “Time-average interference microscopy for vibration testing of silicon microelements,” Proc. SPIE 6158, 615806 (2006).
[CrossRef]

A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, H. S. Abdul-Rahman, and F. Lilley, “Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform,” Proc. SPIE 7000, 70000Q (2008).
[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).
[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).
[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).
[CrossRef]

Strain (1)

M. Ragulskis and Z. Navickas, “Interpretation of fringes produced by time-averaged projection moiré,” Strain 45, doi: 10.1111/j.1475–1305.2009.00625x (2009) and references therein.
[CrossRef]

Other (7)

A. S. Kobayashi, Handbook on Experimental Mechanics, 2nd ed. (SEM, 1993).

K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993).

S. Malat, A Wavelet Tour of Signal Processing (Academic, 1999).

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives (Cambridge U. Press, 2008).

Z. Wang and H. Ma, “Automatic analysis of photomechanics interferogram using wavelet transform,” in Proceedings of 2005 SEM Annual Conference and Exposition on Experimental and Applied Mechanics (Society of Experimental Mechanics, 2005).

L. Debnath, Wavelets and Signal Processing (Birkhauser, 2003).
[CrossRef]

YAWTb: Yet Another Wavelet Toolbox, http://rhea.tele.ucl.ac.be/yawtb/ (accessed 4 March 2009).

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Figures (16)

Fig. 1
Fig. 1

Noise resistance algorithm comparison.

Fig. 2
Fig. 2

Carrier frequency influence comparison.

Fig. 3
Fig. 3

Carrier inclination angle influence comparison.

Fig. 4
Fig. 4

Modulation function frequency influence comparison.

Fig. 5
Fig. 5

Carrier fringe frequency gradient influence comparison.

Fig. 6
Fig. 6

One-dimensional modified Morlet m optimization: (a) 1D signal, (b) extracted modulation of the signal for m = 1 , and (c) extracted modulation of the signal for m = 2 .

Fig. 7
Fig. 7

Interferograms of (a) modulation extraction using different 1D wavelets: (b) Morlet m = 2 , (c) Paul n = 4 , (d) Mexican Hat, (e) Morlet m = 0.5 , and (f) Paul n = 20 .

Fig. 8
Fig. 8

One-dimensional wavelet noise resistance comparison.

Fig. 9
Fig. 9

Interferograms of (a) a nonvibrating and (b) a vibrating circular silicon micromembrane, and modulation extraction for case (b) using different 2D wavelets: (c) Fan wavelet, (d) Morlet wavelet.

Fig. 10
Fig. 10

One-dimensional CWT normalization: (a) 1D signal, (b) extracted modulation for η = 0.98 , and (c) extracted modulation for η = 0.88 .

Fig. 11
Fig. 11

Vibrating membrane modulation maps, f rez = 178 kHz , obtained using different ridge extraction algorithms: (a) 1D direct maximum, (b) 2D direct maximum, and (c) 2D two-frame algorithms.

Fig. 12
Fig. 12

Membrane modulation maps obtained with different values of parameter m, f rez = 833 kHz : (a) m = 0.5 , (b) m = 1 , and (c) m = 2 .

Fig. 13
Fig. 13

Time-average interferogram modulation maps for different resonant modes obtained using the (a), (b), (c) CWT and (d), (e), (f) TPS methods.

Fig. 14
Fig. 14

Modulation profiles for a membrane shown in Figs. 13a, 13d obtained using the (a) CWT and (b) TPS methods (cross section taken along the central membrane diameter).

Fig. 15
Fig. 15

Real-time patterns of (a) Δ U / Δ x and (b) Δ U / Δ y for a loaded cantilever beam. x and y are horizontal and vertical coordinates, respectively; U is the x component of specimen displacements. Lateral shear values: (a) Δ x = 1.2 mm and (b) Δ y = 0.9 mm . Note the double image of a cross marked on the specimen, which defines the shear magnitude and direction [45].

Fig. 16
Fig. 16

Two-dimensional CWT processing results of additive moiré patterns shown in Fig. 15.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

I ( x ) = I 1 ( x ) + I 2 ( x ) = 1 + cos { π [ ( 1 / d 1 ) ( 1 / d 2 ) ] x } cos { π [ ( 1 / d 1 ) + ( 1 / d 2 ) ] x } = 1 + cos { π [ ( ν 1 ν 2 ) ] x } cos { π [ ( ν 1 + ν 2 ) ] x } ,
I vib ( x , y ) = K ( x , y ) { 1 + C stat ( x , y ) J 0 [ 4 π λ a 0 ( x , y ) ] cos φ vib ( x , y ) } ,
S 1 D ( b , s ) = s η R ψ * ( s 1 ( x b ) ) f ( x ) d x ,
2 π R | ψ ^ ( k ) | 2 | k | d k < ,
ψ Morlet ( x ) = e i k 0 x e m x 2 ,
ψ Paul ( x ) = 2 n n ! ( 1 i x ) ( n + 1 ) 2 π ( 2 n ) ! / 2 ,
ψ DoG ( x ) = d n d | x | n ( e | x | 2 / 2 ) .
S 2 D ( s , b , θ ) = s η R 2 ψ * ( s 1 r θ ( x b ) ) f ( x ) d 2 x ,
r θ = ( cos θ sin θ sin θ cos θ ) .
c ψ = ( 2 π ) 2 R 2 | ψ ^ ( k ) | 2 | k | 2 d 2 k < .
ψ Morelt ( x ) = e i k 0 x e m | x | 2 ,
ψ Fan ( x ) = j = 0 N θ 1 e i k j x e m | x | 2 ,
M = | S | = ( Re 2 [ S ] + Im 2 [ S ] ) .
RMS = x = 5 K 5 y = 5 L 5 [ M ( x , y ) O ( x , y ) ] 2 ( K 10 ) ( L 10 ) ,
ϕ ( x , y ) = 3 ( 1 x ) 2 e x 2 ( y + 1 ) 2 10 ( x 5 x 3 y 5 ) e x 2 y 2 1 3 e ( x + 1 ) 2 y 2 .
p ( x , y ) = 0.5 sin ( 2 π 15 x 1 + x / 500 ) + 0.5 .
p ( x , y ) = cos [ 0.5 x + 0.5 ϕ ( x , y ) ]
M ( x , y ) = e { [ ( x 256 ) 2 + ( y 256 ) 2 ] / 30 , 000 } .
I ( x , y ) = p ( x , y ) M ( x , y ) + 1 + GN .

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