Abstract

A temporal wavelet analysis algorithm is proposed for shadow-moiré-based three-dimensional surface profiling on objects having discontinuous height steps. A grating is positioned close to an object, and its shadow is observed through the grating. The moiré fringe patterns vary when the grating is in-plane rotating. A series of fringe patterns are captured by a CCD camera at different rotating angles. Phase values are evaluated point by point with the continuous wavelet transform. From the phase values of each point on the object, the distance between the object and the grating can be retrieved. The surface profile is obtained without temporal or spatial phase unwrapping. This technique is applicable to objects with discontinuous height steps, which are impossible to measure with conventional shadow moiré topography. Two specimens are tested to demonstrate the validity of the method: One is an object with a height step of 1.6 mm, and another is a small coin with unevenness of less than 0.2 mm. The experimental results are compared with test results by use of the mechanical stylus method.

© 2005 Optical Society of America

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  1. D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9, 942–947 (1970).
    [CrossRef] [PubMed]
  2. H. Takasaki, “Moiré topography,” Appl. Opt. 9, 1467–1472 (1970).
    [CrossRef] [PubMed]
  3. G. Mauvoisin, F. Bremand, A. Lagarde, “Three-dimensional shape reconstruction by phase-shifting shadow moiré,” Appl. Opt. 33, 2163–2169 (1994).
    [CrossRef] [PubMed]
  4. X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
    [CrossRef]
  5. T. Yoshizawa, T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
    [CrossRef]
  6. L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
    [CrossRef]
  7. J. Degrieck, W. Van Paepegem, P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surface,” Opt. Lasers Eng. 36, 29–40 (2001).
    [CrossRef]
  8. R. Henan, A. Tagliaferri, R. Torroba, “A contouring approach using single grating digital shadow moiré with a phase stepping technique,” Optik (Stuttgart) 110, 199–201 (1999).
  9. J. M. Huntley, “Challenges in phase unwrapping,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi, D. Inaudi, eds. (Elsevier Science, Amsterdam, 2000), pp. 37–44.
  10. L. H. Jin, Y. Otani, T. Yoshizawa, “Shadow moiré profilometry by frequency sweeping,” Opt. Eng. 40, 1383–1386 (2001).
    [CrossRef]
  11. Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
    [CrossRef]
  12. Y. Y. Hung, H. M. Shang, “A novel shadow moiré technique for absolute surface shape measurement,” in Proceedings of the SEM Ninth International Conference on Experimental Mechanics (Society for Experimental Mechanics, Orlando, Fla., 2000), pp. 96–99.
  13. H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
    [CrossRef]
  14. M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef] [PubMed]
  15. C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230, 23–33 (2004).
    [CrossRef]
  16. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  17. I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992).
    [CrossRef]
  18. A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
    [CrossRef]
  19. Y. Morimoto, M. Fujigaki, S. Yoneyama, “Shape, stress, and strain measurement using phase analysis of grating or fringe patterns,” in Third International Conference on Experimental Mechanics, X. Wu, Y. Qin, J. Fang, J. Ke, eds., Proc. SPIE4537, 47–52 (2002).
    [CrossRef]
  20. K. Qian, H. S. Seah, A. Asundi, “Instantaneous frequency and its application to strain extraction in moiré interferometry,” Appl. Opt. 42, 6504–6513 (2003).
    [CrossRef]
  21. L. R. Watkins, S. M. Tan, T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
    [CrossRef]
  22. X. Colonna de Lega, “Continuous deformation measurement using dynamic phase-shifting and wavelet transform,” in Applied Optics and Optoelectronics 1996, K. T. V. Grattan, ed. (Institute of Physics, Bristol, UK, 1996), pp. 261–267.
  23. M. Cherbuliez, P. Jacquot, X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 692–702 (1999).
    [CrossRef]
  24. X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Theses no. 1666 (Swiss Federal Institute of Technology, Lausanne, Switzerland, 1997).
  25. S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1998).
  26. C. J. Tay, C. Quan, Y. Fu, 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]
  27. Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
    [CrossRef]
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fotran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Chap. 13.
  29. M. Cherbuliez, P. Jacquot, “Phase computation through wavelet analysis: yesterday and nowadays,” in Fringe 2001, W. Osten, W. Juptner, eds. (Elsevier, Paris, 2001), pp. 154–162.

2004 (3)

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230, 23–33 (2004).
[CrossRef]

C. J. Tay, C. Quan, Y. Fu, 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]

Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
[CrossRef]

2003 (1)

2002 (1)

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

2001 (2)

L. H. Jin, Y. Otani, T. Yoshizawa, “Shadow moiré profilometry by frequency sweeping,” Opt. Eng. 40, 1383–1386 (2001).
[CrossRef]

J. Degrieck, W. Van Paepegem, P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surface,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

2000 (1)

L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

1999 (2)

R. Henan, A. Tagliaferri, R. Torroba, “A contouring approach using single grating digital shadow moiré with a phase stepping technique,” Optik (Stuttgart) 110, 199–201 (1999).

L. R. Watkins, S. M. Tan, T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[CrossRef]

1997 (2)

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
[CrossRef]

1994 (2)

1993 (1)

T. Yoshizawa, T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

1982 (1)

1977 (1)

Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
[CrossRef]

1970 (2)

Allen, J. B.

Asundi, A.

Barnes, T. H.

Boone, P.

J. Degrieck, W. Van Paepegem, P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surface,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Bremand, F.

Burton, D. R.

X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
[CrossRef]

Chen, L. J.

Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
[CrossRef]

Cherbuliez, M.

M. Cherbuliez, P. Jacquot, “Phase computation through wavelet analysis: yesterday and nowadays,” in Fringe 2001, W. Osten, W. Juptner, eds. (Elsevier, Paris, 2001), pp. 154–162.

M. Cherbuliez, P. Jacquot, X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 692–702 (1999).
[CrossRef]

Colonna de Lega, X.

X. Colonna de Lega, “Continuous deformation measurement using dynamic phase-shifting and wavelet transform,” in Applied Optics and Optoelectronics 1996, K. T. V. Grattan, ed. (Institute of Physics, Bristol, UK, 1996), pp. 261–267.

M. Cherbuliez, P. Jacquot, X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 692–702 (1999).
[CrossRef]

X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Theses no. 1666 (Swiss Federal Institute of Technology, Lausanne, Switzerland, 1997).

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992).
[CrossRef]

Degrieck, J.

J. Degrieck, W. Van Paepegem, P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surface,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Durelli, A. J.

Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
[CrossRef]

Federico, A.

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fotran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Chap. 13.

Franze, B.

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Fu, Y.

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230, 23–33 (2004).
[CrossRef]

C. J. Tay, C. Quan, Y. Fu, 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]

Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
[CrossRef]

Fujigaki, M.

Y. Morimoto, M. Fujigaki, S. Yoneyama, “Shape, stress, and strain measurement using phase analysis of grating or fringe patterns,” in Third International Conference on Experimental Mechanics, X. Wu, Y. Qin, J. Fang, J. Ke, eds., Proc. SPIE4537, 47–52 (2002).
[CrossRef]

Haible, P.

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Henan, R.

R. Henan, A. Tagliaferri, R. Torroba, “A contouring approach using single grating digital shadow moiré with a phase stepping technique,” Optik (Stuttgart) 110, 199–201 (1999).

Hovanesian, J. D.

Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
[CrossRef]

Huang, Y.

Hung, Y. Y.

Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
[CrossRef]

Y. Y. Hung, H. M. Shang, “A novel shadow moiré technique for absolute surface shape measurement,” in Proceedings of the SEM Ninth International Conference on Experimental Mechanics (Society for Experimental Mechanics, Orlando, Fla., 2000), pp. 96–99.

Huntley, J. M.

J. M. Huntley, “Challenges in phase unwrapping,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi, D. Inaudi, eds. (Elsevier Science, Amsterdam, 2000), pp. 37–44.

Ina, H.

Jacquot, P.

M. Cherbuliez, P. Jacquot, X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 692–702 (1999).
[CrossRef]

M. Cherbuliez, P. Jacquot, “Phase computation through wavelet analysis: yesterday and nowadays,” in Fringe 2001, W. Osten, W. Juptner, eds. (Elsevier, Paris, 2001), pp. 154–162.

Jin, L.

L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Jin, L. H.

L. H. Jin, Y. Otani, T. Yoshizawa, “Shadow moiré profilometry by frequency sweeping,” Opt. Eng. 40, 1383–1386 (2001).
[CrossRef]

Johnson, W. O.

Kaufmann, G. H.

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

Kobayashi, S.

Kodera, Y.

L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Lagarde, A.

Lalor, M. J.

X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
[CrossRef]

Liang, C. Y.

Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
[CrossRef]

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1998).

Mauvoisin, G.

Meadows, D. M.

Morimoto, Y.

Y. Morimoto, M. Fujigaki, S. Yoneyama, “Shape, stress, and strain measurement using phase analysis of grating or fringe patterns,” in Third International Conference on Experimental Mechanics, X. Wu, Y. Qin, J. Fang, J. Ke, eds., Proc. SPIE4537, 47–52 (2002).
[CrossRef]

Otani, Y.

L. H. Jin, Y. Otani, T. Yoshizawa, “Shadow moiré profilometry by frequency sweeping,” Opt. Eng. 40, 1383–1386 (2001).
[CrossRef]

L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fotran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Chap. 13.

Qian, K.

Quan, C.

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230, 23–33 (2004).
[CrossRef]

C. J. Tay, C. Quan, Y. Fu, 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]

Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
[CrossRef]

Seah, H. S.

Shang, H. M.

Y. Y. Hung, H. M. Shang, “A novel shadow moiré technique for absolute surface shape measurement,” in Proceedings of the SEM Ninth International Conference on Experimental Mechanics (Society for Experimental Mechanics, Orlando, Fla., 2000), pp. 96–99.

Shaw, M. M.

X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
[CrossRef]

Tagliaferri, A.

R. Henan, A. Tagliaferri, R. Torroba, “A contouring approach using single grating digital shadow moiré with a phase stepping technique,” Optik (Stuttgart) 110, 199–201 (1999).

Takasaki, H.

Takeda, M.

Tan, S. M.

Tay, C. J.

Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
[CrossRef]

C. J. Tay, C. Quan, Y. Fu, 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, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230, 23–33 (2004).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fotran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Chap. 13.

Tiziani, H.

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Tomisawa, T.

T. Yoshizawa, T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

Torroba, R.

R. Henan, A. Tagliaferri, R. Torroba, “A contouring approach using single grating digital shadow moiré with a phase stepping technique,” Optik (Stuttgart) 110, 199–201 (1999).

Van Paepegem, W.

J. Degrieck, W. Van Paepegem, P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surface,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fotran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Chap. 13.

Watkins, L. R.

Xie, X.

X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
[CrossRef]

Yamamoto, H.

Yoneyama, S.

Y. Morimoto, M. Fujigaki, S. Yoneyama, “Shape, stress, and strain measurement using phase analysis of grating or fringe patterns,” in Third International Conference on Experimental Mechanics, X. Wu, Y. Qin, J. Fang, J. Ke, eds., Proc. SPIE4537, 47–52 (2002).
[CrossRef]

Yoshizawa, T.

L. H. Jin, Y. Otani, T. Yoshizawa, “Shadow moiré profilometry by frequency sweeping,” Opt. Eng. 40, 1383–1386 (2001).
[CrossRef]

L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

T. Yoshizawa, T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

Appl. Opt. (6)

J. Mod. Opt. (1)

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Mech. Res. Comm. (1)

Y. Y. Hung, C. Y. Liang, A. J. Durelli, J. D. Hovanesian, “A shadow-moiré method with continuously variable sensitivity,” Mech. Res. Comm. 4, 157–162 (1977).
[CrossRef]

Opt. Commun. (1)

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230, 23–33 (2004).
[CrossRef]

Opt. Eng. (6)

L. H. Jin, Y. Otani, T. Yoshizawa, “Shadow moiré profilometry by frequency sweeping,” Opt. Eng. 40, 1383–1386 (2001).
[CrossRef]

X. Xie, M. J. Lalor, D. R. Burton, M. M. Shaw, “Four-map absolute distance contouring,” Opt. Eng. 36, 2517–1520 (1997).
[CrossRef]

T. Yoshizawa, T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

L. Jin, Y. Kodera, T. Yoshizawa, Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Y. Fu, C. J. Tay, C. Quan, L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780–2787 (2004).
[CrossRef]

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

J. Degrieck, W. Van Paepegem, P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surface,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

R. Henan, A. Tagliaferri, R. Torroba, “A contouring approach using single grating digital shadow moiré with a phase stepping technique,” Optik (Stuttgart) 110, 199–201 (1999).

Other (10)

J. M. Huntley, “Challenges in phase unwrapping,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi, D. Inaudi, eds. (Elsevier Science, Amsterdam, 2000), pp. 37–44.

Y. Y. Hung, H. M. Shang, “A novel shadow moiré technique for absolute surface shape measurement,” in Proceedings of the SEM Ninth International Conference on Experimental Mechanics (Society for Experimental Mechanics, Orlando, Fla., 2000), pp. 96–99.

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992).
[CrossRef]

X. Colonna de Lega, “Continuous deformation measurement using dynamic phase-shifting and wavelet transform,” in Applied Optics and Optoelectronics 1996, K. T. V. Grattan, ed. (Institute of Physics, Bristol, UK, 1996), pp. 261–267.

M. Cherbuliez, P. Jacquot, X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 692–702 (1999).
[CrossRef]

X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Theses no. 1666 (Swiss Federal Institute of Technology, Lausanne, Switzerland, 1997).

S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1998).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fotran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Chap. 13.

M. Cherbuliez, P. Jacquot, “Phase computation through wavelet analysis: yesterday and nowadays,” in Fringe 2001, W. Osten, W. Juptner, eds. (Elsevier, Paris, 2001), pp. 154–162.

Y. Morimoto, M. Fujigaki, S. Yoneyama, “Shape, stress, and strain measurement using phase analysis of grating or fringe patterns,” in Third International Conference on Experimental Mechanics, X. Wu, Y. Qin, J. Fang, J. Ke, eds., Proc. SPIE4537, 47–52 (2002).
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Figures (9)

Fig. 1
Fig. 1

Schematic layout of the shadow moiré system.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

(a) Dimension of the height step. (b) Area of interest on a specimen with a height step.

Fig. 4
Fig. 4

(a) Gray-value variation of point A; (b) gray-value variation of point B.

Fig. 5
Fig. 5

(a) Modulus of the Morlet wavelet transform at point A; (b) modulus of the Morlet wavelet transform at point B.

Fig. 6
Fig. 6

(a) Gray-scale map of the area of interest; (b) 3-D plot of the area of interest.

Fig. 7
Fig. 7

(a) Area of interest on a coin; typical moiré fringe patterns at (b) α = 30° and (c) α = 40°.

Fig. 8
Fig. 8

(a) Gray-scale map of the area of interest on a coin; (b) 3-D plot of the area of interest.

Fig. 9
Fig. 9

Comparison of the surface profile of a coin at cross section C–C between the shadow moiré and the mechanical stylus methods.

Equations (14)

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I ( x , y ) = A ( x , y ) + B ( x , y ) cos ϕ x y = A ( x , y ) + B ( x , y ) cos { 2 π h ( x , y ) d p [ l + h ( x , y ) ] } ,
I ( x , y ) = A ( x , y ) + B ( x , y ) cos [ 2 π cos α p 0 H ( x , y ) ] ,
ψ a , b ( t ) = 1 a ψ ( t b a ) , b R , a > 0 ,
W S ( a , b ) = + s ( t ) Ψ a , b * ( t ) d t ,
s ( t ) = 1 C Ψ + + W S ( a , b ) Ψ ( t b a ) d a a 2 d b ,
C Ψ = 2 π + | Ψ ̂ ( ω ) | 2 ω d w < + ,
Ψ ( t ) = g ( t ) exp ( i ω 0 t ) ,
W x y ( a , b ) = a 2 A x y ( b ) ( ĝ { a [ ζ ϕ x y ( b ) ] } + ( b , ζ ) ) × { exp [ i ϕ x y ( b ) ] } ,
ω 0 2 | A x y ( b ) | | ϕ x y ( b ) | 2 | A x y ( b ) | 1 ,
ω 0 2 | ϕ x y ( b ) | | ϕ x y ( b ) | 2 1 .
ϕ x y ( b ) = ζ r b = ω 0 a r b ,
W x y ( a r b , b ) a r b 2 A x y ( b ) ĝ ( 0 ) exp [ i ϕ x y ( b ) ] .
H ( x , y ) = p 0 Δ ϕ 2 π ( cos α 1 cos α 2 ) .
h ( x , y ) = H ( x , y ) l d H ( x , y ) .

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