Abstract

We present what we believe to be a novel complex phase tracing method for fringe pattern analysis related to the phase-locked loop idea. The image with deformed complex fringes is analyzed with lexicographic scansion that leads directly to the investigated phase without unwrapping. Robustness of the procedure is ensured by the delay mechanism in the process of calculating the reference value. A numerical model and examples of application of the presented method are given.

© 1999 Optical Society of America

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  1. M. Takeda, “Spatial-carrier fringe-pattern analysis and its application to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79–99 (1990).
    [CrossRef]
  2. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, Amsterdam, 1993), Chap. 13.
  3. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-differences measurements,” J. Opt. Soc. Am. 67, 370–378 (1977).
    [CrossRef]
  4. D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
    [CrossRef]
  5. J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. 12, 2393–2400 (1995).
    [CrossRef]
  6. M. Servin, J. L. Marroquin, D. Malacara-Hernandez, “Some applications of quadratic cost functionals in fringe analysis,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2860, 24–33 (1996).
  7. M. Rivera, M. Servin, J. L. Marroquin, “Fourier transform technique for phase unwrapping with minimized boundary effects,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds. Proc. SPIE2860, 54–60 (1996).
  8. R. Rodriguez-Vera, M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26, 393–397 (1994).
    [CrossRef]
  9. M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
    [CrossRef]
  10. J. Kozłowski, G. Serra, “A new modified PLL method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
    [CrossRef]
  11. J. L. Marguin, M. Servin, R. Rodriguez-Vera, “Adaptative quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. 14, 1742–1753 (1977).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. Y. Ichioka, M. Inuiya, “Direct phase detecting system,” Appl. Opt. 11, 1507–1514 (1972).
    [CrossRef] [PubMed]
  15. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 56–160 (1982).
    [CrossRef]
  16. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [CrossRef] [PubMed]
  17. W. W. Macy, “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983).
    [CrossRef] [PubMed]
  18. M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
    [CrossRef]
  19. T. Kreis, Holographic Interferometry (Akademie, Berlin, 1996).
  20. J. Kozłowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. (1999), in press.
  21. A. Papoulis, Circuits and Systems: A Modern Approach (Holt, Rinehart & Wilson, New York, 1980).

1997 (1)

J. Kozłowski, G. Serra, “A new modified PLL method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

1995 (2)

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. 12, 2393–2400 (1995).
[CrossRef]

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

1994 (2)

D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

R. Rodriguez-Vera, M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26, 393–397 (1994).
[CrossRef]

1991 (1)

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

1990 (1)

M. Takeda, “Spatial-carrier fringe-pattern analysis and its application to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79–99 (1990).
[CrossRef]

1987 (1)

1983 (1)

1982 (1)

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 56–160 (1982).
[CrossRef]

1977 (2)

J. L. Marguin, M. Servin, R. Rodriguez-Vera, “Adaptative quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. 14, 1742–1753 (1977).
[CrossRef]

D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-differences measurements,” J. Opt. Soc. Am. 67, 370–378 (1977).
[CrossRef]

1974 (1)

1972 (1)

Brangaccio, D. J.

Bruning, J. H.

Fried, D. L.

Gallagher, J. E.

Ghiglia, D. C.

D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

Herriot, D. R.

Ichioka, Y.

Ina, H.

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 56–160 (1982).
[CrossRef]

Inuiya, M.

Kobayashi, S.

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 56–160 (1982).
[CrossRef]

Kozlowski, J.

J. Kozłowski, G. Serra, “A new modified PLL method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

J. Kozłowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. (1999), in press.

Kreis, T.

T. Kreis, Holographic Interferometry (Akademie, Berlin, 1996).

Kujawinska, M.

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Macy, W. W.

Malacara, D.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

Malacara-Hernandez, D.

M. Servin, J. L. Marroquin, D. Malacara-Hernandez, “Some applications of quadratic cost functionals in fringe analysis,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2860, 24–33 (1996).

Marguin, J. L.

J. L. Marguin, M. Servin, R. Rodriguez-Vera, “Adaptative quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. 14, 1742–1753 (1977).
[CrossRef]

Marroquin, J. L.

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. 12, 2393–2400 (1995).
[CrossRef]

M. Rivera, M. Servin, J. L. Marroquin, “Fourier transform technique for phase unwrapping with minimized boundary effects,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds. Proc. SPIE2860, 54–60 (1996).

M. Servin, J. L. Marroquin, D. Malacara-Hernandez, “Some applications of quadratic cost functionals in fringe analysis,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2860, 24–33 (1996).

Papoulis, A.

A. Papoulis, Circuits and Systems: A Modern Approach (Holt, Rinehart & Wilson, New York, 1980).

Patorski, K.

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, Amsterdam, 1993), Chap. 13.

Reid, G. T.

G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–68 (1986/1987).
[CrossRef]

Rivera, M.

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. 12, 2393–2400 (1995).
[CrossRef]

M. Rivera, M. Servin, J. L. Marroquin, “Fourier transform technique for phase unwrapping with minimized boundary effects,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds. Proc. SPIE2860, 54–60 (1996).

Roddier, C.

Roddier, F.

Rodriguez-Vera, R.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

R. Rodriguez-Vera, M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26, 393–397 (1994).
[CrossRef]

J. L. Marguin, M. Servin, R. Rodriguez-Vera, “Adaptative quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. 14, 1742–1753 (1977).
[CrossRef]

Romero, L. A.

D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

Rosenfield, D. P.

Serra, G.

J. Kozłowski, G. Serra, “A new modified PLL method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

J. Kozłowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. (1999), in press.

Servin, M.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

R. Rodriguez-Vera, M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26, 393–397 (1994).
[CrossRef]

J. L. Marguin, M. Servin, R. Rodriguez-Vera, “Adaptative quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. 14, 1742–1753 (1977).
[CrossRef]

M. Rivera, M. Servin, J. L. Marroquin, “Fourier transform technique for phase unwrapping with minimized boundary effects,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds. Proc. SPIE2860, 54–60 (1996).

M. Servin, J. L. Marroquin, D. Malacara-Hernandez, “Some applications of quadratic cost functionals in fringe analysis,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2860, 24–33 (1996).

Takeda, M.

M. Takeda, “Spatial-carrier fringe-pattern analysis and its application to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79–99 (1990).
[CrossRef]

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 56–160 (1982).
[CrossRef]

White, A. D.

Wójciak, J.

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Appl. Opt. (4)

Ind. Metrol. (1)

M. Takeda, “Spatial-carrier fringe-pattern analysis and its application to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79–99 (1990).
[CrossRef]

J. Opt. Soc. Am. (5)

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 56–160 (1982).
[CrossRef]

D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-differences measurements,” J. Opt. Soc. Am. 67, 370–378 (1977).
[CrossRef]

D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. 12, 2393–2400 (1995).
[CrossRef]

J. L. Marguin, M. Servin, R. Rodriguez-Vera, “Adaptative quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. 14, 1742–1753 (1977).
[CrossRef]

Opt. Eng. (1)

J. Kozłowski, G. Serra, “A new modified PLL method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

Opt. Laser Technol. (1)

R. Rodriguez-Vera, M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26, 393–397 (1994).
[CrossRef]

Opt. Lasers Eng. (3)

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–68 (1986/1987).
[CrossRef]

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Other (6)

T. Kreis, Holographic Interferometry (Akademie, Berlin, 1996).

J. Kozłowski, G. Serra, “Analysis of the complex phase error introduced by the application of the Fourier transform method,” J. Mod. Opt. (1999), in press.

A. Papoulis, Circuits and Systems: A Modern Approach (Holt, Rinehart & Wilson, New York, 1980).

M. Servin, J. L. Marroquin, D. Malacara-Hernandez, “Some applications of quadratic cost functionals in fringe analysis,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2860, 24–33 (1996).

M. Rivera, M. Servin, J. L. Marroquin, “Fourier transform technique for phase unwrapping with minimized boundary effects,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds. Proc. SPIE2860, 54–60 (1996).

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, Amsterdam, 1993), Chap. 13.

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