Abstract

A method for automatic phase extraction from a single fringe pattern based on the guidance of an extreme map is introduced. The method uses an adaptive weighted filter to reduce noise and enhance contrast and to locate the fringe extremes. Wrapped phase values are calculated by use of an arccosine function obtained from the extreme map. With this method, wrapped phase values can be efficiently demodulated from a single fringe pattern without the need for assigning fringe order or interpolating fractional fringe order. The validity of the method is demonstrated by use of closed-fringe patterns generated by digital speckle interferometry.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  6. M. Servin, J. L. Marroquin, F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001).
    [CrossRef]
  7. J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998).
    [CrossRef]
  8. J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez-Vera, M. Servin, “Regularization methods for processing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
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    [CrossRef]
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    [CrossRef]
  13. F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, “A parametric method applied to phase recovery from a fringe pattern based on genetic algorithm,” Opt. Commun. 203, 213–223 (2002).
    [CrossRef]
  14. R. S. Lin, Y. C. Hsueh, “Multichannel filtering by gradient information,” Signal Process. 80, 279–293 (2000).
    [CrossRef]
  15. S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
    [CrossRef]
  16. M. Spann, A. Nieminen, “Adaptive Guassian weighted filtering for image segmentation,” Pattern Recogn. Lett. 8, 251–255 (1998).
    [CrossRef]
  17. G. T. Reid, “Image processing techniques for fringe pattern analysis,” in Advanced Processing of Semiconductor Devices II,H. G. Craighead, J. Narayan, eds., Proc. SPIE945, 468–477 (1988).
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    [CrossRef]
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  21. D. Malacara, M. Serven, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

2002

F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, “A parametric method applied to phase recovery from a fringe pattern based on genetic algorithm,” Opt. Commun. 203, 213–223 (2002).
[CrossRef]

2001

2000

R. S. Lin, Y. C. Hsueh, “Multichannel filtering by gradient information,” Signal Process. 80, 279–293 (2000).
[CrossRef]

F. J. Cuevas, M. Servin, O. N. Stavroudis, R. Rodriguez-Vera, “Multi-layer neural network applied to phase and depth recovery from fringe patterns,” Opt. Commun. 181, 239–259 (2000).
[CrossRef]

1999

1998

E. Yu, S. S. Cha, “Two-dimensional regression for interferometric phase extraction,” Appl. Opt. 37, 1370–1376 (1998).
[CrossRef]

J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998).
[CrossRef]

S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
[CrossRef]

M. Spann, A. Nieminen, “Adaptive Guassian weighted filtering for image segmentation,” Pattern Recogn. Lett. 8, 251–255 (1998).
[CrossRef]

1997

1995

1993

J. L. Marroquin, “Deterministic interactive particle models for image processing and computer graphics,” Comput. Vis. Graph. Image Process. 55, 408–417 (1993).

M. Servin, R. Rodriguez-Vera, “Two dimensional phase locked loop demodulation of carrier frequency interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

1986

1982

Balou, P.

S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
[CrossRef]

Botello, S.

Cha, S. S.

Cuevas, F. J.

F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, “A parametric method applied to phase recovery from a fringe pattern based on genetic algorithm,” Opt. Commun. 203, 213–223 (2002).
[CrossRef]

M. Servin, J. L. Marroquin, F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001).
[CrossRef]

F. J. Cuevas, M. Servin, O. N. Stavroudis, R. Rodriguez-Vera, “Multi-layer neural network applied to phase and depth recovery from fringe patterns,” Opt. Commun. 181, 239–259 (2000).
[CrossRef]

M. Servin, J. L. Marroquin, F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997).
[CrossRef] [PubMed]

Ge, Z.

Guillon, S.

S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
[CrossRef]

Hsueh, Y. C.

R. S. Lin, Y. C. Hsueh, “Multichannel filtering by gradient information,” Signal Process. 80, 279–293 (2000).
[CrossRef]

Ina, H.

Joo, W.

Keskes, N.

S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
[CrossRef]

Kobayashi, F.

Kobayashi, S.

Kokal, J. V.

Kreis, T.

Lin, R. S.

R. S. Lin, Y. C. Hsueh, “Multichannel filtering by gradient information,” Signal Process. 80, 279–293 (2000).
[CrossRef]

Malacara, D.

D. Malacara, M. Serven, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Malacara, Z.

D. Malacara, M. Serven, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Marroquin, J. L.

Mass, A.

H. A. Vrooman, A. Mass, “Interferogram analysis using image processing techniques,” in Interferometry ’89,Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1989).
[CrossRef]

Matsuda, S.

Najim, M.

S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
[CrossRef]

Nieminen, A.

M. Spann, A. Nieminen, “Adaptive Guassian weighted filtering for image segmentation,” Pattern Recogn. Lett. 8, 251–255 (1998).
[CrossRef]

Ransom, P. L.

Reid, G. T.

G. T. Reid, “Image processing techniques for fringe pattern analysis,” in Advanced Processing of Semiconductor Devices II,H. G. Craighead, J. Narayan, eds., Proc. SPIE945, 468–477 (1988).

Rivera, M.

Rodriguez-Vera, R.

F. J. Cuevas, M. Servin, O. N. Stavroudis, R. Rodriguez-Vera, “Multi-layer neural network applied to phase and depth recovery from fringe patterns,” Opt. Commun. 181, 239–259 (2000).
[CrossRef]

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez-Vera, M. Servin, “Regularization methods for processing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[CrossRef]

J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998).
[CrossRef]

M. Servin, R. Rodriguez-Vera, “Two dimensional phase locked loop demodulation of carrier frequency interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

Serven, M.

D. Malacara, M. Serven, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Servin, M.

F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, “A parametric method applied to phase recovery from a fringe pattern based on genetic algorithm,” Opt. Commun. 203, 213–223 (2002).
[CrossRef]

M. Servin, J. L. Marroquin, F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001).
[CrossRef]

F. J. Cuevas, M. Servin, O. N. Stavroudis, R. Rodriguez-Vera, “Multi-layer neural network applied to phase and depth recovery from fringe patterns,” Opt. Commun. 181, 239–259 (2000).
[CrossRef]

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez-Vera, M. Servin, “Regularization methods for processing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[CrossRef]

J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998).
[CrossRef]

M. Servin, J. L. Marroquin, F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997).
[CrossRef] [PubMed]

M. Servin, R. Rodriguez-Vera, “Two dimensional phase locked loop demodulation of carrier frequency interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

Sossa-Azuela, J. H.

F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, “A parametric method applied to phase recovery from a fringe pattern based on genetic algorithm,” Opt. Commun. 203, 213–223 (2002).
[CrossRef]

Spann, M.

M. Spann, A. Nieminen, “Adaptive Guassian weighted filtering for image segmentation,” Pattern Recogn. Lett. 8, 251–255 (1998).
[CrossRef]

Stavroudis, O. N.

F. J. Cuevas, M. Servin, O. N. Stavroudis, R. Rodriguez-Vera, “Multi-layer neural network applied to phase and depth recovery from fringe patterns,” Opt. Commun. 181, 239–259 (2000).
[CrossRef]

Takeda, M.

Taketa, M.

Vrooman, H. A.

H. A. Vrooman, A. Mass, “Interferogram analysis using image processing techniques,” in Interferometry ’89,Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1989).
[CrossRef]

Yatagai, T.

T. Yatagai, “Intensity based analysis methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques,D. W. Robinson, G. T. Reid, eds. (Institute of Physics Publishing, 1993), p. 72.

Yu, E.

Appl. Opt.

Comput. Vis. Graph. Image Process.

J. L. Marroquin, “Deterministic interactive particle models for image processing and computer graphics,” Comput. Vis. Graph. Image Process. 55, 408–417 (1993).

J. Mod. Opt.

M. Servin, R. Rodriguez-Vera, “Two dimensional phase locked loop demodulation of carrier frequency interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

F. J. Cuevas, M. Servin, O. N. Stavroudis, R. Rodriguez-Vera, “Multi-layer neural network applied to phase and depth recovery from fringe patterns,” Opt. Commun. 181, 239–259 (2000).
[CrossRef]

F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, “A parametric method applied to phase recovery from a fringe pattern based on genetic algorithm,” Opt. Commun. 203, 213–223 (2002).
[CrossRef]

Pattern Recogn. Lett.

M. Spann, A. Nieminen, “Adaptive Guassian weighted filtering for image segmentation,” Pattern Recogn. Lett. 8, 251–255 (1998).
[CrossRef]

Signal Process.

R. S. Lin, Y. C. Hsueh, “Multichannel filtering by gradient information,” Signal Process. 80, 279–293 (2000).
[CrossRef]

S. Guillon, P. Balou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D image enhancement,” Signal Process. 67, 237–254 (1998).
[CrossRef]

Other

G. T. Reid, “Image processing techniques for fringe pattern analysis,” in Advanced Processing of Semiconductor Devices II,H. G. Craighead, J. Narayan, eds., Proc. SPIE945, 468–477 (1988).

H. A. Vrooman, A. Mass, “Interferogram analysis using image processing techniques,” in Interferometry ’89,Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1989).
[CrossRef]

T. Yatagai, “Intensity based analysis methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques,D. W. Robinson, G. T. Reid, eds. (Institute of Physics Publishing, 1993), p. 72.

D. Malacara, M. Serven, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

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Figures (12)

Fig. 1
Fig. 1

(a) One-dimensional fringe intensity distribution. (b) Phase distribution obtained from the fringe pattern in (a). (c) Phase distribution after a change of sign.

Fig. 2
Fig. 2

DSSI fringes.

Fig. 3
Fig. 3

Fringe pattern obtained with fast-Fourier-transform filtering.

Fig. 4
Fig. 4

3 × 3 mask window.

Fig. 5
Fig. 5

Fringe pattern obtained with adaptive weighted filtering and median filtering.

Fig. 6
Fig. 6

(a) Extreme maps obtained by binarization and thinning algorithms: (b) results of Fig. 2 superimposed upon (a), (c) peaks and troughs obtained by the Yatagai method, and (d) peaks and troughs detected by the proposed method.

Fig. 7
Fig. 7

Mask windows for line connection.

Fig. 8
Fig. 8

Schematic of large discontinuity and an erroneous side line.

Fig. 9
Fig. 9

ESPI fringes.

Fig. 10
Fig. 10

Wrapped phase maps.

Fig. 11
Fig. 11

Extreme maps obtained by the proposed method: (a) extreme map of the fringe pattern shown in Fig. 2, (b) extreme map of the fringe pattern shown in Fig. 9.

Fig. 12
Fig. 12

Three-dimensional unwrapped phase distributions.

Equations (22)

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

g ( r ) = a ( r ) + b ( r ) cos ϕ ( r ) ,
I ( r ) = b ( r ) cos ϕ ( r ) .
f ( r ) = cos ϕ ( r ) .
ϕ ( r ) = arccos [ f ( r ) ] .
G ( k ) = g ( p k ) - g ( p 4 ) ,             k = 0 , 1 , , 8 ,
F ( p 4 ) = k = 0 8 w p 4 ( k ) g ( p k ) k = 0 8 w p 4 ( k ) = k = 0 8 g ( p k ) exp [ G ( k ) ] k = 0 8 exp [ G ( k ) ] ,
p 4 > p 3 ,             p 4 > p 5 ,
p 4 < p 3 ,             p 4 < p 5 ;
p 4 > p 1 ,             p 4 > p 7 ,
p 4 < p 1 ,             p 4 < p 7 ;
p 4 > p 0 ,             p 4 > p 8 ,
p 4 < p 0 ,             p 4 < p 8 ;
p 4 > p 2 ,             p 4 > p 6 ,
p 4 < p 2 ,             p 4 < p 6 .
p i p 8 - i = 1             or             p i p i + 5 = 1 ,             i = 0 , 1 , 2 , 3 ,
p i p i + 7 = 1 ,             i = 0 , 1 ,
p 2 p 3 = 1             or             p 5 p 6 = 1.
( p i p i + 5 p i + 10 ) = 1 ,             p 4 + p 9 + p 14 = 0 , i = 0 , 1 , 2 , 3 ,
( q i q i + 1 q i + 2 ) = 1 ,             q 12 + q 13 + q 14 = 0 , i = 0 , 3 , 6 , 9.
k 0 k 6 k 12 k 18 = 1 ,             k i = 0 ,             i 0 , 6 , 12 , 18 ,
k 4 k 8 k 12 k 16 = 1 ,             k i = 0 ,             i 4 , 8 , 12 , 16.
f ( r ) = 2 [ I ( r ) - min t t I ( t ) ] max t T I ( t ) - min t T I ( t ) - 1 ,

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