Abstract

Automated fringe-pattern processing is important in a great number of industrial applications, such as optical data testing and quality control. One of the main problems that arises with these processes is the automated phase unwrapping of the phase map associated with the fringe pattern. Usually the phase map presents problems such as noise, and low-modulation areas. A new phase-unwrapping algorithm with high noise immunity is presented. The algorithm is easily implemented and can process arbitrary shapes. The main features of this algorithm are the use of a queue for the processing of arbitrary shapes and a selection criterion that determines which pixels are going to be processed.

© 1994 Optical Society of America

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References

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  1. K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
    [CrossRef]
  2. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987).
    [CrossRef] [PubMed]
  3. P. Andrä, U. Mieth, W. Osten, “Strategies for unwrapping noisy interferograms in phase sampling interferometry,” in Industrial Applications of Holographic and Speckle Measuring Techniques, W. P. Jueptner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1508, 50–72 (1991).
  4. D. P. Towers, T. R. Judge, P. J. Bryaston-Cross, “A quasi heterodyne technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).
  5. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
    [CrossRef] [PubMed]
  6. D. J. Bone, “Fourier fringe analysis, the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
    [CrossRef] [PubMed]
  7. D. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–279 (1987).
    [CrossRef]
  8. J. M. Huntley, R. Cusack, H. Saldner, “New phase unwrapping algorithms,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 148–153.
  9. K. Itoh, “Analysis of the phase-unwrapping algorithm,” Appl. Opt. 21, 2470–2476 (1982).
    [CrossRef] [PubMed]
  10. H. A. Vrooman, A. M. Maas, “Image processing algorithms for the analysis of phase-shifted speckle interference patterns,” Appl. Opt. 30, 1636–1641 (1991).
    [CrossRef] [PubMed]
  11. D. Dirksen, X. Su, D. Vukicevic, G. Von Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin1993), pp. 72–77.

1991

1989

1988

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

1987

1982

Andrä, P.

P. Andrä, U. Mieth, W. Osten, “Strategies for unwrapping noisy interferograms in phase sampling interferometry,” in Industrial Applications of Holographic and Speckle Measuring Techniques, W. P. Jueptner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1508, 50–72 (1991).

Bone, D. J.

Bryaston-Cross, P. J.

D. P. Towers, T. R. Judge, P. J. Bryaston-Cross, “A quasi heterodyne technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Cusack, R.

J. M. Huntley, R. Cusack, H. Saldner, “New phase unwrapping algorithms,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 148–153.

Dirksen, D.

D. Dirksen, X. Su, D. Vukicevic, G. Von Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin1993), pp. 72–77.

Ghiglia, D.

Greivenkamp, J. E.

Huntley, J. M.

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
[CrossRef] [PubMed]

J. M. Huntley, R. Cusack, H. Saldner, “New phase unwrapping algorithms,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 148–153.

Itoh, K.

Judge, T. R.

D. P. Towers, T. R. Judge, P. J. Bryaston-Cross, “A quasi heterodyne technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

Maas, A. M.

Mastin, G. A.

Mieth, U.

P. Andrä, U. Mieth, W. Osten, “Strategies for unwrapping noisy interferograms in phase sampling interferometry,” in Industrial Applications of Holographic and Speckle Measuring Techniques, W. P. Jueptner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1508, 50–72 (1991).

Osten, W.

P. Andrä, U. Mieth, W. Osten, “Strategies for unwrapping noisy interferograms in phase sampling interferometry,” in Industrial Applications of Holographic and Speckle Measuring Techniques, W. P. Jueptner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1508, 50–72 (1991).

Romero, L. A.

Saldner, H.

J. M. Huntley, R. Cusack, H. Saldner, “New phase unwrapping algorithms,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 148–153.

Su, X.

D. Dirksen, X. Su, D. Vukicevic, G. Von Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin1993), pp. 72–77.

Towers, D. P.

D. P. Towers, T. R. Judge, P. J. Bryaston-Cross, “A quasi heterodyne technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

Von Bally, G.

D. Dirksen, X. Su, D. Vukicevic, G. Von Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin1993), pp. 72–77.

Vrooman, H. A.

Vukicevic, D.

D. Dirksen, X. Su, D. Vukicevic, G. Von Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin1993), pp. 72–77.

Appl. Opt.

J. Opt. Soc. Am. A

Prog. Opt.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Other

J. M. Huntley, R. Cusack, H. Saldner, “New phase unwrapping algorithms,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 148–153.

D. Dirksen, X. Su, D. Vukicevic, G. Von Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in Proceedings FRINGE 93, W. Jüptner, W. Osten, eds. (Akademie, Berlin1993), pp. 72–77.

P. Andrä, U. Mieth, W. Osten, “Strategies for unwrapping noisy interferograms in phase sampling interferometry,” in Industrial Applications of Holographic and Speckle Measuring Techniques, W. P. Jueptner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1508, 50–72 (1991).

D. P. Towers, T. R. Judge, P. J. Bryaston-Cross, “A quasi heterodyne technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

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Figures (9)

Fig. 1
Fig. 1

Flow chart of the algorithm.

Fig. 2
Fig. 2

Phase map with processing mask, representing a positive ramp from left to right. The orientations of the X and Y axes are also shown. This orientation is the same for Figs. 3 5.

Fig. 3
Fig. 3

Corrupted phase map with a processing mask.

Fig. 4
Fig. 4

(a) Noisy image of Fig. 3 processed by algorithm A, (b) noisy image of Fig. 3 processed by algorithm B, (c) noisy image of Fig. 3 processed by algorithm C.

Fig. 5
Fig. 5

Result of the bilinear interpolation of the holes of Fig. 4(a).

Fig. 6
Fig. 6

(a) Three-dimensionarel preesentation of the continuous phase that results from unwrapping the clean phase map of Fig. 3, (b) three-dimensional representation of the continuous phase of Fig. 5, (c) difference between (a) and (b).

Fig. 7
Fig. 7

Noisy phase map representing the out-of-plane displacement of a tooth and its filling measured with a speckle interferometer. The orientations of the X and Y axes are also shown. This orientation is the same for Fig. 8.

Fig. 8
Fig. 8

Complete processing of Fig. 7, that is, unwrapping and further bilinear interpolation of the nonprocessed points. The tooth and the filling are processed separately.

Fig. 9
Fig. 9

Three-dimensional representation of the continuous phase map of Fig. 8.

Equations (5)

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s ( x , y ) = [ ϕ ( x + 1 , y ) ϕ ( x , y ) ] + [ ϕ ( x + 1 , y + 1 ) ϕ ( x + 1 , y ) ] + [ ϕ ( x , y + 1 ) ϕ ( x + 1 , y + 1 ) ] + [ ϕ ( x , y ) ϕ ( x , y + 1 ) ]
Φ ( M ) = ϕ ( 0 ) + n = 1 M W { Δ [ ϕ ( n ) ] } .
Φ ( m , n ) = Φ ( 0 , n ) + j = 1 m W 1 { Δ m [ ϕ ( j , n ) ] } ,
Δ ( m , n ) = Φ ( m , 0 ) + l = 1 n W 2 { Δ n [ ϕ ( m , l ) ] } .
Φ ( P 2 ) = Φ ( P 1 ) + W [ ϕ ( P 2 ) ϕ ( P 1 ) ] ,

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