Abstract

A filtering algorithm is proposed for processing images generated by TV holography that contain phase jumps and a high noise level. This algorithm first performs phase unwrapping without removing the noise. After that, it removes the noise by use of a conventional low-pass filter. The new approach allows for using low-pass filters with narrow passbands, leading to a better signal-to-noise ratio in the desired signal. Simulation results are presented and discussed. The new algorithm has been applied successfully under real conditions in a holographic station.

© 1998 Optical Society of America

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References

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  1. G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–68 (1986).
    [CrossRef]
  2. C. A. Sciammarela, G. Bhat, N. Longinow, M. Zhao, “A high accuracy micromechanics displacement measure optical technique,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers (American Society of Mechanical Engineers, New York, 1988), pp. 121–132.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. E. Vikhagen, “Nondestructive testing by use of TV holography and deformation phase gradient calculation,” Appl. Opt. 29, 137–144 (1990).
    [CrossRef] [PubMed]
  6. A. A. Gonçalves, “Determination of displacements, strain and rotations from holographic interferometry data using 2-D fringe order function,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 64–70 (1991).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. M. A. Herráez, D. R. Burton, M. J. Lalor, D. B. Clegg, “Robust, simple, and fast algorithm for phase unwrapping,” Appl. Opt. 35, 5847–5852 (1996).
    [CrossRef]
  14. K. A. Stetson, J. Wahid, P. Gauthier, “Noise-immune phase unwrapping by use of calculated wrap regions,” Appl. Opt. 36, 4830–4838 (1997).
    [CrossRef] [PubMed]
  15. M. Lehmann, “Decorrelation-induced phase errors in phase-shifting speckle interferometry,” Appl. Opt. 36, 3667–3632 (1997).
    [CrossRef]
  16. A. A. Gonçalves, R. Seara, P. B. Uliana, “A new amplitude weighted filtering technique for noise reduction in images with 2π phase jumps,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 312–322 (1993).
  17. T. W. Bushman, M. A. Gennert, R. J. Pryputniewicz, “Phase unwrapping by least squares error minimization of phase curvature,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 334–348 (1993).
  18. M. D. Pritt, J. S. Shipman, “Least-squares two dimensional phase unwrapping using FFT’s,” IEEE Trans. Geosci. Remote. Sens. 32, 706–708 (1994).
    [CrossRef]
  19. B. Friedlander, J. M. Francos, “Model based phase unwrapping of 2-D signals,” IEEE Trans. Signal Process. 44, 2999–3007 (1996).
    [CrossRef]
  20. A. A. Gonçalves, “Holographic station: a practical system for applying TV holography,” in Interferometry VI: Applications, Proc. SPIE2004, 215–223 (1993).

1997 (2)

K. A. Stetson, J. Wahid, P. Gauthier, “Noise-immune phase unwrapping by use of calculated wrap regions,” Appl. Opt. 36, 4830–4838 (1997).
[CrossRef] [PubMed]

M. Lehmann, “Decorrelation-induced phase errors in phase-shifting speckle interferometry,” Appl. Opt. 36, 3667–3632 (1997).
[CrossRef]

1996 (3)

1995 (1)

1994 (1)

M. D. Pritt, J. S. Shipman, “Least-squares two dimensional phase unwrapping using FFT’s,” IEEE Trans. Geosci. Remote. Sens. 32, 706–708 (1994).
[CrossRef]

1993 (1)

1991 (1)

1990 (1)

1989 (1)

1987 (1)

1986 (2)

1982 (1)

Bachor, A.

Bhat, G.

C. A. Sciammarela, G. Bhat, N. Longinow, M. Zhao, “A high accuracy micromechanics displacement measure optical technique,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers (American Society of Mechanical Engineers, New York, 1988), pp. 121–132.

Bone, D. J.

Burton, D. R.

Bushman, T. W.

T. W. Bushman, M. A. Gennert, R. J. Pryputniewicz, “Phase unwrapping by least squares error minimization of phase curvature,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 334–348 (1993).

Clegg, D. B.

Cusak, R.

Francos, J. M.

B. Friedlander, J. M. Francos, “Model based phase unwrapping of 2-D signals,” IEEE Trans. Signal Process. 44, 2999–3007 (1996).
[CrossRef]

Friedlander, B.

B. Friedlander, J. M. Francos, “Model based phase unwrapping of 2-D signals,” IEEE Trans. Signal Process. 44, 2999–3007 (1996).
[CrossRef]

Gauthier, P.

Gennert, M. A.

T. W. Bushman, M. A. Gennert, R. J. Pryputniewicz, “Phase unwrapping by least squares error minimization of phase curvature,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 334–348 (1993).

Ghiglia, D. C.

Goldrein, H.

Gonçalves, A. A.

A. A. Gonçalves, R. Seara, P. B. Uliana, “A new amplitude weighted filtering technique for noise reduction in images with 2π phase jumps,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 312–322 (1993).

A. A. Gonçalves, “Determination of displacements, strain and rotations from holographic interferometry data using 2-D fringe order function,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 64–70 (1991).

A. A. Gonçalves, “Holographic station: a practical system for applying TV holography,” in Interferometry VI: Applications, Proc. SPIE2004, 215–223 (1993).

Herráez, M. A.

Huntley, J.

Huntley, J. M.

Itoh, K.

Lalor, M. J.

Lehmann, M.

M. Lehmann, “Decorrelation-induced phase errors in phase-shifting speckle interferometry,” Appl. Opt. 36, 3667–3632 (1997).
[CrossRef]

Longinow, N.

C. A. Sciammarela, G. Bhat, N. Longinow, M. Zhao, “A high accuracy micromechanics displacement measure optical technique,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers (American Society of Mechanical Engineers, New York, 1988), pp. 121–132.

Mastin, G. A.

Pritt, M. D.

M. D. Pritt, J. S. Shipman, “Least-squares two dimensional phase unwrapping using FFT’s,” IEEE Trans. Geosci. Remote. Sens. 32, 706–708 (1994).
[CrossRef]

Pryputniewicz, R. J.

T. W. Bushman, M. A. Gennert, R. J. Pryputniewicz, “Phase unwrapping by least squares error minimization of phase curvature,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 334–348 (1993).

Reid, G. T.

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

Romero, L. A.

Saldner, H.

Sandeman, R. J.

Sciammarela, C. A.

C. A. Sciammarela, G. Bhat, N. Longinow, M. Zhao, “A high accuracy micromechanics displacement measure optical technique,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers (American Society of Mechanical Engineers, New York, 1988), pp. 121–132.

Seara, R.

A. A. Gonçalves, R. Seara, P. B. Uliana, “A new amplitude weighted filtering technique for noise reduction in images with 2π phase jumps,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 312–322 (1993).

Shipman, J. S.

M. D. Pritt, J. S. Shipman, “Least-squares two dimensional phase unwrapping using FFT’s,” IEEE Trans. Geosci. Remote. Sens. 32, 706–708 (1994).
[CrossRef]

Stetson, K. A.

Uliana, P. B.

A. A. Gonçalves, R. Seara, P. B. Uliana, “A new amplitude weighted filtering technique for noise reduction in images with 2π phase jumps,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 312–322 (1993).

Vikhagen, E.

Wahid, J.

Zhao, M.

C. A. Sciammarela, G. Bhat, N. Longinow, M. Zhao, “A high accuracy micromechanics displacement measure optical technique,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers (American Society of Mechanical Engineers, New York, 1988), pp. 121–132.

Appl. Opt. (10)

IEEE Trans. Geosci. Remote. Sens. (1)

M. D. Pritt, J. S. Shipman, “Least-squares two dimensional phase unwrapping using FFT’s,” IEEE Trans. Geosci. Remote. Sens. 32, 706–708 (1994).
[CrossRef]

IEEE Trans. Signal Process. (1)

B. Friedlander, J. M. Francos, “Model based phase unwrapping of 2-D signals,” IEEE Trans. Signal Process. 44, 2999–3007 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lasers Eng. (1)

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

Other (5)

C. A. Sciammarela, G. Bhat, N. Longinow, M. Zhao, “A high accuracy micromechanics displacement measure optical technique,” in Proceedings of the Winter Annual Meeting of the American Society of Mechanical Engineers (American Society of Mechanical Engineers, New York, 1988), pp. 121–132.

A. A. Gonçalves, “Holographic station: a practical system for applying TV holography,” in Interferometry VI: Applications, Proc. SPIE2004, 215–223 (1993).

A. A. Gonçalves, R. Seara, P. B. Uliana, “A new amplitude weighted filtering technique for noise reduction in images with 2π phase jumps,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 312–322 (1993).

T. W. Bushman, M. A. Gennert, R. J. Pryputniewicz, “Phase unwrapping by least squares error minimization of phase curvature,” in Interferometry: Techniques and Analysis II, O. Y. Kwon, G. M. Brown, M. Kujawinska, eds., Proc. SPIE2003, 334–348 (1993).

A. A. Gonçalves, “Determination of displacements, strain and rotations from holographic interferometry data using 2-D fringe order function,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 64–70 (1991).

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Figures (3)

Fig. 1
Fig. 1

One-dimensional illustration of phase-jump removals: (a) Signal with phase jumps. (b) Number of laps. (c) Signal with removed phase jumps.

Fig. 2
Fig. 2

Illustrations of a one-dimensional phase-map spectrum: (a) For the actual signal. (b) For the transformed signal.

Fig. 3
Fig. 3

SNR obtained by the application of filtering with the trigonometric transform (represented by the asterisks) and of the AUF (represented by the plus signs) for different low-pass filters.

Equations (13)

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ϕ x ,   y = φ x ,   y - 2 π N x ,   y + e x ,   y ,
N x ,   y = ϕ x ,   y - ϕ k ,   l / 2 π + N k ,   l ,
ϕ r x ,   y = tan - 1 ( sin ϕ x ,   y   *   *   h x ,   y / cos ϕ x ,   y   *   *   h x ,   y ) ,
φ r x ,   y = φ x ,   y + e r x ,   y ,
N n x ,   y = φ r x ,   y - ϕ x ,   y / 2 π .
N n x ,   y = N x ,   y + e r x ,   y - e x ,   y / 2 π .
| e x ,   y - e r x ,   y | < π .
φ i x ,   y = ϕ x ,   y + 2 π N n x ,   y .
φ i x ,   y = φ x ,   y + e x ,   y .
φ n x ,   y = h i x ,   y   *   *   φ i x ,   y = h i x ,   y   *   *   φ x ,   y + e x ,   y = h i x ,   y   *   *   φ x ,   y + h i x ,   y   *   *   e x ,   y .
e n x ,   y = h i x ,   y   *   *   e x ,   y .
φ n x ,   y φ x ,   y + e n x ,   y .
SNR i = 10   log x y   φ 2 x ,   y x y   e i 2 x ,   y ,

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