Abstract

A novel fringe processing method is proposed to segment whole-field strain distributions from interferometric deformation patterns by use of Gabor filters. This novel strategy is specifically proposed for strain measurement with a Gabor filter used as a set of wavelets. To increase computational speed as well as for selection of contour intervals, judicious design of the filter bank, based on the fringe pattern and the requirements of the user, is crucial in this methodology. A filter design strategy is developed and, based on the proposed filter design scheme, properly designed filter banks are generated and applied for strain contouring in low-strain and strain concentration regions. This scheme allows one to measure engineering strains within regions of interest and hence provides the design engineer great flexibility of monitoring, testing, or analysis.

© 2002 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. A. C. Bovik, C. Marianna, W. S. Geisler, “Multichannel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
    [CrossRef]
  16. T. P. Weldon, W. E. Higgins, “Designing multiple Gabor filters for multi-texture image segmentation,” Opt. Eng. 38, 1478–1489 (1999).
    [CrossRef]

2002

A. Asundi, J. Wang, “Strain contouring using Gabor filters: principle and algorithm,” Opt. Eng. 14, 1400–1405 (2002).
[CrossRef]

2001

V. Krishnakumar, V. M. Murukeshan, A. Kishen, A. Asundi, “Opto-digitial system for curvature measurement,” Opt. Eng. 40, 340–341 (2001).
[CrossRef]

1999

T. P. Weldon, W. E. Higgins, “Designing multiple Gabor filters for multi-texture image segmentation,” Opt. Eng. 38, 1478–1489 (1999).
[CrossRef]

G. Paez, M. Strojnik, “Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front,” J. Opt. Soc. Am. A 16, 475–480 (1999).
[CrossRef]

1994

1993

A. Asundi, “Moiré methods using computer-generated gratings,” Opt. Eng. 32, 107–116 (1993).
[CrossRef]

1990

A. C. Bovik, C. Marianna, W. S. Geisler, “Multichannel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

1987

A. Asundi, M. T. Cheng, “Moiré of moiré interferometry,” Exp. Mech. 11, 28–30 (1987).

1986

1983

1982

C. A. Sciamarella, “The moiré method—a review,” Exp. Mech. 22, 418–433 (1982).
[CrossRef]

1981

Asundi, A.

A. Asundi, J. Wang, “Strain contouring using Gabor filters: principle and algorithm,” Opt. Eng. 14, 1400–1405 (2002).
[CrossRef]

V. Krishnakumar, V. M. Murukeshan, A. Kishen, A. Asundi, “Opto-digitial system for curvature measurement,” Opt. Eng. 40, 340–341 (2001).
[CrossRef]

A. Asundi, “Moiré methods using computer-generated gratings,” Opt. Eng. 32, 107–116 (1993).
[CrossRef]

A. Asundi, M. T. Cheng, “Moiré of moiré interferometry,” Exp. Mech. 11, 28–30 (1987).

A. Asundi, J. Wang, “Strain contouring using Gabor filters,” presented at the Fourth International Workshop on Automatic Processing of Fringe Patterns, Bremen, Germany, 17–19 September 2001.

Bachor, H. A.

Bone, D. J.

Bovik, A. C.

A. C. Bovik, C. Marianna, W. S. Geisler, “Multichannel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Cheng, M. T.

A. Asundi, M. T. Cheng, “Moiré of moiré interferometry,” Exp. Mech. 11, 28–30 (1987).

Chiang, F. P.

F. P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, 5th ed., J. F. Doyle, J. W. Phillips, eds. (Society for Experimental Mechanics, Bethel, Conn., 1982), pp. 107–135.

Creath, K.

K. Creath, “Phase-measuring interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.

Geisler, W. S.

A. C. Bovik, C. Marianna, W. S. Geisler, “Multichannel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Han, B.

D. Post, B. Han, P. Ifju, High Sensitivity Moire (Springer-Verlag, New York, 1994).

Higgins, W. E.

T. P. Weldon, W. E. Higgins, “Designing multiple Gabor filters for multi-texture image segmentation,” Opt. Eng. 38, 1478–1489 (1999).
[CrossRef]

Ifju, P.

D. Post, B. Han, P. Ifju, High Sensitivity Moire (Springer-Verlag, New York, 1994).

Kishen, A.

V. Krishnakumar, V. M. Murukeshan, A. Kishen, A. Asundi, “Opto-digitial system for curvature measurement,” Opt. Eng. 40, 340–341 (2001).
[CrossRef]

Krishnakumar, V.

V. Krishnakumar, V. M. Murukeshan, A. Kishen, A. Asundi, “Opto-digitial system for curvature measurement,” Opt. Eng. 40, 340–341 (2001).
[CrossRef]

Marianna, C.

A. C. Bovik, C. Marianna, W. S. Geisler, “Multichannel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Monneret, J.

Murukeshan, V. M.

V. Krishnakumar, V. M. Murukeshan, A. Kishen, A. Asundi, “Opto-digitial system for curvature measurement,” Opt. Eng. 40, 340–341 (2001).
[CrossRef]

Mutoh, K.

Paez, G.

Post, D.

D. Post, B. Han, P. Ifju, High Sensitivity Moire (Springer-Verlag, New York, 1994).

Rostogi, P. K.

Sandeman, R. J.

Sciamarella, C. A.

C. A. Sciamarella, “The moiré method—a review,” Exp. Mech. 22, 418–433 (1982).
[CrossRef]

Singh, H.

Sirkis, J. S.

Spajer, M.

Strojnik, M.

Takeda, M.

Wang, J.

A. Asundi, J. Wang, “Strain contouring using Gabor filters: principle and algorithm,” Opt. Eng. 14, 1400–1405 (2002).
[CrossRef]

A. Asundi, J. Wang, “Strain contouring using Gabor filters,” presented at the Fourth International Workshop on Automatic Processing of Fringe Patterns, Bremen, Germany, 17–19 September 2001.

Weldon, T. P.

T. P. Weldon, W. E. Higgins, “Designing multiple Gabor filters for multi-texture image segmentation,” Opt. Eng. 38, 1478–1489 (1999).
[CrossRef]

Appl. Opt.

Exp. Mech.

C. A. Sciamarella, “The moiré method—a review,” Exp. Mech. 22, 418–433 (1982).
[CrossRef]

A. Asundi, M. T. Cheng, “Moiré of moiré interferometry,” Exp. Mech. 11, 28–30 (1987).

IEEE Trans. Pattern Anal. Mach. Intell.

A. C. Bovik, C. Marianna, W. S. Geisler, “Multichannel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

A. Asundi, J. Wang, “Strain contouring using Gabor filters: principle and algorithm,” Opt. Eng. 14, 1400–1405 (2002).
[CrossRef]

T. P. Weldon, W. E. Higgins, “Designing multiple Gabor filters for multi-texture image segmentation,” Opt. Eng. 38, 1478–1489 (1999).
[CrossRef]

A. Asundi, “Moiré methods using computer-generated gratings,” Opt. Eng. 32, 107–116 (1993).
[CrossRef]

V. Krishnakumar, V. M. Murukeshan, A. Kishen, A. Asundi, “Opto-digitial system for curvature measurement,” Opt. Eng. 40, 340–341 (2001).
[CrossRef]

Other

F. P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, 5th ed., J. F. Doyle, J. W. Phillips, eds. (Society for Experimental Mechanics, Bethel, Conn., 1982), pp. 107–135.

D. Post, B. Han, P. Ifju, High Sensitivity Moire (Springer-Verlag, New York, 1994).

K. Creath, “Phase-measuring interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.

A. Asundi, J. Wang, “Strain contouring using Gabor filters,” presented at the Fourth International Workshop on Automatic Processing of Fringe Patterns, Bremen, Germany, 17–19 September 2001.

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Figures (11)

Fig. 1
Fig. 1

(a) Moire fringes, showing the contours of displacement in the vertical (load) direction. (b) The filter bank to be used is superimposed onto the frequency spectrum.

Fig. 2
Fig. 2

Derivatives of displacement along the (a) horizontal and (b) vertical directions. Contour interval, 1.08 × 10-4.

Fig. 3
Fig. 3

Mixed filter bank superimposed upon the frequency spectrum of the moire pattern of Fig. 1(a).

Fig. 4
Fig. 4

Derivatives of displacement along the (a) horizontal and (b) vertical directions. Finer contour interval, 4.17 × 10-5.

Fig. 5
Fig. 5

Moire-of-moire fringes representing the derivatives for (a) the horizontal (x) direction and (b) the vertical (y) direction.

Fig. 6
Fig. 6

Distribution of the derivative for the x direction along a diagonal that results from the equispacing filter design (Looser) and the mixed design (Mixed), compared with the moire-of-moire (MOM) fringes.

Fig. 7
Fig. 7

Distributions of displacement derivatives in the y direction along a peripheral curve from the equispacing bank (Loose) and the mixed bank (Mixed), compared with the moire-of-moire (MOM) fringes.

Fig. 8
Fig. 8

Gabor filter bank (a) for measuring the derivative (b) for the x direction within the strain concentration region.

Fig. 9
Fig. 9

Gabor filter bank (a) for measuring normal strain (b) in the y direction within the strain concentration region.

Fig. 10
Fig. 10

Distribution of the derivative for the x direction along a diagonal within the strain concentration region that results from the mixed filter bank in Fig. 8(a) (Mixed-Higher Strain) compared with the moire-of-moire (MOM) contours.

Fig. 11
Fig. 11

Distribution of the derivative for the y direction along a peripheral curve within the strain concentration region that results from the mixed filter bank in Fig. 9(a) (Mixed-Higher Strain) compared with the moire-of-moire (MOM) contours.

Equations (10)

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

hx, y=gx, yexpj2πUx+Vy,
gx, y=12πσxσyexp-12x2σx2+y2σy2,
Hu, v=exp-0.5u-Fσu2+ vσv2,
εx=fxU/f,  εy=fyV/f  γxy=fyU/f+fxV/f,
fx, fy=U+Um, V+Vn.
Δf1=1/2πσ,
σ=2B+12B-1απF,
Δf2=1/8π2σ2,
Δf1=12πσ=12π2B+12B-1απF=0.26,
Δf2=18π2σ2= F8π2=0.10.

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