Abstract

In recent years phase-measuring techniques have been applied to the problem of extracting information of photoelastic data. We present a new phase-measuring algorithm for extraction of the isochromatics of photoelastic fringe patterns. The algorithm permits the extraction of the isochromatic phase with almost no influence from the isoclinics, thus avoiding the usual problems of low-modulation areas associated with isoclinics. The isochromatic phase map obtained with this algorithm is well suited for a full separation of the stress components in a sample. The algorithm can be used with any commercial diffuse-light circular polariscope.

© 1997 Optical Society of America

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References

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  1. M. M. Frocht, Photoelasticity (Wiley, New York, 1941 and 1948).
  2. J. Carazo-Álvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Laser Eng. 21, 133–149 (1994).
    [CrossRef]
  3. T. Franz, A. Maidhof, J. Sun, “Verfahren und Vorrichtung zur Bestimmung der Isochromatenwerte in der Spannungsoptik,” German patentDE-195 03 851 A1 (10August1995).
  4. G. M. Brown, J. L. Sullivan, “The computer aided holo-photoelastic method: theory and experiment,” in Proceedings of SEM conference on Hologram Interferometry and Speckle Metrology, Baltimore, 5–8 November 1990 (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 102–109.
  5. C. Buckberry, D. Towers, “Automatic analysis of isochromatic and isoclinic fringes in photoelasticity using phase-measuring techniques,” Meas. Sci. Technol. 6, 1227–1235 (1995).
    [CrossRef]
  6. R. Wernicke, K. P. Gründer, J. Munschau, W. Winde, “A computer-aided photoelastic measuring system,” in Fringe ’93, Proceedings of the 2nd International Workshop on Automatic of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 276–281.
  7. A. Asundi, “Phase shifting in photoelasticity,” Exp. Tech. 17, 19–23 (1993).
    [CrossRef]
  8. E. A. Patterson, Z. F. Wang, “Towards full field automated photoelastic analysis of complex components,” Strain 27, 49–53 (1991).
    [CrossRef]
  9. A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
    [CrossRef]
  10. Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
    [CrossRef]
  11. frames-dt 2.1 Reference Guide (Steinbichler Optotechnik GmbH, Neubeuern, Germany, 1995).
  12. D. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–279 (1987).
    [CrossRef]
  13. J. E. Greivenkamp, J. H. Bruning, “Phase-shifting interferometers,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 522ff.

1995

C. Buckberry, D. Towers, “Automatic analysis of isochromatic and isoclinic fringes in photoelasticity using phase-measuring techniques,” Meas. Sci. Technol. 6, 1227–1235 (1995).
[CrossRef]

1994

J. Carazo-Álvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Laser Eng. 21, 133–149 (1994).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

1993

A. Asundi, “Phase shifting in photoelasticity,” Exp. Tech. 17, 19–23 (1993).
[CrossRef]

1992

A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
[CrossRef]

1991

E. A. Patterson, Z. F. Wang, “Towards full field automated photoelastic analysis of complex components,” Strain 27, 49–53 (1991).
[CrossRef]

1987

Asundi, A.

A. Asundi, “Phase shifting in photoelasticity,” Exp. Tech. 17, 19–23 (1993).
[CrossRef]

Brown, G. M.

G. M. Brown, J. L. Sullivan, “The computer aided holo-photoelastic method: theory and experiment,” in Proceedings of SEM conference on Hologram Interferometry and Speckle Metrology, Baltimore, 5–8 November 1990 (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 102–109.

Bruning, J. H.

J. E. Greivenkamp, J. H. Bruning, “Phase-shifting interferometers,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 522ff.

Buckberry, C.

C. Buckberry, D. Towers, “Automatic analysis of isochromatic and isoclinic fringes in photoelasticity using phase-measuring techniques,” Meas. Sci. Technol. 6, 1227–1235 (1995).
[CrossRef]

Carazo-Álvarez, J.

J. Carazo-Álvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Laser Eng. 21, 133–149 (1994).
[CrossRef]

Franz, T.

T. Franz, A. Maidhof, J. Sun, “Verfahren und Vorrichtung zur Bestimmung der Isochromatenwerte in der Spannungsoptik,” German patentDE-195 03 851 A1 (10August1995).

Frocht, M. M.

M. M. Frocht, Photoelasticity (Wiley, New York, 1941 and 1948).

Ghiglia, D.

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase-shifting interferometers,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 522ff.

Gründer, K. P.

R. Wernicke, K. P. Gründer, J. Munschau, W. Winde, “A computer-aided photoelastic measuring system,” in Fringe ’93, Proceedings of the 2nd International Workshop on Automatic of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 276–281.

Haake, S. J.

J. Carazo-Álvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Laser Eng. 21, 133–149 (1994).
[CrossRef]

Maidhof, A.

T. Franz, A. Maidhof, J. Sun, “Verfahren und Vorrichtung zur Bestimmung der Isochromatenwerte in der Spannungsoptik,” German patentDE-195 03 851 A1 (10August1995).

Mastin, G. A.

Munschau, J.

R. Wernicke, K. P. Gründer, J. Munschau, W. Winde, “A computer-aided photoelastic measuring system,” in Fringe ’93, Proceedings of the 2nd International Workshop on Automatic of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 276–281.

Otani, Y.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Patterson, E. A.

J. Carazo-Álvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Laser Eng. 21, 133–149 (1994).
[CrossRef]

E. A. Patterson, Z. F. Wang, “Towards full field automated photoelastic analysis of complex components,” Strain 27, 49–53 (1991).
[CrossRef]

Pillai, S. A.

A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
[CrossRef]

Romero, L. A.

Sarma, A. V. S. S. R.

A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
[CrossRef]

Shimada, T.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Subramanian, G.

A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
[CrossRef]

Sullivan, J. L.

G. M. Brown, J. L. Sullivan, “The computer aided holo-photoelastic method: theory and experiment,” in Proceedings of SEM conference on Hologram Interferometry and Speckle Metrology, Baltimore, 5–8 November 1990 (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 102–109.

Sun, J.

T. Franz, A. Maidhof, J. Sun, “Verfahren und Vorrichtung zur Bestimmung der Isochromatenwerte in der Spannungsoptik,” German patentDE-195 03 851 A1 (10August1995).

Towers, D.

C. Buckberry, D. Towers, “Automatic analysis of isochromatic and isoclinic fringes in photoelasticity using phase-measuring techniques,” Meas. Sci. Technol. 6, 1227–1235 (1995).
[CrossRef]

Umeda, N.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Varadan, T. K.

A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
[CrossRef]

Wang, Z. F.

E. A. Patterson, Z. F. Wang, “Towards full field automated photoelastic analysis of complex components,” Strain 27, 49–53 (1991).
[CrossRef]

Wernicke, R.

R. Wernicke, K. P. Gründer, J. Munschau, W. Winde, “A computer-aided photoelastic measuring system,” in Fringe ’93, Proceedings of the 2nd International Workshop on Automatic of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 276–281.

Winde, W.

R. Wernicke, K. P. Gründer, J. Munschau, W. Winde, “A computer-aided photoelastic measuring system,” in Fringe ’93, Proceedings of the 2nd International Workshop on Automatic of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 276–281.

Yoshizawa, T.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Exp. Mech.

A. V. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–29 (1992).
[CrossRef]

Exp. Tech.

A. Asundi, “Phase shifting in photoelasticity,” Exp. Tech. 17, 19–23 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

C. Buckberry, D. Towers, “Automatic analysis of isochromatic and isoclinic fringes in photoelasticity using phase-measuring techniques,” Meas. Sci. Technol. 6, 1227–1235 (1995).
[CrossRef]

Opt. Eng.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Opt. Laser Eng.

J. Carazo-Álvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Laser Eng. 21, 133–149 (1994).
[CrossRef]

Strain

E. A. Patterson, Z. F. Wang, “Towards full field automated photoelastic analysis of complex components,” Strain 27, 49–53 (1991).
[CrossRef]

Other

M. M. Frocht, Photoelasticity (Wiley, New York, 1941 and 1948).

T. Franz, A. Maidhof, J. Sun, “Verfahren und Vorrichtung zur Bestimmung der Isochromatenwerte in der Spannungsoptik,” German patentDE-195 03 851 A1 (10August1995).

G. M. Brown, J. L. Sullivan, “The computer aided holo-photoelastic method: theory and experiment,” in Proceedings of SEM conference on Hologram Interferometry and Speckle Metrology, Baltimore, 5–8 November 1990 (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 102–109.

R. Wernicke, K. P. Gründer, J. Munschau, W. Winde, “A computer-aided photoelastic measuring system,” in Fringe ’93, Proceedings of the 2nd International Workshop on Automatic of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 276–281.

frames-dt 2.1 Reference Guide (Steinbichler Optotechnik GmbH, Neubeuern, Germany, 1995).

J. E. Greivenkamp, J. H. Bruning, “Phase-shifting interferometers,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 522ff.

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Figures (5)

Fig. 1
Fig. 1

Arrangement of optical elements for the general configuration of a circular polariscope. F and S stand for fast and slow axes, respectively. P, A, and Q stand for polarizer, analyzer, and quarter-wave plate, respectively, and R α (δ) for the stressed sample taken as a retardation plate of retardation δ and whose fast axis is at an angle α with the x axis. The polarizer and the first quarter-wave plate form an angle of 45° with respect to each other; therefore the light incident upon the sample is circularly polarized.

Fig. 2
Fig. 2

Schematic representation of the behavior of the estimations I and II of the wrapped isochromatic phase, W(δ). A low-pass filtering is needed to combine smoothly WI) and WII) in the transition zone between the high-modulation areas.

Fig. 3
Fig. 3

Isochromatic phase map for a diametrically loaded disk, calculated with Eq. (10) with n = 2. The arrows point to the broken fringes produced by the low-pass effect of this equation.

Fig. 4
Fig. 4

Isochromatic phase map for the object of Fig. 3 calculated with Eq. (13). The resulting phase map is valid for unwrapping and further processing.

Fig. 5
Fig. 5

Results of application of the algorithm to a rectangular plate with a hole and a cut. The diagram shows the compression force applied.

Tables (2)

Tables Icon

Table 1 Polariscope Configurations and Output Intensities of First Four Images for Isochromatic Calculation

Tables Icon

Table 2 Polariscope Configurations and Output Intensities of Last Four Images for Isochromatic Calculation

Equations (13)

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

I=1-sin 2ψ-φcos δ-sin 2φ-α×cos 2ψ-φsin δ,
sin δI=1cos 2αI1-I2,
cos δI=I4-I3.
WδI=arctanI1-I2I4-I3·1cos 2α.
mII2-I12+I4-I32cos2 2α1/2=cos 2α,
sin δII=1sin 2αI5-I6,
cos δII=I8-I7.
WδII=arctanI5-I6I8-I7·1sin 2α.
mIII6-I52+I8-I72sin2 2α1/2=sin 2α.
Wδ=WδIcos 2αn+WδIIsin 2αncos 2αn+sin 2αn,
I1-I2cos 2α+I5-I6sin 2α=sin δ,
12I4-I3+I8-I7=cos δ,
Wδ=arctanI1-I2cos 2α+I5-I6sin 2α12I4-I3+I8-I7.

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