Abstract

The application of phase-shifting photoelasticity to a real-time dynamic event involves simultaneous recording of the four phase-shifted images. Here an instrument, believed to be novel, is developed and described for this purpose. Use of a Multispec Imager is introduced into digital photoelasticity for the first time to our knowledge. This device enables splitting the optical energy of an object into four identical paths, thus permitting recording of the required four phase-shifted images. Experimental demonstration is provided for validation.

© 2001 Optical Society of America

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References

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  1. K. Ramesh, S. K. Mangal, “Data acquisition techniques in digital photoelasticity: a review,” Opt. Lasers Eng. 30, 53–75 (1998).
    [CrossRef]
  2. N. Plouzennec, J.-C. Dupré, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
    [CrossRef]
  3. K. Ramesh, V. Ganapathy, “Phase-shifting methodologies in photoelastic analysis—the application of Jones calculus,” J. Strain Anal. 31, 423–432 (1996).
    [CrossRef]
  4. A. Asundi, Liu Tong, Chai Gin Boay, “Phase-shifting method with a normal polariscope,” Appl. Opt. 38, 5931–5935 (1999).
    [CrossRef]
  5. C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
    [CrossRef]
  6. A. D. Nurse, “Full-field automated photoelasticity using a three-wavelength approach to phase stepping,” Appl. Opt. 36, 5781–5786 (1997).
    [CrossRef] [PubMed]
  7. M. J. Ekman, A. D. Nurse, “Absolute determination of the isochromatic parameter by load-stepping photoelasticity,” Exp. Mech. 38, 189–195 (1998).
    [CrossRef]
  8. M. J. Ekman, A. D. Nurse, “Completely automated determination of two-dimenstional photoelastic parameters using load stepping,” Opt. Eng. 37, 1845–1851 (1998).
    [CrossRef]
  9. A. Asundi, Liu Tong, Chai Gin Boay, “Determination of isoclinic and isochromatic parameters using three-load method,” Meas. Sci. Technol. 11, 532–537 (2000).
    [CrossRef]
  10. E. A. Patterson, Z. F. Wang, “Simultaneous observation of phase-stepped images for automated photoelasticity,” J. Strain Anal. 33, 1–15 (1998).
    [CrossRef]
  11. L. Tong, A. Asundi, C. G. Boay, “Full-field automated photoelasticity using two-load-step method,” Opt. Eng. (2001) (to be published).
  12. A. Asundi, M. R. Sajan, “Digital dynamic visualization system,” in Advances in Mechanical Engineering (ICAME), T. S. Mruthyunjaya, ed. (Indian Institute of Science, Bangalore, India, 1996), Vol. 2, pp. 1331–1350.

2000 (1)

A. Asundi, Liu Tong, Chai Gin Boay, “Determination of isoclinic and isochromatic parameters using three-load method,” Meas. Sci. Technol. 11, 532–537 (2000).
[CrossRef]

1999 (2)

N. Plouzennec, J.-C. Dupré, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
[CrossRef]

A. Asundi, Liu Tong, Chai Gin Boay, “Phase-shifting method with a normal polariscope,” Appl. Opt. 38, 5931–5935 (1999).
[CrossRef]

1998 (4)

M. J. Ekman, A. D. Nurse, “Absolute determination of the isochromatic parameter by load-stepping photoelasticity,” Exp. Mech. 38, 189–195 (1998).
[CrossRef]

M. J. Ekman, A. D. Nurse, “Completely automated determination of two-dimenstional photoelastic parameters using load stepping,” Opt. Eng. 37, 1845–1851 (1998).
[CrossRef]

E. A. Patterson, Z. F. Wang, “Simultaneous observation of phase-stepped images for automated photoelasticity,” J. Strain Anal. 33, 1–15 (1998).
[CrossRef]

K. Ramesh, S. K. Mangal, “Data acquisition techniques in digital photoelasticity: a review,” Opt. Lasers Eng. 30, 53–75 (1998).
[CrossRef]

1997 (1)

1996 (2)

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

K. Ramesh, V. Ganapathy, “Phase-shifting methodologies in photoelastic analysis—the application of Jones calculus,” J. Strain Anal. 31, 423–432 (1996).
[CrossRef]

Asundi, A.

A. Asundi, Liu Tong, Chai Gin Boay, “Determination of isoclinic and isochromatic parameters using three-load method,” Meas. Sci. Technol. 11, 532–537 (2000).
[CrossRef]

A. Asundi, Liu Tong, Chai Gin Boay, “Phase-shifting method with a normal polariscope,” Appl. Opt. 38, 5931–5935 (1999).
[CrossRef]

L. Tong, A. Asundi, C. G. Boay, “Full-field automated photoelasticity using two-load-step method,” Opt. Eng. (2001) (to be published).

A. Asundi, M. R. Sajan, “Digital dynamic visualization system,” in Advances in Mechanical Engineering (ICAME), T. S. Mruthyunjaya, ed. (Indian Institute of Science, Bangalore, India, 1996), Vol. 2, pp. 1331–1350.

Boay, C. G.

L. Tong, A. Asundi, C. G. Boay, “Full-field automated photoelasticity using two-load-step method,” Opt. Eng. (2001) (to be published).

Boay, Chai Gin

A. Asundi, Liu Tong, Chai Gin Boay, “Determination of isoclinic and isochromatic parameters using three-load method,” Meas. Sci. Technol. 11, 532–537 (2000).
[CrossRef]

A. Asundi, Liu Tong, Chai Gin Boay, “Phase-shifting method with a normal polariscope,” Appl. Opt. 38, 5931–5935 (1999).
[CrossRef]

Buckberry, C.

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

Dupré, J.-C.

N. Plouzennec, J.-C. Dupré, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
[CrossRef]

Ekman, M. J.

M. J. Ekman, A. D. Nurse, “Completely automated determination of two-dimenstional photoelastic parameters using load stepping,” Opt. Eng. 37, 1845–1851 (1998).
[CrossRef]

M. J. Ekman, A. D. Nurse, “Absolute determination of the isochromatic parameter by load-stepping photoelasticity,” Exp. Mech. 38, 189–195 (1998).
[CrossRef]

Ganapathy, V.

K. Ramesh, V. Ganapathy, “Phase-shifting methodologies in photoelastic analysis—the application of Jones calculus,” J. Strain Anal. 31, 423–432 (1996).
[CrossRef]

Logarde, A.

N. Plouzennec, J.-C. Dupré, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
[CrossRef]

Mangal, S. K.

K. Ramesh, S. K. Mangal, “Data acquisition techniques in digital photoelasticity: a review,” Opt. Lasers Eng. 30, 53–75 (1998).
[CrossRef]

Nurse, A. D.

M. J. Ekman, A. D. Nurse, “Absolute determination of the isochromatic parameter by load-stepping photoelasticity,” Exp. Mech. 38, 189–195 (1998).
[CrossRef]

M. J. Ekman, A. D. Nurse, “Completely automated determination of two-dimenstional photoelastic parameters using load stepping,” Opt. Eng. 37, 1845–1851 (1998).
[CrossRef]

A. D. Nurse, “Full-field automated photoelasticity using a three-wavelength approach to phase stepping,” Appl. Opt. 36, 5781–5786 (1997).
[CrossRef] [PubMed]

Patterson, E. A.

E. A. Patterson, Z. F. Wang, “Simultaneous observation of phase-stepped images for automated photoelasticity,” J. Strain Anal. 33, 1–15 (1998).
[CrossRef]

Plouzennec, N.

N. Plouzennec, J.-C. Dupré, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
[CrossRef]

Ramesh, K.

K. Ramesh, S. K. Mangal, “Data acquisition techniques in digital photoelasticity: a review,” Opt. Lasers Eng. 30, 53–75 (1998).
[CrossRef]

K. Ramesh, V. Ganapathy, “Phase-shifting methodologies in photoelastic analysis—the application of Jones calculus,” J. Strain Anal. 31, 423–432 (1996).
[CrossRef]

Sajan, M. R.

A. Asundi, M. R. Sajan, “Digital dynamic visualization system,” in Advances in Mechanical Engineering (ICAME), T. S. Mruthyunjaya, ed. (Indian Institute of Science, Bangalore, India, 1996), Vol. 2, pp. 1331–1350.

Tong, L.

L. Tong, A. Asundi, C. G. Boay, “Full-field automated photoelasticity using two-load-step method,” Opt. Eng. (2001) (to be published).

Tong, Liu

A. Asundi, Liu Tong, Chai Gin Boay, “Determination of isoclinic and isochromatic parameters using three-load method,” Meas. Sci. Technol. 11, 532–537 (2000).
[CrossRef]

A. Asundi, Liu Tong, Chai Gin Boay, “Phase-shifting method with a normal polariscope,” Appl. Opt. 38, 5931–5935 (1999).
[CrossRef]

Towers, D.

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

Wang, Z. F.

E. A. Patterson, Z. F. Wang, “Simultaneous observation of phase-stepped images for automated photoelasticity,” J. Strain Anal. 33, 1–15 (1998).
[CrossRef]

Appl. Opt. (2)

Exp. Mech. (1)

M. J. Ekman, A. D. Nurse, “Absolute determination of the isochromatic parameter by load-stepping photoelasticity,” Exp. Mech. 38, 189–195 (1998).
[CrossRef]

Exp. Tech. (1)

N. Plouzennec, J.-C. Dupré, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
[CrossRef]

J. Strain Anal. (2)

K. Ramesh, V. Ganapathy, “Phase-shifting methodologies in photoelastic analysis—the application of Jones calculus,” J. Strain Anal. 31, 423–432 (1996).
[CrossRef]

E. A. Patterson, Z. F. Wang, “Simultaneous observation of phase-stepped images for automated photoelasticity,” J. Strain Anal. 33, 1–15 (1998).
[CrossRef]

Meas. Sci. Technol. (1)

A. Asundi, Liu Tong, Chai Gin Boay, “Determination of isoclinic and isochromatic parameters using three-load method,” Meas. Sci. Technol. 11, 532–537 (2000).
[CrossRef]

Opt. Eng. (1)

M. J. Ekman, A. D. Nurse, “Completely automated determination of two-dimenstional photoelastic parameters using load stepping,” Opt. Eng. 37, 1845–1851 (1998).
[CrossRef]

Opt. Lasers Eng. (2)

K. Ramesh, S. K. Mangal, “Data acquisition techniques in digital photoelasticity: a review,” Opt. Lasers Eng. 30, 53–75 (1998).
[CrossRef]

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

Other (2)

L. Tong, A. Asundi, C. G. Boay, “Full-field automated photoelasticity using two-load-step method,” Opt. Eng. (2001) (to be published).

A. Asundi, M. R. Sajan, “Digital dynamic visualization system,” in Advances in Mechanical Engineering (ICAME), T. S. Mruthyunjaya, ed. (Indian Institute of Science, Bangalore, India, 1996), Vol. 2, pp. 1331–1350.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the new observation system for a real-time event.

Fig. 2
Fig. 2

Picture of the multiple imager and the slide for holding quarter-wave plate and analyzer.

Fig. 3
Fig. 3

Schematic diagram of a C-shaped specimen under vertical compression.

Fig. 4
Fig. 4

Four configurations of the second quarter-wave plate and the analyzer when the axis of the polarizer and the fast axis of the first quarter-wave plate are set as in Fig. 1. Q2, slow axis of the second quarter-wave plate; A, analyzer. The arrangements of (a), (b), (c), and (d) correspond to Eqs. (1), (2), (3), and (4).

Fig. 5
Fig. 5

Schematic diagram of separating the four subimages in an original image into four individual images.

Fig. 6
Fig. 6

Three samples captured at different times in a loading circle. The subimages are arranged consistently with the configurations of quarter-wave plate and analyzer in Fig. 4.

Fig. 7
Fig. 7

(a) Isochromatic map and (b) isoclinic map obtained by use of the phase-shifting technique on one load image. (c) Corrected isoclinic map by use of the two-load-step to phase-shifting technique.

Fig. 8
Fig. 8

Isochromatic maps for the three samples obtained by use of the two-load-step to phase-shifting method.

Fig. 9
Fig. 9

Unwrapped phase maps of the three examples and their distributions along the same line. The fringe orders at the end points of specimen are given for comparison.

Equations (9)

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I1i=I0i+Imi cos δi,
I2i=I0i-Imi cos δi,
I3i=I0i+Imi sin δi cos 2θ,
I4i=I0i+Imi sin δi sin 2θ,
I0i=I1i+I2i/2,
θi=12arctanI3i-I0iI4i-I0i,
δi=arctanI4i-I0iI1i-I2isin 2θi.
θti=θi-π4θiπ4δti=δi-πδiπ when 0<δ2-δ1<πor δ1-δ2>π,
θti=θi±π2-π4θiπ4δti=-δi-πδiπ when 0<δ1-δ2<πor δ2-δ1>π,

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