Abstract

In many laboratories of universities and industrial organizations, commercial polariscopes have the feature that the relative position of the two quarter-wave plates is fixed. This is due to the requirement of transforming a plane polariscope to a circular polariscope with greater precision and ease. Unfortunately, these polariscopes cannot implement Patterson and Wang’s [Strain 27, 49–56 (1991)] phase-shifting algorithm because this algorithm requires that the second quarter-wave plate and the analyzer of the circular polariscope be capable of independent rotation. A new phase-shifting method that can be applied under these constraints is proposed. A comparative study with Patterson and Wang’s [Strain 27, 49–56 (1991)] algorithm shows very good agreement. Furthermore, it is shown that four phase steps are sufficient to determine both the isoclinic and the isochromatic parameters.

© 1999 Optical Society of America

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References

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  1. F. W. Hecker, B. Morche, “Computer-aided measurement of relative retardation in plane photoelasticity,” in Experimental Stress Analysis, H. Wieringa, ed. (Martinus Nijhoff, Dordrecht, the Netherlands), pp. 535–542.
  2. E. A. Patterson, Z. F. Wang, “Toward full-field automated photoelastic analysis of complex components,” Strain 27, 49–56 (1991).
    [CrossRef]
  3. A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
    [CrossRef]
  4. A. Asundi, “Phase shifting in photoelasticity,” Exp. Tech. 17, 19–23 (1993).
    [CrossRef]
  5. K. Ramesh, V. Ganapathy, “Phase-shifting methodologies in photoelastic analysis–the application of Jones calculus,” J. Strain Anal. 31, 423–432 (1996).
    [CrossRef]
  6. N. Plouzennec, J.-C. Dupre, A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–32 (1999).
    [CrossRef]

1999

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

1996

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

1993

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

1992

A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
[CrossRef]

1991

E. A. Patterson, Z. F. Wang, “Toward full-field automated photoelastic analysis of complex components,” Strain 27, 49–56 (1991).
[CrossRef]

Asundi, A.

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

Dupre, J.-C.

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

Patterson, E. A.

E. A. Patterson, Z. F. Wang, “Toward full-field automated photoelastic analysis of complex components,” Strain 27, 49–56 (1991).
[CrossRef]

Pillai, S. A.

A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
[CrossRef]

Plouzennec, N.

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

Ramesh, K.

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

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

A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
[CrossRef]

Subramanian, G.

A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
[CrossRef]

Varadan, T. K.

A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
[CrossRef]

Wang, Z. F.

E. A. Patterson, Z. F. Wang, “Toward full-field automated photoelastic analysis of complex components,” Strain 27, 49–56 (1991).
[CrossRef]

Exp. Mech.

A. V. S. S. S. R. Sarma, S. A. Pillai, G. Subramanian, T. K. Varadan, “Computerized image processing for whole-field automated determination of isoclinics and isochromatics,” Exp. Mech. 32, 24–39 (1992).
[CrossRef]

Exp. Tech.

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

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

J. Strain Anal.

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

Strain

E. A. Patterson, Z. F. Wang, “Toward full-field automated photoelastic analysis of complex components,” Strain 27, 49–56 (1991).
[CrossRef]

Other

F. W. Hecker, B. Morche, “Computer-aided measurement of relative retardation in plane photoelasticity,” in Experimental Stress Analysis, H. Wieringa, ed. (Martinus Nijhoff, Dordrecht, the Netherlands), pp. 535–542.

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Figures (8)

Fig. 1
Fig. 1

Optical arrangement required for a general polariscope (φ, ϕ, β all independently adjustable). For a normal circular polariscope, only available settings are φ = ϕ = 45° for circular polariscope and φ = ϕ = 90° for plane polariscope.

Fig. 2
Fig. 2

Direction map (left) and wrapped phase map (right) of a disc under diametral compression: (a) by Patterson and Wang’s2 algorithm, (b) by the author’s algorithm (four steps), (c) by the author’s algorithm (six steps).

Fig. 3
Fig. 3

Comparison between Patterson and Wang’s2 algorithm and the author’s algorithm (six steps): (a) phase distribution along vertical diameter and (b) phase distribution along horizontal diameter.

Fig. 4
Fig. 4

Comparison between the four-step and the six-step methods of the author’s algorithm: (a) phase distribution along vertical diameter and (b) phase distribution along horizontal diameter.

Fig. 5
Fig. 5

Unwrapped full-field phase map of a disc under diametral compression.

Fig. 6
Fig. 6

(a) Unwrapped phase distribution along horizontal diameter. (b) Unwrapped phase distribution along vertical diameter.

Fig. 7
Fig. 7

Contour of phase map (represented by fringe order).

Fig. 8
Fig. 8

Contour of isoclinics.

Tables (2)

Tables Icon

Table 1 Intensity Equations Used in Patterson and Wang’sa Algorithm (φ = 45°)

Tables Icon

Table 2 Summary of Intensity Equations Used in the New Method (ϕ = φ)

Equations (9)

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UV=12cos βsin β-sin βcos β1-cos 2ϕ-i sin 2ϕ-i sin 2ϕ1+i cos 2ϕ×cos δ/2-i sin δ/2 cos 2θ-i sin δ/2 sin 2θ-i sin δ/2 sin 2θcos δ/2+i sin δ/2 cos 2θ1ii101a expiωt,
I=Ib+Imcos δ sin 2β-ϕ-sin δ sin 2θ-ϕ×cos 2ϕ-β,
θ=12tan-1I5-I3I4-I6
δ=tan-12I5-I4/I1-I2sin 2θ-cos 2θ.
UV=12cos βsin β-sin βcos β1-i cos 2φ-i sin 2φ-i sin 2φ1+i cos 2φ×cos δ/2-i sin δ/2 cos 2θ-i sin δ/2 sin 2θ-i sin δ/2 sin 2θcos δ/2+i sin δ/2 cos 2θ×1+i cos 2φi sin 2φi sin 2φ1-i cos 2φ01a expiωt.
I=I0+a2cos2 β sin2 δ/2 sin2 2φ-θ+ sin2 β cos2 δ/2+12sin 2β sin δ sin 2φ-θ+sin2 δ/2 cos2 2θ-φsin2β-2φ,
Ib=12I1+I2,
θ=12tan-1I5-IbI4-Ib
δ=tan-12I4-I5/I1-I2cos 2θ- sin 2θ

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