Abstract

Previous phase-shifting schemes in computer-aided photoelasticity required the processing of six fringe patterns to derive the phase difference due to retardation. A technique in which a carrier fringe is used is demonstrated to reduce to four the number of fringe patterns required. The use of fewer fringe patterns lowers the computation time and the number of phase-step errors. The basis of the technique is outlined in detail, and experimental results are presented as well.

© 1997 Optical Society of America

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References

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  1. A. Kuske, G. Robertson, Photoelastic Stress Analysis (Wiley, London, 1974).
  2. D. Post, “Developments in moiré interferometry,” Opt. Eng. 21, 458–467 (1982).
    [CrossRef]
  3. C. Wykes, R. Jones, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).
  4. A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the techniques,” Exp. Mech. 28, 252–257 (1989).
    [CrossRef]
  5. S. J. Haake, E. A. Patterson, “Photoelastic analysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
    [CrossRef]
  6. J. Carazo-Alvarez, S. J. Haake, E. A. Patterson, “Completely automated photoelastic fringe analysis,” Opt. Lasers Eng. 21, 133–149 (1994).
    [CrossRef]
  7. T. W. Ng, “Derivation of phase in computer-aided photoelasticity,” Opt. Lett. 20, 669–670 (1995).
    [CrossRef] [PubMed]
  8. C. Quan, P. J. Bryanston-Cross, T. R. Judge, “Photoelasticity stress analysis using carrier fringe and FFT techniques,” Opt. Lasers Eng. 18, 79–108 (1993).
    [CrossRef]
  9. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform method of fringe pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  10. T. W. Ng, “High-speed phase-shift computation using dynamic memory processing,” Opt. Eng. 35, 3482–3484 (1996).
    [CrossRef]
  11. D. W. Robinson, “Phase unwrapping methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 194–229.

1996 (1)

T. W. Ng, “High-speed phase-shift computation using dynamic memory processing,” Opt. Eng. 35, 3482–3484 (1996).
[CrossRef]

1995 (1)

1994 (1)

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

1993 (1)

C. Quan, P. J. Bryanston-Cross, T. R. Judge, “Photoelasticity stress analysis using carrier fringe and FFT techniques,” Opt. Lasers Eng. 18, 79–108 (1993).
[CrossRef]

1992 (1)

S. J. Haake, E. A. Patterson, “Photoelastic analysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

1989 (1)

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the techniques,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

1982 (2)

Bryanston-Cross, P. J.

C. Quan, P. J. Bryanston-Cross, T. R. Judge, “Photoelasticity stress analysis using carrier fringe and FFT techniques,” Opt. Lasers Eng. 18, 79–108 (1993).
[CrossRef]

Carazo-Alvarez, J.

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

Haake, S. J.

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

S. J. Haake, E. A. Patterson, “Photoelastic analysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

Ina, H.

Jones, R.

C. Wykes, R. Jones, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).

Judge, T. R.

C. Quan, P. J. Bryanston-Cross, T. R. Judge, “Photoelasticity stress analysis using carrier fringe and FFT techniques,” Opt. Lasers Eng. 18, 79–108 (1993).
[CrossRef]

Kobayashi, S.

Kuske, A.

A. Kuske, G. Robertson, Photoelastic Stress Analysis (Wiley, London, 1974).

Ng, T. W.

T. W. Ng, “High-speed phase-shift computation using dynamic memory processing,” Opt. Eng. 35, 3482–3484 (1996).
[CrossRef]

T. W. Ng, “Derivation of phase in computer-aided photoelasticity,” Opt. Lett. 20, 669–670 (1995).
[CrossRef] [PubMed]

Patterson, E. A.

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

S. J. Haake, E. A. Patterson, “Photoelastic analysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

Post, D.

D. Post, “Developments in moiré interferometry,” Opt. Eng. 21, 458–467 (1982).
[CrossRef]

Quan, C.

C. Quan, P. J. Bryanston-Cross, T. R. Judge, “Photoelasticity stress analysis using carrier fringe and FFT techniques,” Opt. Lasers Eng. 18, 79–108 (1993).
[CrossRef]

Redner, A. S.

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the techniques,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

Robertson, G.

A. Kuske, G. Robertson, Photoelastic Stress Analysis (Wiley, London, 1974).

Robinson, D. W.

D. W. Robinson, “Phase unwrapping methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 194–229.

Takeda, M.

Voloshin, A. S.

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the techniques,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

Wykes, C.

C. Wykes, R. Jones, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).

Exp. Mech. (2)

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the techniques,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

S. J. Haake, E. A. Patterson, “Photoelastic analysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

D. Post, “Developments in moiré interferometry,” Opt. Eng. 21, 458–467 (1982).
[CrossRef]

T. W. Ng, “High-speed phase-shift computation using dynamic memory processing,” Opt. Eng. 35, 3482–3484 (1996).
[CrossRef]

Opt. Lasers Eng. (2)

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

C. Quan, P. J. Bryanston-Cross, T. R. Judge, “Photoelasticity stress analysis using carrier fringe and FFT techniques,” Opt. Lasers Eng. 18, 79–108 (1993).
[CrossRef]

Opt. Lett. (1)

Other (3)

A. Kuske, G. Robertson, Photoelastic Stress Analysis (Wiley, London, 1974).

D. W. Robinson, “Phase unwrapping methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 194–229.

C. Wykes, R. Jones, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for the carrier fringe phase-shifting technique in computer-aided photoelasticity.

Fig. 2
Fig. 2

Optical paths involved in fringe-pattern formation in photoelasticity by using the circular polarizing mode.

Fig. 3
Fig. 3

Schematic description of a crystalline quartz wedge.

Fig. 4
Fig. 4

Photoelastic fringe pattern of the wedge and specimen in the (a) bright-field and (b) dark-field mode before wedge translation as well as in the (c) bright-field and (d) dark-field mode after wedge translation.

Fig. 5
Fig. 5

Retardation phase distribution, measuring 0–2π rad, of the fringe pattern derived by using the carrier fringe phase-shifting technique.

Fig. 6
Fig. 6

Retardation phase of the specimen alone, measuring 0–2π rad, obtained by subtracting from the linear phase distribution of the wedge in the x direction.

Equations (22)

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

X=a cos ωt2,
Y=a sin ωt2,
X=a cosωt+α2,
Y=a sin ωt2.
x=X cos β+Y sin β,
y=Y cos β-X sin β.
x=acos β cosωt+α+sin β sin ωt2,
y=acos β cos ωt+sinβ sin ωt+α2.
x=x-y2=acosβ+ωt+α-cosβ+ωt2=acosβ+α-cos β2=acos α-1cos β-sin α sin β2,
a0x=acos α-12+sin2 α21/2=a1-cos α1/2=a sinα/22.
y=x+y2=acosβ-ωt-α+cosβ-ωt2=acosβ-α+cos β2=acos α+1cos β+sin α sin β2,
a0y=acos α+12+sin2 α21/2=a1+cos α1/2=a cosα/22.
IOx=a22 sin2α2=a241-cos α,
IOy=a22 cos2α2=a241+cos α,
I=IOy-IOx=a22 cosα.
I=a22 cosαw+αs.
I=a2 cosαs+αw+π/2=-a2 sinαs+αw.
αs+αw=-tan-1II.
αw=2πλdne-n0,
π2=2πλd-dne-no
d-d=λ4ne-no.
x=d-dtan θ=λ4tan θne-no.

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