Abstract

The computation of a continuous map of isochromatic fringe order from an isochromatic phase map or relative retardation based on a photoelastic fringe pattern is a difficult task, particularly when the direction of the principal stress is ambiguous. This happens in most experiments and introduces abrupt changes in the slope of the computed relative retardation map. We present a novel regularized phase-tracking method that at each pixel chooses the unambiguous relative retardation value. This unambiguous relative retardation map is wrapped, however the unwrapping is straightforward and fast using the already known techniques. With the presented method we have been able to process successfully complex experimental data with several isotropic points, high fringe density and low resolution, as is shown in a number of examples.

© 2009 Optical Society of America

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    [CrossRef]
  5. K. Ramesh, Digital Photoelasticity (Springer, 2000).
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    [CrossRef]
  7. M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital phtoelasticity: issue, implementation and application,” Opt. Lasers Eng. 46, 257-271 (2008).
    [CrossRef]
  8. C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
    [CrossRef]
  9. J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
    [CrossRef]
  10. H. Aben, J. Anton, and A. Errapart, “Modern photoelasticity for residual stress measurement in glass,” Strain 44, 40-48 (2008).
    [CrossRef]
  11. J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
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    [CrossRef]
  14. A. Curtis, L. Sokolikova-Csaderova, and G. Aitchison, “Measuring cell forces by a photoelastic method,” Biophys. J. 92, 2255-2261 (2007).
    [CrossRef]
  15. M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
    [CrossRef]
  16. T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
    [CrossRef]
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    [CrossRef]
  19. C. W. Chang, P. H. Chen, and H. S. Lien, “Separation of photoelastic principal tresses by analytical evaluation and digital image processing,” J. Mech. 25 (1), 19-25 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain doi: 10.1111/j.1475-1305.2008.00431.x.
    [CrossRef]
  29. Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
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    [CrossRef]
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  32. J. A. Quiroga, E. Pascual, and J. Villa-Hernandez, “Robust isoclinic calculation for automatic analysis of photoelastic fringe pattern,” Proc. SPIE 7155, 715530 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  36. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

2009

C. W. Chang, P. H. Chen, and H. S. Lien, “Separation of photoelastic principal tresses by analytical evaluation and digital image processing,” J. Mech. 25 (1), 19-25 (2009).
[CrossRef]

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

2008

J. Villa, J. A. Quiroga, and E. Pascual, “Determination of isoclinics in photoelasticity with a fast regularized estimator,” Opt. Lasers Eng. 46, 236-242 (2008).
[CrossRef]

J. A. Quiroga, E. Pascual, and J. Villa-Hernandez, “Robust isoclinic calculation for automatic analysis of photoelastic fringe pattern,” Proc. SPIE 7155, 715530 (2008).
[CrossRef]

L. Ainola and A. Hillar, “On the generalized Wertheim law in integrated photoelasticity,” J. Opt. Soc. Am. A 25, 1843-1849(2008).

T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
[CrossRef]

D. Rajamohan, “Hyperstatic method of photoelasticity,” Exp. Mech. 48, 693-696 (2008).
[CrossRef]

M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital phtoelasticity: issue, implementation and application,” Opt. Lasers Eng. 46, 257-271 (2008).
[CrossRef]

C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
[CrossRef]

H. Aben, J. Anton, and A. Errapart, “Modern photoelasticity for residual stress measurement in glass,” Strain 44, 40-48 (2008).
[CrossRef]

J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
[CrossRef]

M. L. L. Wijerathne, K. Oguni, and M. Hori, “Stress field tomography based on 3D photoelasticity,” J. Mech. Phys. Solids 56 (3), 1065-1085 (2008).
[CrossRef]

2007

A. Curtis, L. Sokolikova-Csaderova, and G. Aitchison, “Measuring cell forces by a photoelastic method,” Biophys. J. 92, 2255-2261 (2007).
[CrossRef]

P. Pinit and E. Umezaki, “Digital whole field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique,” Opt. Lasers Eng. 45, 795-807 (2007).
[CrossRef]

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Phase shifting photoelasticity in white light,” Opt. Lasers Eng. 45, 596-611(2007).
[CrossRef]

2006

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

E. A. Patterson, P. Brailly, and M. Taroni, “High frequency quantitative photoelasticity applied to jet engine components,” Exp. Mech. 46, 661-668 (2006).
[CrossRef]

2005

P. Siegmann, D. Backman, and E. A. Patterson, “A robust approach to demodulating and unwrapping phase-stepped photoelastic data,” Exp. Mech. 45 (3), 278-289 (2005).
[CrossRef]

2002

E. A. Patterson, “Digital photoelasticity: principles, practice and potential,” Strain 38, 27-39 (2002).
[CrossRef]

2001

J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
[CrossRef]

2000

1999

N. Plouzennec, J. C. Depuré, and A. Lagarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Techniques 23, 30-33 (1999).
[CrossRef]

1997

1996

S. J. Haake, Z. F. Wang, and E. A. Patterson, “2D and 3D separation of stresses using automated photoelasticity,” Exp. Mech. 36 (3), 269-276 (1996).
[CrossRef]

1995

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

Z. F. Wang and E. A. Patterson, “Use of phase-stepping with demodulation and fuzzy sets for birefringence measurement,” Opt. Lasers Eng. 22, 91-104 (1995).
[CrossRef]

1991

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

Aben, H.

J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
[CrossRef]

H. Aben, J. Anton, and A. Errapart, “Modern photoelasticity for residual stress measurement in glass,” Strain 44, 40-48 (2008).
[CrossRef]

Aiello, L.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Ainola, L.

L. Ainola and A. Hillar, “On the generalized Wertheim law in integrated photoelasticity,” J. Opt. Soc. Am. A 25, 1843-1849(2008).

J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
[CrossRef]

Aitchison, G.

A. Curtis, L. Sokolikova-Csaderova, and G. Aitchison, “Measuring cell forces by a photoelastic method,” Biophys. J. 92, 2255-2261 (2007).
[CrossRef]

Ajovalasit, A.

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Phase shifting photoelasticity in white light,” Opt. Lasers Eng. 45, 596-611(2007).
[CrossRef]

Angelis, M.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Anton, J.

H. Aben, J. Anton, and A. Errapart, “Modern photoelasticity for residual stress measurement in glass,” Strain 44, 40-48 (2008).
[CrossRef]

J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
[CrossRef]

Asundi, A. K.

A. K. Asundi, MATLAB for Photomechanics: a Primer(Elsevier, 2002).

Backman, D.

P. Siegmann, D. Backman, and E. A. Patterson, “A robust approach to demodulating and unwrapping phase-stepped photoelastic data,” Exp. Mech. 45 (3), 278-289 (2005).
[CrossRef]

Beck, S. B. M.

T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
[CrossRef]

Brailly, P.

E. A. Patterson, P. Brailly, and M. Taroni, “High frequency quantitative photoelasticity applied to jet engine components,” Exp. Mech. 46, 661-668 (2006).
[CrossRef]

Buckberry, C.

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

Burguete, R. L.

J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
[CrossRef]

Chang, C. W.

C. W. Chang, P. H. Chen, and H. S. Lien, “Separation of photoelastic principal tresses by analytical evaluation and digital image processing,” J. Mech. 25 (1), 19-25 (2009).
[CrossRef]

Chen, P. H.

C. W. Chang, P. H. Chen, and H. S. Lien, “Separation of photoelastic principal tresses by analytical evaluation and digital image processing,” J. Mech. 25 (1), 19-25 (2009).
[CrossRef]

Christopher, C. J.

C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
[CrossRef]

Cloud, G.

G. Cloud, Optical Methods of Engineering Analysis (Cambridge University Press, 1998).

Cuevas, F. J.

Curtis, A.

A. Curtis, L. Sokolikova-Csaderova, and G. Aitchison, “Measuring cell forces by a photoelastic method,” Biophys. J. 92, 2255-2261 (2007).
[CrossRef]

Dally, J. W.

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

F. Zandman, S. Redner, and J. W. Dally, Photoelastic Coatings (Iowa State University Press, 1977).

Depuré, J. C.

N. Plouzennec, J. C. Depuré, and A. Lagarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Techniques 23, 30-33 (1999).
[CrossRef]

Errapart, A.

J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
[CrossRef]

H. Aben, J. Anton, and A. Errapart, “Modern photoelasticity for residual stress measurement in glass,” Strain 44, 40-48 (2008).
[CrossRef]

Ferraro, P.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Garrard, A. E.

T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

González-Cano, A.

Haake, S. J.

S. J. Haake, Z. F. Wang, and E. A. Patterson, “2D and 3D separation of stresses using automated photoelasticity,” Exp. Mech. 36 (3), 269-276 (1996).
[CrossRef]

Heyes, P.

J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
[CrossRef]

Hillar, A.

Hobbs, J. W.

J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
[CrossRef]

Hori, M.

M. L. L. Wijerathne, K. Oguni, and M. Hori, “Stress field tomography based on 3D photoelasticity,” J. Mech. Phys. Solids 56 (3), 1065-1085 (2008).
[CrossRef]

James, M. N.

C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
[CrossRef]

Lagarde, A.

N. Plouzennec, J. C. Depuré, and A. Lagarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Techniques 23, 30-33 (1999).
[CrossRef]

Lei, Z.

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

Lien, H. S.

C. W. Chang, P. H. Chen, and H. S. Lien, “Separation of photoelastic principal tresses by analytical evaluation and digital image processing,” J. Mech. 25 (1), 19-25 (2009).
[CrossRef]

Marroquin, J. L.

Natale, P.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Nicola, S.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Oguni, K.

M. L. L. Wijerathne, K. Oguni, and M. Hori, “Stress field tomography based on 3D photoelasticity,” J. Mech. Phys. Solids 56 (3), 1065-1085 (2008).
[CrossRef]

Pan, X.

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

Pascual, E.

J. A. Quiroga, E. Pascual, and J. Villa-Hernandez, “Robust isoclinic calculation for automatic analysis of photoelastic fringe pattern,” Proc. SPIE 7155, 715530 (2008).
[CrossRef]

J. Villa, J. A. Quiroga, and E. Pascual, “Determination of isoclinics in photoelasticity with a fast regularized estimator,” Opt. Lasers Eng. 46, 236-242 (2008).
[CrossRef]

Patterson, E. A.

C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
[CrossRef]

E. A. Patterson, P. Brailly, and M. Taroni, “High frequency quantitative photoelasticity applied to jet engine components,” Exp. Mech. 46, 661-668 (2006).
[CrossRef]

P. Siegmann, D. Backman, and E. A. Patterson, “A robust approach to demodulating and unwrapping phase-stepped photoelastic data,” Exp. Mech. 45 (3), 278-289 (2005).
[CrossRef]

E. A. Patterson, “Digital photoelasticity: principles, practice and potential,” Strain 38, 27-39 (2002).
[CrossRef]

J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
[CrossRef]

S. J. Haake, Z. F. Wang, and E. A. Patterson, “2D and 3D separation of stresses using automated photoelasticity,” Exp. Mech. 36 (3), 269-276 (1996).
[CrossRef]

Z. F. Wang and E. A. Patterson, “Use of phase-stepping with demodulation and fuzzy sets for birefringence measurement,” Opt. Lasers Eng. 22, 91-104 (1995).
[CrossRef]

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

Paturzo, M.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Petrucci, G.

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Phase shifting photoelasticity in white light,” Opt. Lasers Eng. 45, 596-611(2007).
[CrossRef]

Pignatiello, F.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Pinit, P.

P. Pinit and E. Umezaki, “Digital whole field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique,” Opt. Lasers Eng. 45, 795-807 (2007).
[CrossRef]

Plouzennec, N.

N. Plouzennec, J. C. Depuré, and A. Lagarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Techniques 23, 30-33 (1999).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

Quiroga, J. A.

J. Villa, J. A. Quiroga, and E. Pascual, “Determination of isoclinics in photoelasticity with a fast regularized estimator,” Opt. Lasers Eng. 46, 236-242 (2008).
[CrossRef]

J. A. Quiroga, E. Pascual, and J. Villa-Hernandez, “Robust isoclinic calculation for automatic analysis of photoelastic fringe pattern,” Proc. SPIE 7155, 715530 (2008).
[CrossRef]

J. A. Quiroga and A. González-Cano, “Separation of isoclinics and isochromatics from photoelastic data with a regularized phase-tracking technique,” Appl. Opt. 39, 2931-2940 (2000).
[CrossRef]

J. A. Quiroga and A. González-Cano. “Phase measuring algorithm for extraction of isochromatics of photoelastic fringe pattern,” Appl. Opt. 36, 8397-8402 (1997).
[CrossRef]

Rajamohan, D.

D. Rajamohan, “Hyperstatic method of photoelasticity,” Exp. Mech. 48, 693-696 (2008).
[CrossRef]

Ramesh, K.

M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital phtoelasticity: issue, implementation and application,” Opt. Lasers Eng. 46, 257-271 (2008).
[CrossRef]

M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain doi: 10.1111/j.1475-1305.2008.00431.x.
[CrossRef]

K. Ramesh, Digital Photoelasticity (Springer, 2000).
[CrossRef]

Ramji, M.

M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital phtoelasticity: issue, implementation and application,” Opt. Lasers Eng. 46, 257-271 (2008).
[CrossRef]

M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain doi: 10.1111/j.1475-1305.2008.00431.x.
[CrossRef]

Redner, S.

F. Zandman, S. Redner, and J. W. Dally, Photoelastic Coatings (Iowa State University Press, 1977).

Riley, W. F.

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

Scafidi, M.

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Phase shifting photoelasticity in white light,” Opt. Lasers Eng. 45, 596-611(2007).
[CrossRef]

Servin, M.

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P. Siegmann, D. Backman, and E. A. Patterson, “A robust approach to demodulating and unwrapping phase-stepped photoelastic data,” Exp. Mech. 45 (3), 278-289 (2005).
[CrossRef]

Sokolikova-Csaderova, L.

A. Curtis, L. Sokolikova-Csaderova, and G. Aitchison, “Measuring cell forces by a photoelastic method,” Biophys. J. 92, 2255-2261 (2007).
[CrossRef]

Spalton, T.

T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
[CrossRef]

Taroni, M.

E. A. Patterson, P. Brailly, and M. Taroni, “High frequency quantitative photoelasticity applied to jet engine components,” Exp. Mech. 46, 661-668 (2006).
[CrossRef]

Tee, K. F.

C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
[CrossRef]

Tomlinson, R. A.

T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
[CrossRef]

Tower, D.

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

Umezaki, E.

P. Pinit and E. Umezaki, “Digital whole field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique,” Opt. Lasers Eng. 45, 795-807 (2007).
[CrossRef]

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J. Villa, J. A. Quiroga, and E. Pascual, “Determination of isoclinics in photoelasticity with a fast regularized estimator,” Opt. Lasers Eng. 46, 236-242 (2008).
[CrossRef]

Villa-Hernandez, J.

J. A. Quiroga, E. Pascual, and J. Villa-Hernandez, “Robust isoclinic calculation for automatic analysis of photoelastic fringe pattern,” Proc. SPIE 7155, 715530 (2008).
[CrossRef]

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S. J. Haake, Z. F. Wang, and E. A. Patterson, “2D and 3D separation of stresses using automated photoelasticity,” Exp. Mech. 36 (3), 269-276 (1996).
[CrossRef]

Z. F. Wang and E. A. Patterson, “Use of phase-stepping with demodulation and fuzzy sets for birefringence measurement,” Opt. Lasers Eng. 22, 91-104 (1995).
[CrossRef]

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

Wijerathne, M. L. L.

M. L. L. Wijerathne, K. Oguni, and M. Hori, “Stress field tomography based on 3D photoelasticity,” J. Mech. Phys. Solids 56 (3), 1065-1085 (2008).
[CrossRef]

Xing, Y.

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

Yun, H.

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

Zandman, F.

F. Zandman, S. Redner, and J. W. Dally, Photoelastic Coatings (Iowa State University Press, 1977).

Zhao, Y.

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

Appl. Mech. Mater.

T. Spalton, R. A. Tomlinson, A. E. Garrard, and S. B. M. Beck, “Streaming birefringence-a step forward,” Appl. Mech. Mater. 13-14, 23-28 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Paturzo, L. Aiello, F. Pignatiello, P. Ferraro, P. Natale, M. Angelis, and S. Nicola, “Investigation of optical birefringence at ferroelectric domain wall in LiNbO3 by phase-shift polarimetry,” Appl. Phys. Lett. 88, 151918 (2006).
[CrossRef]

Biophys. J.

A. Curtis, L. Sokolikova-Csaderova, and G. Aitchison, “Measuring cell forces by a photoelastic method,” Biophys. J. 92, 2255-2261 (2007).
[CrossRef]

Eng. Fract. Mech.

C. J. Christopher, M. N. James, E. A. Patterson, and K. F. Tee, “A quantitative evaluation of fatigue crack shielding forces using photoelasticity,” Eng. Fract. Mech. 75, 4190-4199(2008).
[CrossRef]

Exp. Mech.

S. J. Haake, Z. F. Wang, and E. A. Patterson, “2D and 3D separation of stresses using automated photoelasticity,” Exp. Mech. 36 (3), 269-276 (1996).
[CrossRef]

D. Rajamohan, “Hyperstatic method of photoelasticity,” Exp. Mech. 48, 693-696 (2008).
[CrossRef]

J. Anton, A. Errapart, H. Aben, and L. Ainola, “A discrete algorithm of integrated photoelasticity for axisymetric problems,” Exp. Mech. 48, 613-620 (2008).
[CrossRef]

P. Siegmann, D. Backman, and E. A. Patterson, “A robust approach to demodulating and unwrapping phase-stepped photoelastic data,” Exp. Mech. 45 (3), 278-289 (2005).
[CrossRef]

E. A. Patterson, P. Brailly, and M. Taroni, “High frequency quantitative photoelasticity applied to jet engine components,” Exp. Mech. 46, 661-668 (2006).
[CrossRef]

Exp. Techniques

N. Plouzennec, J. C. Depuré, and A. Lagarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Techniques 23, 30-33 (1999).
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C. W. Chang, P. H. Chen, and H. S. Lien, “Separation of photoelastic principal tresses by analytical evaluation and digital image processing,” J. Mech. 25 (1), 19-25 (2009).
[CrossRef]

J. Mech. Phys. Solids

M. L. L. Wijerathne, K. Oguni, and M. Hori, “Stress field tomography based on 3D photoelasticity,” J. Mech. Phys. Solids 56 (3), 1065-1085 (2008).
[CrossRef]

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J. Strain Anal. Eng. Des.

J. W. Hobbs, R. L. Burguete, P. Heyes, and E. A. Patterson, “A photoelastic analysis of crescent-shaped cracks in bolts,” J. Strain Anal. Eng. Des. 36 (1), 93-99 (2001).
[CrossRef]

Meas. Sci. Technol.

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

Opt. Lasers Eng

Z. Lei, H. Yun, Y. Zhao, Y. Xing, and X. Pan, “Study of the shear transfer in Al/epoxy joint by digital photoelasticity,” Opt. Lasers Eng 47, 701-707 (2009).
[CrossRef]

Opt. Lasers Eng.

J. Villa, J. A. Quiroga, and E. Pascual, “Determination of isoclinics in photoelasticity with a fast regularized estimator,” Opt. Lasers Eng. 46, 236-242 (2008).
[CrossRef]

P. Pinit and E. Umezaki, “Digital whole field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique,” Opt. Lasers Eng. 45, 795-807 (2007).
[CrossRef]

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Phase shifting photoelasticity in white light,” Opt. Lasers Eng. 45, 596-611(2007).
[CrossRef]

Z. F. Wang and E. A. Patterson, “Use of phase-stepping with demodulation and fuzzy sets for birefringence measurement,” Opt. Lasers Eng. 22, 91-104 (1995).
[CrossRef]

M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital phtoelasticity: issue, implementation and application,” Opt. Lasers Eng. 46, 257-271 (2008).
[CrossRef]

Proc. SPIE

J. A. Quiroga, E. Pascual, and J. Villa-Hernandez, “Robust isoclinic calculation for automatic analysis of photoelastic fringe pattern,” Proc. SPIE 7155, 715530 (2008).
[CrossRef]

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M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain doi: 10.1111/j.1475-1305.2008.00431.x.
[CrossRef]

E. A. Patterson, “Digital photoelasticity: principles, practice and potential,” Strain 38, 27-39 (2002).
[CrossRef]

H. Aben, J. Anton, and A. Errapart, “Modern photoelasticity for residual stress measurement in glass,” Strain 44, 40-48 (2008).
[CrossRef]

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

Other

K. Ramesh, Digital Photoelasticity (Springer, 2000).
[CrossRef]

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

G. Cloud, Optical Methods of Engineering Analysis (Cambridge University Press, 1998).

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A. K. Asundi, MATLAB for Photomechanics: a Primer(Elsevier, 2002).

MATLAB Function Reference at www.mathworks.com/access/helpdesk/help/techdoc/ref/atan2.html.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

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Figures (6)

Fig. 1
Fig. 1

For a disk subject to diametral compression, maps of wrapped (at modulo π) and ambiguous relative retardation obtained from Eq. (3) (a) directly δ w , a + and (b) inverted δ w , a ; (c) quality map Q used in the regularization process with high quality values ( Q = 1 ) in white and low quality values ( Q = 0 ) in black, i.e., intensity or gray level is proportional to quality; (d) profiles along the horizontal diameter (perpendicular to the line of the load) of δ w , a + (continuous black curve), δ w , a (continuous gray curve), δ w (dotted curve), and Q (dashed curve).

Fig. 2
Fig. 2

Map of (a) wrapped (at modulo 2 π ) relative retardation using the common arctangent or arccotangent function in Eq. (3) instead of arctan f ; (b) diametrical profile.

Fig. 3
Fig. 3

For a disk subject to diametral compression, maps of (a) wrapped unambiguous relative retardation δ w from Fig. 1 following the regularization process shown as a gray-scale map; (b) a plot along the diameter perpendicular to the vertical load of δ w (black solid curve), δ w , a + (black broken curve), δ w , a (gray broken curve); (c) unwrapped and unambiguous isochromatic fringe order for the disk shown as a gray-scale map; and (d) plots along the vertical and horizontal diameters of experimental (solid curves) and theoretical (broken curves) data.

Fig. 4
Fig. 4

Maps of (a)  I 1 , the dark-field isochromatic fringe pattern; (b) ambiguous relative retardation, δ w , a + , obtained from Eq. (3); (c) unambiguous (wrapped) relative retardation obtained from the regularization process [Eq. (4)]; and (d) calibrated (unwrapped) isochromatic fringe order for the node and ligaments in an array of cold-worked holes in a plate with a reflection photoelastic coating. The data were supplied by the Institute for Aerospace Research of the Canadian National Research Council (CNRC).

Fig. 5
Fig. 5

Maps of (a)  I 1 , the dark-field isochromatic fringe pattern; (b) the quality map, Q, obtained from Eq. (5); (c) the wrapped and unambiguous relative retardation with a mask over the plastic zone and an arrow pointing to the crack tip location; and (d) the isochromatic fringe order, N, for a fatigue crack in a polycarbonate CT specimen (after [8]).

Fig. 6
Fig. 6

Maps of (a) the dark-field isochromatic fringe pattern I 1 ; (b) the wrapped and unambiguous relative retardation; (c) the isochromatic fringe order N for a C beam loaded in tension.

Equations (12)

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

I 1 = I m I v cos δ , I 2 = I m + I v cos δ , I 3 = I m I v sin δ sin 2 θ , I 4 = I m + I v sin δ cos 2 θ , I 5 = I m + I v sin δ sin 2 θ , I 6 = I m I v sin δ cos 2 θ ,
θ a = 1 2 arctan f ( I 5 I 3 I 4 I 6 ) ,
δ w , a = arctan f [ ( I 5 I 3 ) sin 2 θ a + ( I 4 I 6 ) cos 2 θ a I 1 I 2 ] ,
U Γ ( i ; λ ) = Q ( i ) A Γ ( i ) + 10 λ Q ( i ) B Γ ( i ) ,
Q ( i ) = sin 2 ( δ w , a ( i ) )
A Γ ( i ) = j ( Γ L ) 1 2 π | δ w ( j ) δ w , a ± ( i ) | s ( j ) ,
B Γ ( i ) = j ( Γ L ) ( h δ w ( j ) x h δ w , a ± ( i ) x ) 2 + ( h δ w ( j ) y h δ w , a ± ( i ) y ) 2 s ( j )
h δ ( x , y ) x = δ ( x + h , y ) δ ( x h , y ) 2 h + 1 ,
q ( i ) 1 = 1 k 2 [ j k × k ( Δ j x Δ ¯ i x ) 2 + j k × k ( Δ j y Δ ¯ i y ) 2 ] ,
N ( i ) = δ ( i ) · N p δ ( i p ) .
N = h F σ ( σ 1 σ 2 ) = 4 P R π F σ R 2 ( x 2 y 2 ) ( x 2 + y 2 + R 2 ) 2 4 y 2 R 2 ,
L i N b O 3

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