Abstract

Studies on photoelasticity have been conducted by many researchers in recent years, and many equations for photoelastic analysis based on digital images were proposed. While these equations were all presented by the light intensity emitted from the analyzer, pixel values of the digital image were actually used in the real calculations. In this paper, a proposal of using relative light intensity obtained by the camera response function to replace the pixel value for photoelastic analysis was investigated. Generation of isochromatic images based on relative light intensity and pixel value were compared to evaluate the effectiveness of the new approach. The results showed that when relative light intensity was used, the quality of an isochromatic image can be greatly improved both visually and quantitatively. We believe that the technique proposed in this paper can also be used to improve the performance for the other types of photoelastic analysis using digital images.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Asundi, L. Tong, and C. G. Boay, “Phase-shifting method with a normal polariscope,” Appl. Opt. 38, 5931–5935 (1999).
    [CrossRef]
  2. M. J. Huang and P.-C. Sung, “Regional phase unwrapping algorithm for photoelastic phase map,” Opt. Express 18, 1419–1429 (2010).
    [CrossRef] [PubMed]
  3. P. Pinit and E. Umezaki, “Digitally whole-field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique,” Opt. Lasers Eng. 45, 795–807(2007).
    [CrossRef]
  4. D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
    [CrossRef]
  5. Z. Lei, D. Yun, and W. Yu, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
    [CrossRef]
  6. K. Ramesh and S. K. Mangal, “Data acquisition techniques in digital photoelasticity: a review,” Opt. Lasers Eng. 30, 53–75 (1998).
    [CrossRef]
  7. F. W. Hecker and B. Morche, “Computer-aided measurement of relative retardation in plane photoelasticity,” in Experimental Stress Analysis, H.Wieringa (ed.) (Martinus Nijhoff, 1986), pp. 535–542.
    [CrossRef]
  8. J. Jirousek and A. Venkatesh, “Generation of optimal assumed stress expansions for hybrid-stress elements,” Comput. Struct. 32, 1413–1417 (1989).
    [CrossRef]
  9. S. A. Mueller and F. A. Moslehy, “An image analysis technique for constructing isostatics from isoclinics in photoelasticity,” Proc. SPIE 2066, 53–62 (1993).
    [CrossRef]
  10. C. Buckberry and D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
    [CrossRef]
  11. N. Plouzennec, J. C. Dupre, and A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–33 (1999).
    [CrossRef]
  12. M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1272–1282 (2004).
    [CrossRef]
  13. D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).
  14. P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proc. ACM SIGGRAPH (ACM Press, 1997), pp. 369–378.
  15. G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
    [CrossRef]
  16. F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process. 14, 1138–1150 (2005).
    [CrossRef] [PubMed]

2010 (1)

2007 (2)

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

D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
[CrossRef]

2005 (1)

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process. 14, 1138–1150 (2005).
[CrossRef] [PubMed]

2004 (1)

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1272–1282 (2004).
[CrossRef]

2003 (1)

Z. Lei, D. Yun, and W. Yu, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

1999 (2)

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

N. Plouzennec, J. C. Dupre, and A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–33 (1999).
[CrossRef]

1998 (1)

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

1996 (1)

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

1994 (1)

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

1993 (1)

S. A. Mueller and F. A. Moslehy, “An image analysis technique for constructing isostatics from isoclinics in photoelasticity,” Proc. SPIE 2066, 53–62 (1993).
[CrossRef]

1989 (1)

J. Jirousek and A. Venkatesh, “Generation of optimal assumed stress expansions for hybrid-stress elements,” Comput. Struct. 32, 1413–1417 (1989).
[CrossRef]

Arola, D.

D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
[CrossRef]

Asundi, A.

Boay, C. G.

Buckberry, C.

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

Candocia, F. M.

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process. 14, 1138–1150 (2005).
[CrossRef] [PubMed]

Debevec, P. E.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proc. ACM SIGGRAPH (ACM Press, 1997), pp. 369–378.

Dupre, J. C.

N. Plouzennec, J. C. Dupre, and A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–33 (1999).
[CrossRef]

Forsyth, D. A.

D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

Grossberg, M. D.

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1272–1282 (2004).
[CrossRef]

Han, Y.

D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
[CrossRef]

Healey, G.

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

Hecker, F. W.

F. W. Hecker and B. Morche, “Computer-aided measurement of relative retardation in plane photoelasticity,” in Experimental Stress Analysis, H.Wieringa (ed.) (Martinus Nijhoff, 1986), pp. 535–542.
[CrossRef]

Huang, M. J.

Jirousek, J.

J. Jirousek and A. Venkatesh, “Generation of optimal assumed stress expansions for hybrid-stress elements,” Comput. Struct. 32, 1413–1417 (1989).
[CrossRef]

Kondepudy, R.

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

Lei, Z.

Z. Lei, D. Yun, and W. Yu, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Logarde, A.

N. Plouzennec, J. C. Dupre, and A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–33 (1999).
[CrossRef]

Malik, J.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proc. ACM SIGGRAPH (ACM Press, 1997), pp. 369–378.

Mandarino, D. A.

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process. 14, 1138–1150 (2005).
[CrossRef] [PubMed]

Mangal, S. K.

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

Morche, B.

F. W. Hecker and B. Morche, “Computer-aided measurement of relative retardation in plane photoelasticity,” in Experimental Stress Analysis, H.Wieringa (ed.) (Martinus Nijhoff, 1986), pp. 535–542.
[CrossRef]

Moslehy, F. A.

S. A. Mueller and F. A. Moslehy, “An image analysis technique for constructing isostatics from isoclinics in photoelasticity,” Proc. SPIE 2066, 53–62 (1993).
[CrossRef]

Mueller, S. A.

S. A. Mueller and F. A. Moslehy, “An image analysis technique for constructing isostatics from isoclinics in photoelasticity,” Proc. SPIE 2066, 53–62 (1993).
[CrossRef]

Nayar, S. K.

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1272–1282 (2004).
[CrossRef]

Pinit, P.

P. Pinit and E. Umezaki, “Digitally 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. Dupre, and A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–33 (1999).
[CrossRef]

Ponce, J.

D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

Ramesh, K.

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

Sung, P.-C.

Tong, L.

Towers, D.

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

Umezaki, E.

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

Venkatesh, A.

J. Jirousek and A. Venkatesh, “Generation of optimal assumed stress expansions for hybrid-stress elements,” Comput. Struct. 32, 1413–1417 (1989).
[CrossRef]

Yu, W.

Z. Lei, D. Yun, and W. Yu, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Yun, D.

Z. Lei, D. Yun, and W. Yu, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Zhang, B.

D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
[CrossRef]

Zhang, D.

D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
[CrossRef]

Appl. Opt. (1)

Comput. Struct. (1)

J. Jirousek and A. Venkatesh, “Generation of optimal assumed stress expansions for hybrid-stress elements,” Comput. Struct. 32, 1413–1417 (1989).
[CrossRef]

Exp. Tech. (1)

N. Plouzennec, J. C. Dupre, and A. Logarde, “Whole field determination of isoclinic and isochromatic parameters,” Exp. Tech. 23, 30–33 (1999).
[CrossRef]

IEEE Trans. Image Process. (1)

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process. 14, 1138–1150 (2005).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Machine Intell. (2)

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1272–1282 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (5)

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

D. Zhang, Y. Han, B. Zhang, and D. Arola, “Automatic determination of parameters in photoelasticity,” Opt. Lasers Eng. 45, 860–867 (2007).
[CrossRef]

Z. Lei, D. Yun, and W. Yu, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

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

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

Proc. SPIE (1)

S. A. Mueller and F. A. Moslehy, “An image analysis technique for constructing isostatics from isoclinics in photoelasticity,” Proc. SPIE 2066, 53–62 (1993).
[CrossRef]

Other (3)

F. W. Hecker and B. Morche, “Computer-aided measurement of relative retardation in plane photoelasticity,” in Experimental Stress Analysis, H.Wieringa (ed.) (Martinus Nijhoff, 1986), pp. 535–542.
[CrossRef]

D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proc. ACM SIGGRAPH (ACM Press, 1997), pp. 369–378.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Plane polariscope constructed in crossed-axes configuration with the polarizer and analyzer maintaining perpendicular to each other in the experiment.

Fig. 2
Fig. 2

Circular polariscope built by inserting two quarter-wave plates into the plane polariscope without moving any devices.

Fig. 3
Fig. 3

Response curve of the Nikon-D40 camera used in our experiment.

Fig. 4
Fig. 4

Dark-field images captured by (a) plane polariscope ( Z β = 0 ), (b) plane polariscope ( Z β = π / 4 ), (c) circular polariscope (standard isochromatic image Z S ).

Fig. 5
Fig. 5

(a) Adjusted combined isochromatic image Z 1 (traditional linear CRF approach). (b) Adjusted combined isochromatic image Z 2 (proposed nonlinear CRF approach).

Fig. 6
Fig. 6

Green channels of images Z 1 , Z 2 , and Z S .

Fig. 7
Fig. 7

Values of SNR m s 1 and SNR m s 2 computed for images Z 1 and Z 2 , respectively, captured under different exposure times.

Tables (1)

Tables Icon

Table 1 The Characteristics of the Images Z 1 and Z 2 Captured Under Four Different Exposure Times a

Equations (24)

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

I = I P sin 2 δ 2 sin 2 2 ( α β ) ,
I β = 0 = I P sin 2 δ 2 sin 2 2 α , I β = π / 4 = I P sin 2 δ 2 cos 2 2 α .
I C h = I β = 0 + I β = π / 4 = I P sin 2 δ 2 .
I C h = I C sin 2 δ 2 ,
Z = f C ( X ) = f C ( E Δ t ) .
E L I E = s I ,
Z = f C ( X ) = f C ( s I Δ t ) I = f C 1 ( Z ) s Δ t .
Z = k 1 X = k 1 s I Δ t = k 1 s Δ t I P sin 2 δ 2 sin 2 2 ( α β ) .
Z β = 0 = k 1 s Δ t I β = 0 = k 1 s Δ t I P sin 2 δ 2 sin 2 2 α , Z β = π / 4 = k 1 s Δ t I β = π / 4 = k 1 s Δ t I P sin 2 δ 2 cos 2 2 α .
Z C h 1 = Z β = 0 + Z β = π / 4 = k 1 s Δ t I C h = k 1 s Δ t I P sin 2 δ 2 .
Z S = k 1 s Δ t I C h = k 1 s Δ t I C sin 2 ( δ 2 ) .
Z max 1 = k 1 s Δ t I P , Z max S = k 1 s Δ t I C .
Z 1 = Z C h 1 I C I P = Z C h 1 Z max S Z max 1 = Z S .
Z = f C ( s Δ t I P sin 2 δ 2 sin 2 2 ( α β ) ) ,
I = I P sin 2 δ 2 sin 2 2 ( α β ) = f C 1 ( Z ) s Δ t .
Z S = f C ( s Δ t I C h ) = f C ( s Δ t I C sin 2 δ 2 ) .
I β = 0 = f C 1 ( Z β = 0 ) s Δ t , I β = π / 4 = f C 1 ( Z β = π / 4 ) s Δ t .
I C h = f C 1 ( Z β = 0 ) + f C 1 ( Z β = π / 4 ) s Δ t .
Z C h 2 = f C ( s Δ t I C h ) = f C [ f C 1 ( Z β = 0 ) + f C 1 ( Z β = π / 4 ) ] .
Z max 2 = f C ( s Δ t I P ) I P = f C 1 ( Z max 2 ) s Δ t .
Z max S = f C ( s Δ t I C ) I C = f C 1 ( Z max S ) s Δ t .
A = I C I P = f C 1 ( Z max S ) f C 1 ( Z max 2 ) .
Z 2 = f C [ A · s Δ t I C h ] = f C [ A · ( f C 1 ( Z β = 0 ) + f C 1 ( Z β = π / 4 ) ) ] = f C [ A · s Δ t I P sin 2 δ 2 ] = Z S .
SNR m s 1 = x = 1 M y = 1 N Z 1 ( x , y ) 2 x = 1 M y = 1 N [ Z 1 ( x , y ) Z S ( x , y ) ] 2 , SNR m s 2 = x = 1 M y = 1 N Z 2 ( x , y ) 2 x = 1 M y = 1 N [ Z 2 ( x , y ) Z S ( x , y ) ] 2 ,

Metrics