Abstract

A new technique based on digital shearography for determining the transient curvature and twist of a continuously deforming object from a series of speckle patterns is presented. The intensity variation of each pixel is analyzed along the time axis by using a complex Morlet wavelet transform. The absolute sign of the phase variation is determined by introduction of a temporal carrier when the speckle patterns are captured by a high-speed camera. A high-quality spatial distribution of the deflection derivative is extracted at any instant without the need for temporal or spatial phase unwrapping. The continuous Haar wavelet transform is subsequently processed as a differentiation operator to reconstruct the instantaneous curvature and twist of a continuously deforming object.

© 2005 Optical Society of America

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2005

2004

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, Opt. Eng. 43, 2780 (2004).
[CrossRef]

2003

F. S. Chau and J. Zhou, Opt. Lasers Eng. 39, 431 (2003).
[CrossRef]

2001

J. Fang, C. Y. Xiong, and Z. L. Yang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

1999

1998

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, Opt. Eng. 37, 1790 (1998).
[CrossRef]

1997

Y. Y. Hung, Opt. Lasers Eng. 26, 421 (1997).
[CrossRef]

1996

1995

1994

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Opt. Laser Technol. 26, 91 (1994).
[CrossRef]

1982

Y. Y. Hung, Opt. Eng. 21, 391 (1982).
[CrossRef]

1974

Y. Y. Hung, Opt. Commun. 11, 132 (1974).
[CrossRef]

1973

J. A. Leendertz and J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Barnes, T. H.

Butters, J. N.

J. A. Leendertz and J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Cao, J.

J. Cao and Y. Sun, in Proc. SPIE 2536, 57 (1995).
[CrossRef]

Chau, F. S.

F. S. Chau and J. Zhou, Opt. Lasers Eng. 39, 431 (2003).
[CrossRef]

Chen, L. J.

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, Opt. Eng. 43, 2780 (2004).
[CrossRef]

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992), Chap. 2.
[CrossRef]

Fang, J.

J. Fang, C. Y. Xiong, and Z. L. Yang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Franze, B.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, Opt. Eng. 37, 1790 (1998).
[CrossRef]

Fu, Y.

Y. Fu, C. J. Tay, C. Quan, and H. Miao, Appl. Opt. 44, 959 (2005).
[CrossRef] [PubMed]

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, Opt. Eng. 43, 2780 (2004).
[CrossRef]

Haible, P.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, Opt. Eng. 37, 1790 (1998).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, Opt. Lasers Eng. 26, 421 (1997).
[CrossRef]

Y. Y. Hung, Opt. Lasers Eng. 24, 161 (1996).
[CrossRef]

Y. Y. Hung, Opt. Eng. 21, 391 (1982).
[CrossRef]

Y. Y. Hung, Opt. Commun. 11, 132 (1974).
[CrossRef]

Y. Y. Hung, Trends in Optical Non-Destructive Testing and Inspection (Elsevier, 2000), Chap. 20.

Joenathan, C.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, Opt. Eng. 37, 1790 (1998).
[CrossRef]

Leendertz, J. A.

J. A. Leendertz and J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Lin, Q. Y.

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Appl. Opt. 34, 2202 (1995).
[CrossRef] [PubMed]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Opt. Laser Technol. 26, 91 (1994).
[CrossRef]

Miao, H.

Quan, C.

Y. Fu, C. J. Tay, C. Quan, and H. Miao, Appl. Opt. 44, 959 (2005).
[CrossRef] [PubMed]

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, Opt. Eng. 43, 2780 (2004).
[CrossRef]

Rastogi, P. K.

Shang, H. M.

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Appl. Opt. 34, 2202 (1995).
[CrossRef] [PubMed]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Opt. Laser Technol. 26, 91 (1994).
[CrossRef]

Sun, Y.

J. Cao and Y. Sun, in Proc. SPIE 2536, 57 (1995).
[CrossRef]

Tan, S. M.

Tay, C. J.

Y. Fu, C. J. Tay, C. Quan, and H. Miao, Appl. Opt. 44, 959 (2005).
[CrossRef] [PubMed]

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, Opt. Eng. 43, 2780 (2004).
[CrossRef]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Appl. Opt. 34, 2202 (1995).
[CrossRef] [PubMed]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Opt. Laser Technol. 26, 91 (1994).
[CrossRef]

Tiziani, H. J.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, Opt. Eng. 37, 1790 (1998).
[CrossRef]

Toh, S. L.

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Appl. Opt. 34, 2202 (1995).
[CrossRef] [PubMed]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Opt. Laser Technol. 26, 91 (1994).
[CrossRef]

Watkins, L. R.

Xiong, C. Y.

J. Fang, C. Y. Xiong, and Z. L. Yang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Yang, Z. L.

J. Fang, C. Y. Xiong, and Z. L. Yang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Zhou, J.

F. S. Chau and J. Zhou, Opt. Lasers Eng. 39, 431 (2003).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

J. Fang, C. Y. Xiong, and Z. L. Yang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

J. Phys. E

J. A. Leendertz and J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Opt. Commun.

Y. Y. Hung, Opt. Commun. 11, 132 (1974).
[CrossRef]

Opt. Eng.

Y. Y. Hung, Opt. Eng. 21, 391 (1982).
[CrossRef]

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, Opt. Eng. 37, 1790 (1998).
[CrossRef]

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, Opt. Eng. 43, 2780 (2004).
[CrossRef]

Opt. Laser Technol.

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, Opt. Laser Technol. 26, 91 (1994).
[CrossRef]

Opt. Lasers Eng.

F. S. Chau and J. Zhou, Opt. Lasers Eng. 39, 431 (2003).
[CrossRef]

Y. Y. Hung, Opt. Lasers Eng. 26, 421 (1997).
[CrossRef]

Y. Y. Hung, Opt. Lasers Eng. 24, 161 (1996).
[CrossRef]

Opt. Lett.

Proc. SPIE

J. Cao and Y. Sun, in Proc. SPIE 2536, 57 (1995).
[CrossRef]

Other

Y. Y. Hung, Trends in Optical Non-Destructive Testing and Inspection (Elsevier, 2000), Chap. 20.

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992), Chap. 2.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic layout of a digital shearography setup. (b) Typical shearography fringe pattern and area of interest.

Fig. 2
Fig. 2

Temporal intensity variations of (a) point R on the reference block and of (b) point A and (c) point B on the square plate.

Fig. 3
Fig. 3

Plot of the modulus of the Morlet wavelet transform at (a) point R, (b) point A, (c) point B.

Fig. 4
Fig. 4

Spatial phase distribution at t = 4 s .

Fig. 5
Fig. 5

Reconstructed values of (a) 2 w y 2 and (b) 2 w x y after a continuous Haar wavelet transform.

Equations (6)

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

I x y ( t ) = I 0 x y ( t ) + A x y ( t ) cos [ φ x y ( t ) ] = I 0 x y ( t ) { 1 + V cos [ ϕ 0 x y + ϕ C ( t ) + 4 π w x y ( t ) y δ y λ ] } ,
W S ( a , b ) = + s ( t ) ψ a , b * ( t ) d t ,
ψ a , b ( t ) = 1 a ψ ( t b a ) , b R , a > 0 .
ψ ( t ) = exp ( t 2 2 ) exp ( i ω 0 t ) .
φ x y ( b ) = ω 0 a r b ,
ψ ( x ) = { 1 x [ 0 , 1 2 ) 1 x [ 1 2 , 1 ) 0 x others } .

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