Abstract

A dynamic electronic speckle pattern interferometry method is applied to investigate thermal expansion of a joint material (ceramic–stainless steel) as a practical industrial object. The speckle interference signal is considered in the temporal domain and the phase is analyzed by the Hilbert transform method. Errors caused by the bias and modulation variations over the phase values are first examined by numerical simulation. Two experiments are performed with in-plane and out-of-plane sensitive systems to study the 3D deformation field thoroughly. The deformation field showed clearly the difference between the thermal expansions of the stainless steel and ceramic. It was also revealed that the boundary of materials and its vicinity suffer very large thermal strain due to the significantly large difference in the linear coefficient of thermal expansions.

© 2006 Optical Society of America

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References

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  1. R. S. Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).
  2. P. K. Rastogi, ed., Photomechanics (Springer-Verlag, 1999).
  3. P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).
  4. D. W. Robinson and C. R. Raed, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, 1993).
  5. J. M. Huntley, G. H. Kaufmann, and D. Kerr, "Phase-shifted dynamic speckle pattern interferometry at 1 kHz," Appl. Opt. 38, 6556-6563 (1999).
    [CrossRef]
  6. C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Speckle interferometry with temporal phase evaluation for measuring large-object deformation," Appl. Opt. 37, 2608-2614 (1998).
    [CrossRef]
  7. G. H. Kaufmann and G. E. Galizzi, "Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and Fourier transform methods," Appl. Opt. 41, 7254-7263 (2002).
    [CrossRef] [PubMed]
  8. V. Madjarova, H. Kadono, and S. Toyooka, "Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform," Opt. Express 11, 617-623 (2003).
    [CrossRef] [PubMed]
  9. Stefan L. Hahn, Hilbert Transform in Signal Processing (Artech House, 1996).
  10. Y. Arai, E. Tsuchida, and J. Miyagaki, "A fractographic study of an edge crack growth near a ceramic-metal interface," in Proceedings of the 11th International Conference on Experimental Mechanics (A. A. Balkema, 1998), pp. 1249-1254.
  11. S. K. Mitra, Digital Signal Processing: A Computer-Based Approach (McGraw-Hill, 2002).
  12. MATLAB Signal Processing Toolbox: User's Guide (The Math-Works, 1996), www.mathworks.com.
  13. V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
    [CrossRef]

2003 (1)

2002 (2)

V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
[CrossRef]

G. H. Kaufmann and G. E. Galizzi, "Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and Fourier transform methods," Appl. Opt. 41, 7254-7263 (2002).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

Arai, Y.

Y. Arai, E. Tsuchida, and J. Miyagaki, "A fractographic study of an edge crack growth near a ceramic-metal interface," in Proceedings of the 11th International Conference on Experimental Mechanics (A. A. Balkema, 1998), pp. 1249-1254.

Franze, B.

Galizzi, G. E.

Hahn, Stefan L.

Stefan L. Hahn, Hilbert Transform in Signal Processing (Artech House, 1996).

Haible, P.

Huntley, J. M.

Joenathan, C.

Kadono, H.

V. Madjarova, H. Kadono, and S. Toyooka, "Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform," Opt. Express 11, 617-623 (2003).
[CrossRef] [PubMed]

V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
[CrossRef]

Kaufmann, G. H.

Kerr, D.

Madjarova, V.

V. Madjarova, H. Kadono, and S. Toyooka, "Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform," Opt. Express 11, 617-623 (2003).
[CrossRef] [PubMed]

V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
[CrossRef]

Mitra, S. K.

S. K. Mitra, Digital Signal Processing: A Computer-Based Approach (McGraw-Hill, 2002).

Miyagaki, J.

Y. Arai, E. Tsuchida, and J. Miyagaki, "A fractographic study of an edge crack growth near a ceramic-metal interface," in Proceedings of the 11th International Conference on Experimental Mechanics (A. A. Balkema, 1998), pp. 1249-1254.

Raed, C. R.

D. W. Robinson and C. R. Raed, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, 1993).

Rastogi, P. K.

P. K. Rastogi, ed., Photomechanics (Springer-Verlag, 1999).

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

Robinson, D. W.

D. W. Robinson and C. R. Raed, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, 1993).

Sirohi, R. S.

R. S. Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).

Tiziani, H. J.

Toyooka, S.

V. Madjarova, H. Kadono, and S. Toyooka, "Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform," Opt. Express 11, 617-623 (2003).
[CrossRef] [PubMed]

V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
[CrossRef]

Tsuchida, E.

Y. Arai, E. Tsuchida, and J. Miyagaki, "A fractographic study of an edge crack growth near a ceramic-metal interface," in Proceedings of the 11th International Conference on Experimental Mechanics (A. A. Balkema, 1998), pp. 1249-1254.

Widiastuti, R.

V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
[CrossRef]

Appl. Opt. (3)

Opt. Commun. (1)

V. Madjarova, S. Toyooka, R. Widiastuti, and H. Kadono, "Dynamic ESPI with subtraction-addition method for obtaining the phase," Opt. Commun. 212, 35-43 (2002).
[CrossRef]

Opt. Express (1)

Other (8)

R. S. Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).

P. K. Rastogi, ed., Photomechanics (Springer-Verlag, 1999).

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

D. W. Robinson and C. R. Raed, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, 1993).

Stefan L. Hahn, Hilbert Transform in Signal Processing (Artech House, 1996).

Y. Arai, E. Tsuchida, and J. Miyagaki, "A fractographic study of an edge crack growth near a ceramic-metal interface," in Proceedings of the 11th International Conference on Experimental Mechanics (A. A. Balkema, 1998), pp. 1249-1254.

S. K. Mitra, Digital Signal Processing: A Computer-Based Approach (McGraw-Hill, 2002).

MATLAB Signal Processing Toolbox: User's Guide (The Math-Works, 1996), www.mathworks.com.

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Figures (10)

Fig. 1
Fig. 1

Out-of-plane sensitive optical system: TC, thermocouple; BS, beam splitter; PC, personal computer.

Fig. 2
Fig. 2

Temporal history of interference signal at a single point.

Fig. 3
Fig. 3

Simulation of the influence of bias intensities on the phase values. (a) Generated signal with the fluctuation of 10 % in bias intensity, (b) obtained phase value, and (c) rms phase error as a function of the fluctuation rate of bias intensity.

Fig. 4
Fig. 4

Influence of the fluctuation degree of the modulation intensity on the rms phase error.

Fig. 5
Fig. 5

Two-dimensional deformation field for out-of-plane measurement at 17 s after the initial heating of the specimen.

Fig. 6
Fig. 6

Cross section of the deformation field for out-of-plane measurement at 17 s after the initial heating of the specimen.

Fig. 7
Fig. 7

In-plane sensitive optical system: PZT, piezoelectric transducer; V, voltage meter; LD, laser diode.

Fig. 8
Fig. 8

In-plane deformation field of the joint material at 10 s after the initial heating of the specimen. Sensitivity vector is parallel to the boundary.

Fig. 9
Fig. 9

In-plane deformation field of the joint material at 10 s after the initial heating of the object. Sensitivity vector is perpendicular to the boundary.

Fig. 10
Fig. 10

Cross section of in-plane deformation field shown in Fig. 9 along the specimen.

Equations (12)

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I ( x , y , t i ) = I 0 ( x , y , t i ) + I m ( x , y , t i ) × cos { ϕ ( x , y , t i ) } , i = 1 , 2 , 3 , . . . ,
v ( t ) = HT { u ( t ) } = 1 π + u ( t ) t t d t .
I c ( x , y , t i ) = I m ( x , y , t i )   cos { ϕ ( x , y , t i ) } , i = 1 , 2 , 3 , . . . .
ϕ ( x , y , t i ) = tan - 1 ( HT { I c ( x , y , t i ) } I c ( x , y , t i ) ) .
H HT [ exp ( i ω ) ] = { i π < ω < 0 - i 0 < ω < π .
H HT ( k ) = { i k = 1 , 2 , .  .  .    , N / 2 1 0 k = 0 , N / 2 i k = N / 2 + 1 , N / 2 + 2 , . . . , N 1 ,
h HT [ n ] = 1 N k = 0 N 1 H HT ( k ) exp ( i 2 π k n / N ) = 1 N k = 1 N / 2 1 sin ( 2 π k n / N ) = { 0 2 π n for   n   even for  n   odd ,
I ( x , y , t i ) = I o ( x , y , t i ) + I m ( x , y , t i ) × cos { ϑ ( x , y , t i ) + φ ( x , y , t i ) + ω t i } .
φ ( x , y , t i ) = a ϕ   cos ( ω p t i + ρ o ) ,
I o = a o ( 1 + γ o   cos α o t i ) ,
rms   phase   error = ( 1 N i = 1 N ( ϕ i ϕ i ) 2 ) 1 / 2 .
I m = 1 2 ( 1 + γ r   cos   α t i )

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