Abstract

A thermal deformation measurement system based on calibrated phase-shifting digital holography is proposed. Two synchronized ordinary CMOS cameras are used in the calibrated phase-shifting digital holography system. One is to record the holograms including the object information, and the other is to record the interference fringes to evaluate phase-shifting errors. The calibrated phase-shifting digital holography can provide the high quality reconstructed images which are applied to calculate the thermal deformation of the object. Meanwhile, the thermal images of the object at different temperatures are recorded by a thermal camera. Nanometer-order thermal deformation measurement of an electronic device is achieved in a real experiment. Our measurement system could be useful for electric packaging materials development or the system design.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (4)

X. He, C. V. Nguyen, M. Pratap, Y. Zheng, Y. Wang, D. R. Nisbet, R. J. Williams, M. Rug, A. G. Maier, and W. M. Lee, “Automated Fourier space region-recognition filtering for off-axis digital holographic microscopy,” Biomed. Opt. Express 7(8), 3111–3123 (2016).
[Crossref] [PubMed]

T. Thanyarat and B. Prathan, “Measuring a thermal expansion of thermoelectric materials by using in-line digital holography,” Proc. SPIE 10022, 100220C (2016).

W. Zhou, H. Zhang, Y. Yu, and T. C. Poon, “Experiments on a simple setup for two-step quadrature phase-shifting holography, IEEE Transactions on Industrial Informatics,” IEEE Trans. Ind. Electron. 12(4), 1564–1570 (2016).

M. Chang, W. Tsai, J. Lin, and K. Jiang, “In-line monitoring of thermal deformation and surface topography of flip chip substrates,” Proc. SPIE 8321, 83211Q (2016).
[Crossref]

2012 (2)

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51(16), 3214–3223 (2012).
[Crossref] [PubMed]

2011 (1)

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase- shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[Crossref]

2010 (3)

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. 35(13), 2281–2283 (2010).
[Crossref] [PubMed]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

2007 (2)

T. Nomura and B. Javidi, “Object recognition by use of polarimetric phase-shifting digital holography,” Opt. Lett. 32(15), 2146–2148 (2007).
[Crossref] [PubMed]

Y. Morimoto, M. Toru, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46(2), 025603 (2007).
[Crossref]

2006 (1)

2005 (1)

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45(1), 65–70 (2005).
[Crossref]

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

2003 (1)

2001 (1)

1998 (1)

1997 (1)

1991 (1)

1989 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Balbás, M.

Beheim, G.

Benkouider, A.

Buytaert, J. A. N.

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase- shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[Crossref]

Cai, L. Z.

Chang, M.

M. Chang, W. Tsai, J. Lin, and K. Jiang, “In-line monitoring of thermal deformation and surface topography of flip chip substrates,” Proc. SPIE 8321, 83211Q (2016).
[Crossref]

Coëtmellec, S.

Dirckx, J. J. J.

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase- shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[Crossref]

Dong, G. Y.

Fraile, D.

Fujigaki, M.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Y. Morimoto, M. Toru, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46(2), 025603 (2007).
[Crossref]

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45(1), 65–70 (2005).
[Crossref]

Gascón, F.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

He, X.

Imbe, M.

Javidi, B.

Jiang, K.

M. Chang, W. Tsai, J. Lin, and K. Jiang, “In-line monitoring of thermal deformation and surface topography of flip chip substrates,” Proc. SPIE 8321, 83211Q (2016).
[Crossref]

Jiao, S.

Kawagishi, N.

Y. Morimoto, M. Toru, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46(2), 025603 (2007).
[Crossref]

Kobayashi, D.

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Larkin, K.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Lebrun, D.

Lee, W. M.

Lin, J.

M. Chang, W. Tsai, J. Lin, and K. Jiang, “In-line monitoring of thermal deformation and surface topography of flip chip substrates,” Proc. SPIE 8321, 83211Q (2016).
[Crossref]

Maier, A. G.

Malek, M.

Meng, X. F.

Mercer, C. R.

Morimoto, Y.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Y. Morimoto, M. Toru, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46(2), 025603 (2007).
[Crossref]

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45(1), 65–70 (2005).
[Crossref]

Muramatsu, T.

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51(16), 3214–3223 (2012).
[Crossref] [PubMed]

Nanbara, K.

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Nguyen, C. V.

Nisbet, D. R.

Nomura, T.

Poon, T. C.

W. Zhou, H. Zhang, Y. Yu, and T. C. Poon, “Experiments on a simple setup for two-step quadrature phase-shifting holography, IEEE Transactions on Industrial Informatics,” IEEE Trans. Ind. Electron. 12(4), 1564–1570 (2016).

Pratap, M.

Prathan, B.

T. Thanyarat and B. Prathan, “Measuring a thermal expansion of thermoelectric materials by using in-line digital holography,” Proc. SPIE 10022, 100220C (2016).

Ri, S.

P. Xia, Q. Wang, S. Ri, and H. Tsuda, “Calibrated phase-shifting digital holography based on a dual-camera system,” Opt. Lett. 42(23), 4954–4957 (2017).
[Crossref] [PubMed]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51(16), 3214–3223 (2012).
[Crossref] [PubMed]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Rug, M.

Saka, M.

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Shen, X. X.

Takahashi, I.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45(1), 65–70 (2005).
[Crossref]

Thanyarat, T.

T. Thanyarat and B. Prathan, “Measuring a thermal expansion of thermoelectric materials by using in-line digital holography,” Proc. SPIE 10022, 100220C (2016).

Toru, M.

Y. Morimoto, M. Toru, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46(2), 025603 (2007).
[Crossref]

Tsai, W.

M. Chang, W. Tsai, J. Lin, and K. Jiang, “In-line monitoring of thermal deformation and surface topography of flip chip substrates,” Proc. SPIE 8321, 83211Q (2016).
[Crossref]

Tsuda, H.

Varadé, A.

Vilarroig, P.

Wang, Q.

Wang, Y.

Wang, Y. R.

Williams, R. J.

Xia, P.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yoneyama, S.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45(1), 65–70 (2005).
[Crossref]

Yu, Y.

W. Zhou, H. Zhang, Y. Yu, and T. C. Poon, “Experiments on a simple setup for two-step quadrature phase-shifting holography, IEEE Transactions on Industrial Informatics,” IEEE Trans. Ind. Electron. 12(4), 1564–1570 (2016).

Zhang, H.

W. Zhou, H. Zhang, Y. Yu, and T. C. Poon, “Experiments on a simple setup for two-step quadrature phase-shifting holography, IEEE Transactions on Industrial Informatics,” IEEE Trans. Ind. Electron. 12(4), 1564–1570 (2016).

Zhang, S.

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

Zhang, T.

Zheng, Y.

Zhou, W.

W. Zhou, H. Zhang, Y. Yu, and T. C. Poon, “Experiments on a simple setup for two-step quadrature phase-shifting holography, IEEE Transactions on Industrial Informatics,” IEEE Trans. Ind. Electron. 12(4), 1564–1570 (2016).

Zou, W.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Biomed. Opt. Express (1)

Exp. Mech. (3)

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45(1), 65–70 (2005).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

IEEE Trans. Ind. Electron. (1)

W. Zhou, H. Zhang, Y. Yu, and T. C. Poon, “Experiments on a simple setup for two-step quadrature phase-shifting holography, IEEE Transactions on Industrial Informatics,” IEEE Trans. Ind. Electron. 12(4), 1564–1570 (2016).

J. Opt. (1)

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase- shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[Crossref]

Opt. Eng. (1)

Y. Morimoto, M. Toru, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46(2), 025603 (2007).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

Opt. Lett. (7)

Proc. SPIE (2)

T. Thanyarat and B. Prathan, “Measuring a thermal expansion of thermoelectric materials by using in-line digital holography,” Proc. SPIE 10022, 100220C (2016).

M. Chang, W. Tsai, J. Lin, and K. Jiang, “In-line monitoring of thermal deformation and surface topography of flip chip substrates,” Proc. SPIE 8321, 83211Q (2016).
[Crossref]

Other (1)

W. Jeong, K. Son, and H. Yang, “Image reconstruction algorithm for speckle noise reduction of 2-step parallel phase-shift digital holography,” in Mathematics in Imaging 2017, OSA Technical Digest (Optical Society of America, 2017), paper MTu2C.3.

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Figures (8)

Fig. 1
Fig. 1 Optical setup of the calibrated phase-shifting digital holography system.
Fig. 2
Fig. 2 Principle of the sampling Moiré technique to analyze the phase distribution of a single fringe pattern.
Fig. 3
Fig. 3 Principle of the sampling Moiré technique to determine the phase-shifting errors.
Fig. 4
Fig. 4 Experimental setup of the thermal deformation measurement system based on the calibrated phase-shifting digital holography.
Fig. 5
Fig. 5 (a) The photography of the object, (b) schematic of the thermal camera setting.
Fig. 6
Fig. 6 (a) One hologram recorded by camera 1, (b) one interferogram recorded by camera 2, (c) reconstructed amplitude image by the CPSDH, and (d) magnified image of the area indicated by the rectangle with dotted line in (c).
Fig. 7
Fig. 7 Experiment results: (a)-(d) are the thermal images of the object, (e) is the phase image of the area indicated by the rectangle with dotted line when the object at the state in (a), (f)-(h) are the phase difference images between the phase images reconstructed at the state in (b)-(d) with (e).
Fig. 8
Fig. 8 (a) and (c) are the amplitude images reconstructed by the CPSDH and conventional method, (b) and (d) are the phase difference images corresponding with the areas indicated by the red dotted line in (a) and (c), (e) is the phase values from a to a’ in (b), (f) is the unwrapped phase values of (e).

Equations (9)

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

f(x,y)= A g cos{ 2π x P + ϕ g0 }+ B g = A g cos{ ϕ g (x,y) }+ B g ,
f m (x,y;k)= A m cos{ 2π( 1 P 1 T )x+2π k T + ϕ g0 }+ B m = A m cos{ ϕ m (x,y)+2π k T }+ B m .
ϕ m (x,y)= tan 1 k=0 T1 f m (x,y;k)sin(2πk/T) k=0 T1 f m (x,y;k)cos(2πk/T) .
Δ δ j = n=1 j Δ φ n j φ s ( j= 1, 2, 3, ... ),
I(x,y; ϕ R )= A 2 + A R 2 +A A R exp[i(ϕ ϕ R )]+A A R exp[i( ϕ R ϕ)],
A(x,y)= ( a 3 M+ a 2 N) 2 + ( a 4 M a 1 N) 2 2 A R ( a 1 a 3 + a 2 a 4 ) ,
ϕ(x,y)= tan 1 a 4 M a 1 N a 3 M+ a 2 N ,
a 1 =1+cos(Δ δ 2 ), a 2 =sin(Δ δ 2 ), a 3 =cos(Δ δ 3 )+cos(Δ δ 1 ), a 4 =sin(Δ δ 3 )+sin(Δ δ 1 ), M=I(x,y;0)I(x,y;π+Δ δ 2 ), N=I(x,y; 3π 2 +Δ δ 3 )I(x,y; π 2 +Δ δ 1 ).
h(x,y)= λΔ ϕ obj 4π ,

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