Abstract

An updated B-scan method is proposed for measuring the evolution of thermal deformation fields in polymers. In order to measure the distributions of out-of-plane deformation and normal strain field, phase-contrast spectral optical coherence tomography (PC-SOCT) was performed with the depth range and resolution of 4.3 mm and 10.7 μm, respectively, as thermal loads were applied to three different multilayer samples. The relation between temperature and material refractive index was predetermined before the measurement. After accounting for the refractive index, the thermal deformation fields in the polymer were obtained. The measured thermal expansion coefficient of silicone sealant was approximately equal to its reference value. This method allows correctly assessing the mechanical properties in semitransparent polymers.

© 2015 Optical Society of America

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References

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2014 (2)

2013 (3)

Y. Yan, Z. Ding, Y. Shen, Z. Chen, C. Zhao, and Y. Ni, “High-sensitive and broad-dynamic-range quantitative phase imaging with spectral domain phase microscopy,” Opt. Express 21(22), 25734–25743 (2013).
[Crossref] [PubMed]

J. E. Pye and C. B. Roth, “Physical aging of polymer films quenched and measured free-standing via ellipsometry: controlling stress imparted by thermal expansion mismatch between film and support,” Macromolecules 46(23), 9455–9463 (2013).
[Crossref]

Y. G. Wang and W. Tong, “A high resolution DIC technique for measuring small thermal expansion of film specimens,” Opt. Lasers Eng. 51(1), 30–33 (2013).
[Crossref]

2012 (2)

S. Chakraborty and P. D. Ruiz, “Measurement of all orthogonal components of displacement in the volume of scattering materials using wavelength scanning interferometry,” J. Opt. Soc. Am. A 29(9), 1776–1785 (2012).
[Crossref] [PubMed]

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

2011 (1)

G. Guan, R. Reif, Z. Huang, and R. K. Wang, “Depth profiling of photothermal compound concentrations using phase sensitive optical coherence tomography,” J. Biomed. Opt. 16(12), 126003 (2011).
[Crossref] [PubMed]

2009 (1)

2006 (3)

2001 (1)

C.-C. Lee, C.-L. Tien, W.-S. Sheu, and C.-C. Jaing, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Rev. Sci. Instrum. 72(4), 2128–2133 (2001).

1999 (1)

E. Hack and R. Bronnimann, “Electronic speckle pattern interferometry deformation measurement on lightweight structures under thermal load,” Opt. Lasers Eng. 31(3), 213–222 (1999).
[Crossref]

1998 (1)

T. Watanabe, N. Ooba, Y. Hida, and M. Hikita, “Influence of humidity on refractive index of polymers for optical waveguide and its temperature dependence,” Appl. Phys. Lett. 72(13), 1533–1535 (1998).
[Crossref]

1993 (1)

Aherrahrou, R.

Ahrens, G.

Ansari, R.

Birngruber, R.

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

Bronnimann, R.

E. Hack and R. Bronnimann, “Electronic speckle pattern interferometry deformation measurement on lightweight structures under thermal load,” Opt. Lasers Eng. 31(3), 213–222 (1999).
[Crossref]

Chakraborty, S.

Chen, Z.

De la Torre Ibarra, M. H.

De la Torre-Ibarra, M. H.

Ding, Z.

Duan, L.

Duncan, D. D.

Ellerbee, A. K.

Engelke, R.

Erdmann, J.

Goetzinger, E.

Gruetzner, G.

Guan, G.

G. Guan, R. Reif, Z. Huang, and R. K. Wang, “Depth profiling of photothermal compound concentrations using phase sensitive optical coherence tomography,” J. Biomed. Opt. 16(12), 126003 (2011).
[Crossref] [PubMed]

Hack, E.

E. Hack and R. Bronnimann, “Electronic speckle pattern interferometry deformation measurement on lightweight structures under thermal load,” Opt. Lasers Eng. 31(3), 213–222 (1999).
[Crossref]

Hida, Y.

T. Watanabe, N. Ooba, Y. Hida, and M. Hikita, “Influence of humidity on refractive index of polymers for optical waveguide and its temperature dependence,” Appl. Phys. Lett. 72(13), 1533–1535 (1998).
[Crossref]

Hikita, M.

T. Watanabe, N. Ooba, Y. Hida, and M. Hikita, “Influence of humidity on refractive index of polymers for optical waveguide and its temperature dependence,” Appl. Phys. Lett. 72(13), 1533–1535 (1998).
[Crossref]

Hitzenberger, C. K.

Huang, Z.

G. Guan, R. Reif, Z. Huang, and R. K. Wang, “Depth profiling of photothermal compound concentrations using phase sensitive optical coherence tomography,” J. Biomed. Opt. 16(12), 126003 (2011).
[Crossref] [PubMed]

Huntley, J. M.

Hüttmann, G.

R. Ansari, C. Myrtus, R. Aherrahrou, J. Erdmann, A. Schweikard, and G. Hüttmann, “Ultrahigh-resolution, high-speed spectral domain optical coherence phase microscopy,” Opt. Lett. 39(1), 45–47 (2014).
[Crossref] [PubMed]

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

Jaing, C.-C.

C.-C. Lee, C.-L. Tien, W.-S. Sheu, and C.-C. Jaing, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Rev. Sci. Instrum. 72(4), 2128–2133 (2001).

Kirkpatrick, S. J.

Lee, C.-C.

C.-C. Lee, C.-L. Tien, W.-S. Sheu, and C.-C. Jaing, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Rev. Sci. Instrum. 72(4), 2128–2133 (2001).

Lurie, K. L.

Marvdashti, T.

Müller, H.

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

Myrtus, C.

Ni, Y.

Ooba, N.

T. Watanabe, N. Ooba, Y. Hida, and M. Hikita, “Influence of humidity on refractive index of polymers for optical waveguide and its temperature dependence,” Appl. Phys. Lett. 72(13), 1533–1535 (1998).
[Crossref]

Pircher, M.

Pye, J. E.

J. E. Pye and C. B. Roth, “Physical aging of polymer films quenched and measured free-standing via ellipsometry: controlling stress imparted by thermal expansion mismatch between film and support,” Macromolecules 46(23), 9455–9463 (2013).
[Crossref]

Reif, R.

G. Guan, R. Reif, Z. Huang, and R. K. Wang, “Depth profiling of photothermal compound concentrations using phase sensitive optical coherence tomography,” J. Biomed. Opt. 16(12), 126003 (2011).
[Crossref] [PubMed]

Roth, C. B.

J. E. Pye and C. B. Roth, “Physical aging of polymer films quenched and measured free-standing via ellipsometry: controlling stress imparted by thermal expansion mismatch between film and support,” Macromolecules 46(23), 9455–9463 (2013).
[Crossref]

Rudolph, L.

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

Ruiz, P. D.

Saldner, H.

Schweikard, A.

Shen, Y.

Sheu, W.-S.

C.-C. Lee, C.-L. Tien, W.-S. Sheu, and C.-C. Jaing, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Rev. Sci. Instrum. 72(4), 2128–2133 (2001).

Smith, G. T.

Spahr, H.

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

Stifter, D.

Tien, C.-L.

C.-C. Lee, C.-L. Tien, W.-S. Sheu, and C.-C. Jaing, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Rev. Sci. Instrum. 72(4), 2128–2133 (2001).

Tong, W.

Y. G. Wang and W. Tong, “A high resolution DIC technique for measuring small thermal expansion of film specimens,” Opt. Lasers Eng. 51(1), 30–33 (2013).
[Crossref]

Wang, R. K.

G. Guan, R. Reif, Z. Huang, and R. K. Wang, “Depth profiling of photothermal compound concentrations using phase sensitive optical coherence tomography,” J. Biomed. Opt. 16(12), 126003 (2011).
[Crossref] [PubMed]

S. J. Kirkpatrick, R. K. Wang, and D. D. Duncan, “OCT-based elastography for large and small deformations,” Opt. Express 14(24), 11585–11597 (2006).
[Crossref] [PubMed]

Wang, Y. G.

Y. G. Wang and W. Tong, “A high resolution DIC technique for measuring small thermal expansion of film specimens,” Opt. Lasers Eng. 51(1), 30–33 (2013).
[Crossref]

Watanabe, T.

T. Watanabe, N. Ooba, Y. Hida, and M. Hikita, “Influence of humidity on refractive index of polymers for optical waveguide and its temperature dependence,” Appl. Phys. Lett. 72(13), 1533–1535 (1998).
[Crossref]

Wiesauer, K.

Yan, Y.

Zhao, C.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Watanabe, N. Ooba, Y. Hida, and M. Hikita, “Influence of humidity on refractive index of polymers for optical waveguide and its temperature dependence,” Appl. Phys. Lett. 72(13), 1533–1535 (1998).
[Crossref]

J. Biomed. Opt. (1)

G. Guan, R. Reif, Z. Huang, and R. K. Wang, “Depth profiling of photothermal compound concentrations using phase sensitive optical coherence tomography,” J. Biomed. Opt. 16(12), 126003 (2011).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Macromolecules (1)

J. E. Pye and C. B. Roth, “Physical aging of polymer films quenched and measured free-standing via ellipsometry: controlling stress imparted by thermal expansion mismatch between film and support,” Macromolecules 46(23), 9455–9463 (2013).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (2)

E. Hack and R. Bronnimann, “Electronic speckle pattern interferometry deformation measurement on lightweight structures under thermal load,” Opt. Lasers Eng. 31(3), 213–222 (1999).
[Crossref]

Y. G. Wang and W. Tong, “A high resolution DIC technique for measuring small thermal expansion of film specimens,” Opt. Lasers Eng. 51(1), 30–33 (2013).
[Crossref]

Opt. Lett. (3)

Proc. SPIE (1)

H. Spahr, L. Rudolph, H. Müller, R. Birngruber, and G. Hüttmann, “Imaging of photothermal tissue expansion via phase sensitive optical coherence tomography,” Proc. SPIE 8213, 82131S (2012).
[Crossref]

Rev. Sci. Instrum. (1)

C.-C. Lee, C.-L. Tien, W.-S. Sheu, and C.-C. Jaing, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Rev. Sci. Instrum. 72(4), 2128–2133 (2001).

Other (2)

Dow Corning Corporation, “Production information of Dow Corning® 732 multi-purpose sealant,” https://www.xiameter.com/EN/Pages/RetrieveDocument.aspx?type=Lit&DocumentId=090276fe801dccb7&s=109313 .

P. K. Rastogi, Photomechanics: Topics in Applied Physics (Springer, 2000).

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Figures (10)

Fig. 1
Fig. 1 Experimental setup. (a) Front view of the PC-SOCT. (b) Top view of the PC-SOCT. (c) Photograph of the samples. (d) The sample mounter. (e) The sample cross-section. SLD: Super-luminescent diode; L1-L3: lens; CL: cylindrical lens; S: sample; CBS: cube beam splitter; R: reference plane; G: diffraction grating; CCD: CCD camera.
Fig. 2
Fig. 2 The relations between the refractive index change Δn and the temperature. ○, Chromatography silica gel plate; × , solidified silicone sealant plate.
Fig. 3
Fig. 3 Interference spectra of S1 sample. (a) The amplitude map. (b) The wrapped phase difference map.
Fig. 4
Fig. 4 Distributions of the out-of-plane deformation and normal strain field inside S1 sample. From left to right, the images correspond to the temperature reductions of 2 °C, 4 °C, 6 °C, 8 °C, and 10 °C. Upper row: unwrapped phase difference maps; middle row: contour maps of the out-of-plane deformation field; bottom row: contour maps of the normal strain field.
Fig. 5
Fig. 5 Linear thermal expansion coefficient of S1 sample.
Fig. 6
Fig. 6 Interference spectra of S2 sample. (a) The amplitude map. (b) The wrapped phase difference map.
Fig. 7
Fig. 7 Distributions of the out-of-plane deformation and normal strain field inside S2 sample. From left to right, the images correspond to the temperature reductions of 2 °C, 4 °C, 6 °C, 8 °C, and 10 °C. Upper row: unwrapped phase difference maps; middle row: contour maps of the out-of-plane deformation field; bottom row: contour maps of the normal strain field.
Fig. 8
Fig. 8 Linear thermal expansion coefficients of S2 sample. ○, Layer A; □, layer B.
Fig. 9
Fig. 9 Interference spectra of S3 sample. (a) The amplitude map. (b) The wrapped phase difference map. The measured region is divided into 3 parts: part A, the front of the void; part B, the periphery of the parts A and C; part C, the void.
Fig. 10
Fig. 10 Distributions of the out-of-plane deformation and normal strain field inside S3 sample. From left to right, the images correspond to the temperature reductions of 2 °C, 4 °C, 6 °C, 8 °C, and 10 °C. Upper row: unwrapped phase difference maps; middle row: contour maps of the out-of-plane deformation field; bottom row: contour maps of the normal strain field.

Equations (7)

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

z= Λ(y,z)Λ(y, z l ) n l + i=1 l Λ(y, z i )Λ(y, z i1 ) n i1 ,
ΔΛ(y,z)= 1 2 k c ΔΠ (y,z),
ΔΛ(y,z)= i=1 l { [w(y, z i )w(y, z i1 )]( n i1 +Δ n i1 )+( z i z i1 )Δ n i1 } +[w(y,z)w(y, z l )]( n l +Δ n l )+(z z l )Δ n l ,
w(y,z) ΔΠ(y,z) 2 k c n l + 1 n l i=1 l { [w(y, z i1 )w(y, z i )] n i1 +( z i1 z i )Δ n i1 } +( z l z) Δ n l n l +w(y, z l ),
w d (y,z)=w(y,z) w r ,
ε z (y,z)= w(y,z) z 1 2 k c n l ΔΠ(y,z) z Δ n l n l .
Δn(y)= ΔΠ(y, z 2 ) n 0 +ΔΠ(y, z 1 )( n 1 n 0 ) 2 k c n 0 ( z 2 z 1 ) ,

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