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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17469–17479
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Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film

Zhanwei Liu and Jianxin Gao  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17469-17479 (2011)
http://dx.doi.org/10.1364/OE.19.017469


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Abstract

In this paper, a digital speckle correlation method for coefficient of thermal expansion (CTE) measurement of film is developed, in which CTE is the intrinsic parameter and direct variable. Deformation pattern governed by the CTE and temperature is used to affine transform the image captured after the film is heated. If the values of CTE are properly chosen, the image after affine transformation will have a highest similarity to the original image. This turns CTE measurement into a purely numerical search of an optimal trial CTE. Results of CTEs from this method and conventional DIC methods are compared with the actual CTE, showing an improved accuracy.

© 2011 OSA

1. Introduction

Thin films have widespread applications in microelectronics and micro-electro mechanical systems (MEMS). The rapid growth of the MEMS industry has introduced a need for the characterization of thin film properties at all temperatures encountered during fabrication and application of the devices. Thermal expansion is an important mechanical behavior in MEMS. There are several problems that arise from the thermal expansion effect; for example, the mismatch of thermal expansion between the thin films and the substrate may lead to residual stresses in the thin films [1

1. W. Fang and J. A. Wickert, “Determining mean and gradient residual stress in thin films using micromachined cantilevers,” J. Micromech. Microeng. 6(3), 301–309 (1996). [CrossRef]

]. Therefore damage or deformation of the micromachined structures may occur. On the other hand, the thermal expansion effect can be exploited to drive the microactuator [2

2. M. B. David and V. M. Bright, “Design and performance of a double hot arm polysilicon thermal actuator,” Proc. SPIE, Micromacined devices and components III 3224, 296–306(1997).

,3

3. J. W. Suh, S. F. Glander, R. B. Darling, and C. W. Storment, “Organic thermal and electrostatic ciliary microactuator array for object manipulation,” Sens. Act. A: Physical 58, 51–60 (1997). [CrossRef]

]. In order to design micromachined devices properly, it is necessary to characterize the coefficient of thermal expansion for thin film materials [4

4. H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Thermal expansion coefficient of polycrystalline silicon and silicon dioxide thin films at high temperatures,” J. Appl. Phys. 87(9), 4189–4194 (2000). [CrossRef]

,5

5. W. L. Fang, H. C. Tsai, and C. Y. Lo, “Determining thermal expansion coefficients of thin films using micromachined cantilevers,” Sens. Act. A: Physical 77, 21–27 (1999). [CrossRef]

].

An innovative technique for determining CTE of thin films using multilayered cantilever beams has been developed. The technique is based on the thermally induced curvature of the multilayer that results from the difference in thermal expansion coefficients of the layers. The curvature is measured at temperatures of up to 850 °C using an optical curvature measurement system [6

6. H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Novel imaging system for measuring microscale curvatures at high temperatures,” Rev. Sci. Instrum. 71(1), 161–167 (2000). [CrossRef]

]. Determination of property results from comparing the beam response to a numerical model for curvature of multilayers [7

7. P. H. Townsend, D. M. Barnett, and T. A. Brunner, “Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate,” J. Appl. Phys. 62(11), 4438–4444 (1987). [CrossRef]

]. Full-field optical techniques, such as phase-shifting interferometry [8

8. 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). [CrossRef]

] and Electronic Speckle Pattern Interferometry (ESPI) [9

9. C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterisation of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006). [CrossRef]

] have been applied to determine the thermal expansion of thin film under thermal loading. For example, tests conducted by Dudescu et al. [9

9. C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterisation of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006). [CrossRef]

] successfully determined the CTEs of unidirectional and bidirectional carbon fiber laminates using phase-shifting ESPI.

This fringe based interferometric techniques usually offer high sensitivity and accuracy in displacement and/or deformation measurement [10

10. J. B. Zhang and T. C. Chong, “Fiber electronic speckle pattern interferometry and its applications in residual stress measurements,” Appl. Opt. 37(28), 6707–6715 (1998). [CrossRef] [PubMed]

]. However, since they must use coherent light, interferometric techniques except shearography tend to be prone to environmental disturbances during measurement. This has limited their application to on-site measurement in an engineering environment. Moreover, a subsequent fringe pattern analysis technique (e.g., phase unwrapping) is required to extract the thermal expansion from the obtained fringe patterns, which further increases the complexity of measurement.

Digital speckle/image correlation (DPC/DIC) is a well-known non-interferometric technique, having the capability of measuring the displacement field of an object with an ordinary light source such as white light [11

11. W. H. Peter and W. F. Ranson, “Digital imaging technique in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).

]. Without the need to form an interferometric fringe pattern, the optical set-up of DIC is rather simple. In 2009, Pan etal [12

12. B. Pan, H. M. Xie, T. Hua, and A. Anand, “Measurement of coefficient of thermal expansion of films using digital image correlation method,” Polym. Test. 28(1), 75–83 (2009). [CrossRef]

]measured the CTE of pure copper film and PI/SiO2 composite films using DIC. Generally, in order to measure CTE, the strain components accompanying the thermal expansion will be computed by differentiating the displacement fields, but numerical differentiation will amplify the noise contained in the computed displacements. In document [12

12. B. Pan, H. M. Xie, T. Hua, and A. Anand, “Measurement of coefficient of thermal expansion of films using digital image correlation method,” Polym. Test. 28(1), 75–83 (2009). [CrossRef]

], in order to obtain the average thermal strain of the test film surface and alleviate the influence of noise, linear planes were used to approximate the computed displacement fields of the test film. However, relatively little of deformation information was used during CTE measurement in the above document [12

12. B. Pan, H. M. Xie, T. Hua, and A. Anand, “Measurement of coefficient of thermal expansion of films using digital image correlation method,” Polym. Test. 28(1), 75–83 (2009). [CrossRef]

], a large part of deformation information was not used.

2. Principle of DPDSC for CTE Measurement

The central idea of the DPDSC is to use intrinsic parameters of a measurement task as direct variables in the computation of the correlation coefficient between two images [13

13. J. X. Gao and H. X. Shang, “Deformation-pattern-based digital image correlation method and its application to residual stress measurement,” Appl. Opt. 48(7), 1371–1381 (2009). [CrossRef] [PubMed]

]. In this investigation, the CTE α is selected as intrinsic parameters, and displacement field is governed by the CTE at a special temperature by Eq. (1).
u(r,θ)=ε(r,θ)r=αΔTr
(1)
where (r, θ) are the polar coordinates, u is the in-plane displacement vector, ε is the strain, and ΔT is the temperature change.

3. Algorithms of DPDSC for CTE measurement

Let (x, y) be the coordinate of the optical imaging system, and F and G the digital images corresponding to before and after the sample is heated, i.e.
F={F(xi,yj)},i=1...M,j=1...NG={G(x'i,y'j)},i=1...M,j=1...N
(2)
Where M and N are the numbers of horizontal and vertical pixels of a digital image, respectively. Based on the deformed image G, an inverse affine transformation is defined as:
x''=x'ut(x,y)y''=y'vt(x,y)
(3)
Where ut and vt are the displacement components by thermal loading, (x”, y”) are the new coordinate system. In this way, the intrinsic parameters (CTE) are introduced in the inverse affine transform.
x''=x'ut(x,y)=x'αxx'ΔTy''=y'vt(x,y)=y'αyy'ΔT
(4)
Where αx and αyare the CTE in the x and y axes, respectively, while for isotropic material, theαx=αy=α.

After the above inverse affine transformation, a new image G’ can be formed:

G'={G(x''i,y''j)},i=1...M,j=1...N
(5)

The correlation between this new image G’ and the original image F is calculated as:
C=<FG'><F><G'><(F<F>)2><(G'<G'>)2>
(6)
where <…> denotes an ensemble average over the image domain. |C|≤1, and C = 1 only when F = G’.

It is obvious that the correlation is an explicit function of the pixel intensities of two images. Displacement field or intrinsic parameters are introduced implicitly by the use of an affine transformation of the image coordinate system. Generally, the correlation is finally a function of the intrinsic parameters (αx,αy) in an implicit sense, i.e.

C=C[u(αx),v(αy)]
(7)

Different intrinsic parameters CTE (αx,αy) will result in a different correlation value C. If the trial intrinsic parameters CTE are equal to the actual CTE, image G’ will be exactly transformed back to the original image F. This can be implemented by an optimization process.

In reality, there are some more issues need to be addressed when using DPDSC to measure CTE. Firstly, in-plane rigid body displacement inevitably occurs during image acquisition before and after the testing sample is heated. It consists of rigid body shift, u0 and v0, along the x and y axes respectively, and in-plane rotation ω. They are the result of either the accumulated deformation when heating, or the environmental disturbance during image acquisition. Secondly, out-of-plane displacement w0 often exists too. It is the result of either the movement of the digital camera during image acquisition, or the accumulated deformation of the object. This out-of-plane displacement has a huge effect on the accuracy of strain measurement, because it will result in the change in image magnification during image acquisition. Telecentric lens can be used to resolve this problem. An object-space telecentric lens has a prominent characteristic that its magnification is a constant within a special working distance. The size and shape of an image formed by such a lens is independent of the object's distance or position in the field of view. Object-space telecentric lens creates images of the same size for objects at any distance (within depth of field (DOF)) and has constant angle of view across the entire field of view (FOV). Thus, Out-of-plane rigid body displacement can be ignored if introducing object-space telecentric lens in front of a CCD [14

14. F. P. Zhu, W. W. Liu, H. J. Shi, and X. Y. He, “Accurate 3D measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48(11), 1132–1139 (2010). [CrossRef]

].

C=C(u0,v0,ω,w0,αx,αy)
(9)

4. Optimisation scheme for the correlation search process

5. Validation tests for CTE measurement

(A) Test material and film sample

Two types of polymer films were used. One is Polyimide Film, with a thickness of 50 micron, which is usually used as a dielectric substrate for flexible printed circuits and high density interconnects. The other is Polyetherimide film with a thickness of 250 Micron, which has a broad range of electrical and electronic applications. The two types of film material were cut into specimens with size of 10×10mm2. The surface of the sample was sprayed with black and white high-temperature paint in order to form speckle-like images. Three specimens were fabricated for each type of material. Figure 1
Fig. 1 speckles image of film surface
is a speckled image of one of the film specimens’ surface.

(B) Experimental set-up

The experimental set-up consists of a high temperature furnace and a digital image capturing system. The high temperature furnace can heat the sample from room temperature to 300 °C using the electric resistance wire imbedded under the bottom of the furnace. The temperature within the furnace is measured and controlled by a separate temperature controller. The upper part of the furnace is covered by a quartz glass plate, which serves for thermal insulation and reducing the optical distortion. When the intended temperature is achieved, the corresponding sample surface image is recorded by the digital image capturing system for subsequent DPDSC and DIC analysis. The image capturing system consists of a CMOS camera with resolution of 1600 x 1200 pixels at 256 gray levels and an object-space telecentric lens with a working distance of 120mm mounted in front of the camera.

(C) Experimental procedure

Measurement of CTE of a film sample by the DPDSC method follows the following procedures. At first, the test film sample with artificial speckles was placed horizontally on a polytetrafluoroethylene plate in the high temperature furnace without any restraint. A white light source was used to illuminate the sample surface during thermal expansion. The camera axis should be placed perpendicular to the test sample surface. In order to decline the influence of the residual stresses in the films during manufacture on CTE calculation, only samples after their first exposure to elevated temperatures were used.

After the first exposure, the original temperature was set as 30 °C and the corresponding images were recorded as reference images. After that, the temperature within the furnace was elevated to 100°C and then 150°C, two images under each temperature were captured as deformed images. These images were analyzed by the DPDSC technique to extract the CTE directly. The test process was repeated three times on one sample. When the test on one sample was finished, this process was repeated on another two samples of the same type. Each type of material was tested nine times with three samples at a special temperature difference (from 30°C to 100°C and from 100°C to 150°C), and three times for each sample to obtain the average value at the fixed temperature difference.

It is noted that hot airflow around the furnace may cause the density and the refractive index of the air non-uniform, and finally result in abnormal distortion in local area of the images captured. Thus, the influence of the distorted images used on the CTE calculated cannot be ignored. So it is of very importance to restrain the image distortion to get a good result during heating. Three strategies were applied to resolve this problem effectively in this investigation. (a)At each temperature, the temperature is maintained for at least 30minutes to make sure that the nearby hot airflow is stable and the sample is subjected to a uniform thermal loading. (b) No actions were taken that would affect the airflow, such as moving quickly or, opening or closing the door quickly, etc. when testing and capturing images. (c) When the airflow was stable, a pair of images were captured at specific temperature at a fixed time interval (about 5 minutes), calculating the CTE simply using the image pairs. If the calculated virtual CTE was nearly zero or the correlation coefficient was larger than 0.990, the two images were applied to the final CTE calculation, otherwise, they were recaptured when the hot airflow was stable. After this assessment of image distortion, the images captured were used for the formal CTE calculation.

(D) Experimental results and discussion

The result of calculation is the in-plane rigid body displacement (u, v) and rotation ω, out-of-plane rigid body displacement w, and the CTE components (αx,αy). In this investigation, the film materials used are isotropic one, soαx=αy=α.

Extensive validation measurements have been made to test the accuracy, sensitivity, reliability and repeatability of the proposed method. By selecting images taken at different temperatures, we can form various image pairs which correspond to various temperature differences. These image pairs were loaded into the measurement system, and CTEs were calculated and compared to their actual values, taken from the materials’ supplier’s website [15

15. Ultem* 1000B Film, Product Datasheet, http://www.tekra.com/products/polycarbonate/Ultem-1000B.pdf

,16

16. DuPont Kapton® HN, polyimide film Technical Data Sheet, http://www2.dupont.com/Kapton/en_US/assets/downloads/pdf/HN_datasheet.pdf

]. In this way, the sensitivity and repeatability of the measurement system can be evaluated. In addition, the CTE also were measured using the conventional DIC method, that is, firstly to measure the displacement, secondly to calculate the strain and then to calculate the CTE. The accuracy of this DPDSC method developed for CTE measured can be discussed by comparing the CTE values using DPDSC, DIC methods and the actual values. Figure 2
Fig. 2 CTE calculating window of a polyetherimide film
is the calculating window with a measured CTE result using one of Polyetherimide specimens at the temperature ranges of 30-100°C. From Fig. 2, it can be seen that the in-plane rigid body displacement calculated is −0.247 pixel in the horizontal direction and 0.237 pixel in the vertical direction. The rigid body rotation is −0.070 deg(clockwise direction). When the absolute value of the out-of-plane rigid body displacement is less than 0.01pixel, indicating that the out-of-plane rigid body displacement is no longer necessary to be concerned, in this case, it is directly set to 0 in this program for unambiguity. In fact, in most of the tests, the out-of-plane rigid body displacement is usually very close to zero, which is attributed to the telecentric lens used here. So, in this investigation, the influence of the out-of-plane rigid body displacement on CTE doesn’t need to be taken into account. The total expansion is 3.6359/1000 for the temperature difference of 70°C, so the CTE is 51.94 ppm/°C.

Figure 3(a) and (b)
Fig. 3 thermal deformation field at the temperature difference range of 30-100°C,(1pixel = 0.019mm):(a) U field with rigid body motion, (b) V field with rigid body motion,(c) Resultant displacement with rotation, (d) pure thermal expansion deformation
are the displacement field U and V measured by conventional DIC using the same speckled image pairs as Fig. 2. It can be seen that rigid body motion is included besides thermal expansion deformation. After eliminating the in-plane rigid body displacement using the calculated value of DPDSC above(−0.247 pixel in the U field and 0.237 pixel in the V field), a resultant displacement vector is formed and shown in Fig. 3(c). Figure 3(c) shows a uniform thermal expansion deformation, but rigid body rotation still present. After eliminating the rigid body rotation, an exact uniform thermal expansion deformation field is formed and shown in Fig. 3(d). From these images, it can be concluded that these measured values of in-plane rigid body motion using DPDSC are correct.

After eliminating the in-plane rigid body motion, the resultant displacement field measured using DIC can be applied to calculate strain and CTE according to the common process [12

12. B. Pan, H. M. Xie, T. Hua, and A. Anand, “Measurement of coefficient of thermal expansion of films using digital image correlation method,” Polym. Test. 28(1), 75–83 (2009). [CrossRef]

].

The tests were finished with six samples according to above process, the obtained CTE values by DPDSC and DIC for Polyetherimide and Polyimide Film specimens are listed in Table 1

Table 1. CTE results using different methods

table-icon
View This Table
, and compared with the actual CTEs. The actual value of CTE of Polyetherimide film is 52 ppm/°C according to the test standard IPC-TM-650 [15

15. Ultem* 1000B Film, Product Datasheet, http://www.tekra.com/products/polycarbonate/Ultem-1000B.pdf

], while for Polyimide Film, it is 17 at the temperature range of 30-100°C,and 32 at 100-150°C according to the test standard ASTM D-696-91 [16

16. DuPont Kapton® HN, polyimide film Technical Data Sheet, http://www2.dupont.com/Kapton/en_US/assets/downloads/pdf/HN_datasheet.pdf

]. The mean of the measured values and standard deviation are also listed.

For comparison convenience, the CTE of measured, mean and actual values are also shown in Fig. 4 (a) and (b)
Fig. 4 CTE comparsion of different film materials using different methods: (a) CTE of Polyetherimide material, (b) CTE of Polyimide material
. From these figures, it can be seen that the measured values using DPDSC are closer to the actual values than those using DIC. The absolute error of DPDSC for CTE is less than 2%. That is, the DPDSC method for CTE has higher precision than that of conventional DIC.

In general, the higher the temperature are, the larger of the standard deviation is. DPDSC has a smaller standard deviation. In this investigation, the standard deviation of DPDSC for CTE is less than 1.34 ppm/°C, while DIC is larger than 1.59 ppm/°C, so DPDSC has a better repeatability than DIC. It seems that the result from DPDSC approach is better than conventional DIC, which demonstrates the benefit of taking into account more of the available information during CTE calculations.

6. Conclusions

The proposed approach is implemented through an optimisation procedure. Since the direct variables in such a numerical optimisation process are the intrinsic parameters CTE, the conventional strain measurement procedure in CTE which involves the complex displacement and strain calculation is no longer required. Validation tests have proved the viability of the new approach, and the accuracy and reproducibility of CTE measurement has been improved compared to the conventional DIC method.

Acknowledgements

This work was supported by the Marie Curie International Incoming Fellowship (Project No.221623) of the European Commission, the National Natural Science Foundation of China under grant No. 11072033.

References and links

1.

W. Fang and J. A. Wickert, “Determining mean and gradient residual stress in thin films using micromachined cantilevers,” J. Micromech. Microeng. 6(3), 301–309 (1996). [CrossRef]

2.

M. B. David and V. M. Bright, “Design and performance of a double hot arm polysilicon thermal actuator,” Proc. SPIE, Micromacined devices and components III 3224, 296–306(1997).

3.

J. W. Suh, S. F. Glander, R. B. Darling, and C. W. Storment, “Organic thermal and electrostatic ciliary microactuator array for object manipulation,” Sens. Act. A: Physical 58, 51–60 (1997). [CrossRef]

4.

H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Thermal expansion coefficient of polycrystalline silicon and silicon dioxide thin films at high temperatures,” J. Appl. Phys. 87(9), 4189–4194 (2000). [CrossRef]

5.

W. L. Fang, H. C. Tsai, and C. Y. Lo, “Determining thermal expansion coefficients of thin films using micromachined cantilevers,” Sens. Act. A: Physical 77, 21–27 (1999). [CrossRef]

6.

H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Novel imaging system for measuring microscale curvatures at high temperatures,” Rev. Sci. Instrum. 71(1), 161–167 (2000). [CrossRef]

7.

P. H. Townsend, D. M. Barnett, and T. A. Brunner, “Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate,” J. Appl. Phys. 62(11), 4438–4444 (1987). [CrossRef]

8.

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). [CrossRef]

9.

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterisation of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006). [CrossRef]

10.

J. B. Zhang and T. C. Chong, “Fiber electronic speckle pattern interferometry and its applications in residual stress measurements,” Appl. Opt. 37(28), 6707–6715 (1998). [CrossRef] [PubMed]

11.

W. H. Peter and W. F. Ranson, “Digital imaging technique in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).

12.

B. Pan, H. M. Xie, T. Hua, and A. Anand, “Measurement of coefficient of thermal expansion of films using digital image correlation method,” Polym. Test. 28(1), 75–83 (2009). [CrossRef]

13.

J. X. Gao and H. X. Shang, “Deformation-pattern-based digital image correlation method and its application to residual stress measurement,” Appl. Opt. 48(7), 1371–1381 (2009). [CrossRef] [PubMed]

14.

F. P. Zhu, W. W. Liu, H. J. Shi, and X. Y. He, “Accurate 3D measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48(11), 1132–1139 (2010). [CrossRef]

15.

Ultem* 1000B Film, Product Datasheet, http://www.tekra.com/products/polycarbonate/Ultem-1000B.pdf

16.

DuPont Kapton® HN, polyimide film Technical Data Sheet, http://www2.dupont.com/Kapton/en_US/assets/downloads/pdf/HN_datasheet.pdf

OCIS Codes
(100.0100) Image processing : Image processing
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(310.0310) Thin films : Thin films

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: June 10, 2011
Revised Manuscript: July 20, 2011
Manuscript Accepted: July 21, 2011
Published: August 22, 2011

Citation
Zhanwei Liu and Jianxin Gao, "Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film," Opt. Express 19, 17469-17479 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17469


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References

  1. W. Fang and J. A. Wickert, “Determining mean and gradient residual stress in thin films using micromachined cantilevers,” J. Micromech. Microeng.6(3), 301–309 (1996). [CrossRef]
  2. M. B. David and V. M. Bright, “Design and performance of a double hot arm polysilicon thermal actuator,” Proc. SPIE, Micromacined devices and components III 3224, 296–306(1997).
  3. J. W. Suh, S. F. Glander, R. B. Darling, and C. W. Storment, “Organic thermal and electrostatic ciliary microactuator array for object manipulation,” Sens. Act. A: Physical58, 51–60 (1997). [CrossRef]
  4. H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Thermal expansion coefficient of polycrystalline silicon and silicon dioxide thin films at high temperatures,” J. Appl. Phys.87(9), 4189–4194 (2000). [CrossRef]
  5. W. L. Fang, H. C. Tsai, and C. Y. Lo, “Determining thermal expansion coefficients of thin films using micromachined cantilevers,” Sens. Act. A: Physical77, 21–27 (1999). [CrossRef]
  6. H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Novel imaging system for measuring microscale curvatures at high temperatures,” Rev. Sci. Instrum.71(1), 161–167 (2000). [CrossRef]
  7. P. H. Townsend, D. M. Barnett, and T. A. Brunner, “Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate,” J. Appl. Phys.62(11), 4438–4444 (1987). [CrossRef]
  8. 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). [CrossRef]
  9. C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterisation of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain42(3), 197–205 (2006). [CrossRef]
  10. J. B. Zhang and T. C. Chong, “Fiber electronic speckle pattern interferometry and its applications in residual stress measurements,” Appl. Opt.37(28), 6707–6715 (1998). [CrossRef] [PubMed]
  11. W. H. Peter and W. F. Ranson, “Digital imaging technique in experimental stress analysis,” Opt. Eng.21, 427–431 (1982).
  12. B. Pan, H. M. Xie, T. Hua, and A. Anand, “Measurement of coefficient of thermal expansion of films using digital image correlation method,” Polym. Test.28(1), 75–83 (2009). [CrossRef]
  13. J. X. Gao and H. X. Shang, “Deformation-pattern-based digital image correlation method and its application to residual stress measurement,” Appl. Opt.48(7), 1371–1381 (2009). [CrossRef] [PubMed]
  14. F. P. Zhu, W. W. Liu, H. J. Shi, and X. Y. He, “Accurate 3D measurement system and calibration for speckle projection method,” Opt. Lasers Eng.48(11), 1132–1139 (2010). [CrossRef]
  15. Ultem* 1000B Film, Product Datasheet, http://www.tekra.com/products/polycarbonate/Ultem-1000B.pdf
  16. DuPont Kapton® HN, polyimide film Technical Data Sheet, http://www2.dupont.com/Kapton/en_US/assets/downloads/pdf/HN_datasheet.pdf

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