Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film

Deformation-pattern-based digital speckle

correlation for coefficient of thermal expansion

evaluation of film

Zhanwei Liu1,2,*

and Jianxin Gao2

1Dept. of Mechanics, School of Astronautics, Beijing Institute of Technology, Beijing 100081, China 2TWI Ltd, Granta Park, Great Abington, Cambridge CB21 6AL, UK

* [email protected]

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 Optical Society of America

OCIS codes: (100.0100) Image processing; (120.0120) Instrumentation, measurement, and

metrology; (310.0310) Thin films.

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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

#149045 - $15.00 USD Received 10 Jun 2011; revised 20 Jul 2011; accepted 21 Jul 2011; published 22 Aug 2011(C) 2011 OSA 29 August 2011 / Vol. 19, No. 18 / OPTICS EXPRESS 17469

16. DuPont Kapton® HN, polyimide film Technical Data Sheet,

http://www2.dupont.com/Kapton/en_US/assets/downloads/pdf/HN_datasheet.pdf

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]. 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 [2,3]. In order to design micromachined devices properly, it is

necessary to characterize the coefficient of thermal expansion for thin film materials [4,5].

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]. Determination of property results from comparing the beam response to a

numerical model for curvature of multilayers [7]. Full-field optical techniques, such as phase-

shifting interferometry [8] and Electronic Speckle Pattern Interferometry (ESPI) [9] have been

applied to determine the thermal expansion of thin film under thermal loading. For example,

tests conducted by Dudescu et al. [9] 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]. 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]. Without the need to form an interferometric

fringe pattern, the optical set-up of DIC is rather simple. In 2009, Pan etal [12]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], 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], a large part of deformation information was not used.

This paper presents a novel Deformation-Pattern-based Digital Speckle Correlation

(DPDSC) method for CTE measurement, in which the whole image information before and

after deformation is used to CTE analysis in order to improve the measurement precision.

Direct displacement measurement and strain calculation is no longer necessary. Thus, the

noise will be alleviated and restricted greatly. Instead of using displacement components as

the basic variables in conventional digital image correlation, CTE are taken as the direct

variables. Each selected CTE corresponds to a specific deformation pattern under different

temperature. This deformation pattern as a whole is used to inversely affine transform the

digital image captured after heating. Once the CTE are properly chosen, the digital image


after inverse affine transformation will have the highest similarity to the digital image taken

before the object is heated, or in other words, will recover to the original image. This turns the

CTE measurement issue into a pure numerical computational process, i.e., to search for a CTE

that will maximise the correlation between the original image and the inverse affine

transformed image after heating. This can be implemented through an optimisation procedure.

Since the direct variables in such a numerical optimisation process are the CTE, the

conventional CTE measurement procedure in photomechanics which involves the complex

interpretation of a displacement field is no longer required. All of the calculating process is

programmed in software. This will facilitate the development of a compact system for CTE

measurement of film with ease of use for the operator.

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]. 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 r r T rθ ε θ α= ⋅ = ⋅∆ ⋅ (1)

where (r, θ) are the polar coordinates, u is the in-plane displacement vector, ε is the strain, and

∆T is the temperature change.

The DPDSC for CTE measurement developed in this paper is suitable in the elastic range.

Conventional approach to CTE measurement is to measure the strain under different

temperature expressed in Eq. (1) by measuring the displacement components at several

special locations. Considering the inevitable error in each individual measurement, our

approach does not follow this normal procedure. We know that the basic concept of DIC is a

displacement search process which is based on the criterion of correlation between two

images of an object corresponding to before and after its deformation. When a subset of pixels

in one image is searched out in the other image, i.e., the correlation between the two subset

images reaches the maximum, their coordinate difference is the displacement measured. This

concept of correlation search is adopted in our new approach. The difference is that the basic

variable in the new search process is the CTE, not the displacement components. In the new

approach, the task is to search for intrinsic parameters (CTE). Once they have the CTE values

corresponding to the actual mechanical behaviour and are used to inverse affine transform the

digital image corresponding to the film heated, the new image will recover to the original

image, i.e., the correlation will be a maximum. This can be implemented by an optimisation

process which is purely a numerical computation issue.

Therefore in essence, the new approach has taken full advantage of a known deformation

pattern, which is related to a specific mechanism, in the current case expanding by thermal

loading. Different CTEs correspond to different deformation patterns under the same

temperature. By looking at the deformation pattern over the entire region of interest in an

image, we can make use of the full information from the images, not just isolated

displacements at limited locations or special points.

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.

{ ( , )}, 1... , 1...

{ ( ' , ' )}, 1... , 1...

i j

i j

F F x y i M j N

G G x y i M j 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:


'' ' ( , )

'' ' ( , )

t

t

x x u x y

y y v 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.

'' ' ( , ) ' '

'' ' ( , ) ' '

t x

t y

x x u x y x x T

y y v x y y y T

α

α

= − = − ⋅ ⋅∆

= − = − ⋅ ⋅∆ (4)

Where x

α and y

α are the CTE in the x and y axes, respectively, while for isotropic material,

thex y

α α α= = .

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

' { ( '' , '' )}, 1... , 1...i j

G G x y i M j N= = = (5)

The correlation between this new image G’ and the original image F is calculated as:

2 2

' '

( ) ( ' ' )

F G F GC

F F G G

< ⋅ > − < > ⋅ < >=

< − < > > • < − < > >

(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 (x

α ,y

α ) in an implicit sense, i.e.

[ ( ), ( )]x y

C C u vα α= (7)

Different intrinsic parameters CTE (x

α ,y

α ) 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].


To ensure the new approach works effectively, in-plane rigid body displacement (u0, v0,

ω) should be taken into account in the correlation search process. In this investigation, in

order to check the effect of using telecentric lens, out-of-plane rigid body displacement is also

calculated. Therefore, the affine transformation becomes:

0 0 0 0

0 0 0 0

'' ' ( , ) ' '

'' ' ( , ) ' '

t x

t y

x x u y w x u x y x u y w x x T

y y v x w y v x y y v x w y y T

ω ω α

ω ω α

= − + − − = − + − − ⋅ ⋅∆

= − − − − = − − − − ⋅ ⋅∆ (8)

and the correlation has been a variational function of six variables:

0 0 0

( , , , , , )x y

C C u v wω α α= (9)

During the correlation search process, those trial rigid body displacements and CTE that

maximise the correlation are regarded as the final actual value for the measurement.

In practice, the whole search process is implemented by a two stage approach. The first

stage involves only the detection of the bulk of in-plane rigid body displacement field, i.e.,

only integer pixel rigid body shifts are considered. Once the bulk of rigid body displacement

is obtained, it is compensated for by simply shifting the image G backwards accordingly. This

paves the way for the next stage of a fine search process, focusing on the minute scale

differences between the two images. These minute differences consist of both the remainder

(fractional pixel) of the rigid body displacement field and the result of CTE, deformation,

and/or environmental disturbances. Once this second stage is done, CTE measurement is

completed.

4. Optimisation scheme for the correlation search process

Since there are six variables in the fine search process, the key to success is to design a proper

optimization scheme such that the possibility of being trapped in local maxima is small while

the computational cost of finding the global maxima of correlation is not too high to be

carried out with a conventional computer. In order to minimise the possibility of a false

optimisation result, a bounded exhaust search scheme [13] is adopted. The bound for in-plane

displacement (u, v) is within ±0.1 pixel, ±1% for in-plane rotation ω and ±2% for CTE (CTE).

The search steps for each variable vary, which follows a coarse-to-fine search procedure, such

that the total number of correlation search is not too large (1,000 to 20,000 times) for a

conventional computer to carry out the whole process within a reasonable period of time [13].

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 is a speckled image of one of the film

specimens’ surface.


Fig. 1. speckles image of film 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

After the heating tests, the CTE calculating procedure is as follows. (1) A pair of images, one

before and the other after heating, are loaded into the CTE program edited on the basis of the

DPDSC principle. The image scale factor is calculated automatically by measuring the size of

width or length of the sample in pixel which is then converted to the actual dimension. (2) To

select a region of interest (ROI). This is done by adjusting the radius of a circle of selection or

side length of a square of selection. The pixels of the ROI are used in the subsequent affine

transformation to calculate the CTE. (3) The button on the menu is pressed to start the

correlation optimisation process to calculate directly the CTE. It takes several minutes to

complete the whole computational process, depending on the total number of pixels of the

ROI selected and the optimisation strategy used.

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 ( ,x y

α α ). In this investigation,

the film materials used are isotropic one, sox y

α α 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

[15,16]. 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 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.


Fig. 2. CTE calculating window of a polyetherimide film

Figure 3(a) and (b) 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.


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

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].

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, 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], 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]. 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). 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.


Table 1. CTE results using different methods

Material method

CTE ( 30-1000C, ppm/0C) CTE (100-1500C, ppm/0C)

Sample Mean+std Sample Mean+std

1 2 3 1 2 3

Polyetherimide DPDSC 52.2 51.7 50.56 51.53∓0. 51.41 49.95 52.6 51.33∓1.34

(Ultem 1000B)

250Micrometer

thick

DIC 53.38 50.46 48.91 50.92∓2. 54.7 47.6 51.08 51.15∓3.58

IPC-

TM-

650[15] 52

52

PI

(Kapton HN)

50Micrometer

thick

DPDSC 16.94 16.33 17.41 16.89∓0.54 32.35 31.74 33.02 32.37∓0.64

DIC 15.23 16.90 18.41 16.85∓1. 29.55 32.92 36.92 33.14∓3.69

ASTM

D-696-

91[16]

17

32

Fig. 4. CTE comparsion of different film materials using different methods: (a) CTE of

Polyetherimide material, (b) CTE of Polyimide material


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.

The displacement field is always the direct focus in conventional DIC for CTE

measurement. DPDSC for CTE, however, has shifted that focus from displacement to CTE. In

addition, the current developed approach has turned a CTE measurement task to an

optimisation process based on the criterion of correlation. This is equivalent to looking at the

overall deformation pattern associated with a specific thermal expansion behaviour that is

represented by a set of intrinsic parameters CTE, rather than making isolated displacement

measurements at limited locations within the field of view in DIC. The intrinsic parameter

CTE governs the deformation pattern of an object under investigation, and thus is the prime

concern of a measurement task. By employing an optimisation strategy, the task of CTE

measurement can be turned to a correlation search process. That is, to find a set of intrinsic

parameters that, after being used to perform an affine transformation, will best recover the

deformed digital image to its original one. Apparently, the direct output of the proposed

approach is no longer the displacement field but the intrinsic parameters CTE. Once the

intrinsic parameters are found, the associated deformation patterns are already determined.

6. Conclusions

A novel DPDSC method for CTE measurement is proposed. It uses the intrinsic parameters

CTE as the direct variables in a correlation computation. Each set of such intrinsic parameters

and parameters of rigid body motion corresponds to a specific deformation pattern, which as a

whole is used to affine transform the digital image captured after the object is deformed by

heating. This turns the CTE measurement issue into a pure numerical computation process,

i.e., to search for a set of intrinsic parameters that will maximise the correlation between the

inverse affine transformed image and the actual original image.

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.


Documents

Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film