Metrol. Meas. Syst., Vol. 23 (2016), No. 3, pp. 461–480.
_____________________________________________________________________________________________________________________________________________________________________________________
Article history: received on Oct. 15, 2015; accepted on Apr. 10, 2016; available online on Jul. 18, 2016; DOI: 10.1515/mms-2016-0028.
METROLOGY AND MEASUREMENT SYSTEMS
Index 330930, ISSN 0860-8229
www.metrology.pg.gda.pl
A REVIEW OF SURFACE DEFORMATION AND STRAIN MEASUREMENT
USING TWO-DIMENSIONAL DIGITAL IMAGE CORRELATION
Sze-Wei Khoo
1
, 2
)
, Saravanan Karuppanan
2)
, Ching-Seong Tan
3)
1) Universiti Tunku Abdul Rahman, Jalan Universiti, Department of Industrial Engineering, Bandar Barat, 31900 Kampar, Perak, Malaysia
( khoosw@utar.edu.my, +60 12 557 6382)
2) Universiti Teknologi PETRONAS, Department of Mechanical Engineering, 32610 Bandar Seri Iskandar, Perak, Malaysia
(saravanan_karuppanan@petronas.com.my)
3) Multimedia University, Jalan Multimedia, Faculty of Engineering, 63000 Cyberjaya, Selangor, Malaysia
(cstan@mmu.edu.my)
Abstract
Among the full-field optical measurement methods, the Digital Image Correlation (DIC)
is one of the techniques
which has been given particular attention. Technically, the DIC technique refers to a non-
contact strain
measurement method that mathematically compares the grey intensity changes of the images captured at
two
different states: before and after deformation. The measurement can be performed
by numerically calculating the
displacement of speckles which are deposited on the top of object’s surface. In this paper, the Two-D
imensional
D
igital Image Correlation (2D-DIC) is presented and its
fundamental concepts are discussed. Next, the
development of the 2D-DIC algorithms in the past 33 years is reviewed systematically. The improvement of 2D-
DIC algorithms is presented with respect to two distinct aspects: their
computation efficiency and measurement
accuracy. Furthermore, analysis of the 2D-DIC accuracy is included, followed by a review of the DIC
applications
for two-dimensional measurements.
Keywords: surface deformation, strain measurement, two-dimensional digital image correlation.
© 2016
Polish Academy of Sciences. All rights reserved
1. Introduction
In the 21st century, the man-made structures and machines are getting more complex than
before. As a result, the surface deformation and strain measurement becomes ultimately
important in many engineering applications and − most of the time − the obtained strain values
are used to visualize the strength problems in a structural member. Thus, a precise strain
measurement method is needed as misleading results might cause much financial loss to the
industries and also put human lives in jeopardy. In order to overcome this situation, different
types of surface deformation and strain measurement methods have been invented and
improved to cope with the new challenges faced by the engineers . However, each of the surface
deformation measurement methods has its own advantages and disadvantages. For example,
the scratch strain gauge is valuable in measuring the dynamic events, but it is an expensive
method to determine the strain in a single location [1]. The electrical resistance strain gauges,
although they provide precise results in the measurement of surface deformation, are difficult
in handling which makes them imperfect strain measurement methods. They require especially
tedious procedures of fixing the strain gauges to a specimen [2]. The handling difficulty can
be solved by introduction of an extensometer as it is easily attached to the specimen [3].
However, attaching the extensometer to the specimen produces unwanted stress concentration
at the contact points between the extensometer’s arms and the specimen surfaces. Although,
in the brittle coating method, the preparatory activities − such as applying a coating on the
specimen’s surface − are rather simple, the coating itself encounters both flammability
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and toxicity problems [4]. As a result, the method is not commonly acceptable as safety
precautions against these dangers must be taken into account. The photo-elasticity method
is getting less popular as the finite element analysis grows rapidly. In addition, this technique
is limited to the transparent materials which exhibit the property of birefringence [5]. Therefore,
the photo-elastic coating method is introduced and the above problem is solved as the well-
polished surface of the specimen is covered with a thin sheet of photo-elastic material with
reflective adhesive [6]. However, this technique faces the same problem as the electrical
resistance strain gauges, where a perfect bond between the coating and the specimen is crucial.
Attention must be given to selection of the adhesive and preparation the surface. The geometric
moiré technique also faces the same problem as the electrical resistance strain gauges.
Moreover, this technique is unable to provide accurate results in analysis of the small strain and
is also not suitable for the high-temperature surface deformation measurement [7]. The
holographic interferometry is an advanced optical strain measurement method which provides
full-field deformation measurement results with a high degree of accuracy. This method does
not require surface preparation and it is suitable for all types of material surfaces [8, 9].
Nevertheless, a disadvantage of this method is blurring of the recorded hologram if the
equipment is not isolated from vibrations.
In the recent years, the Digital Image Correlation (DIC) technique is widely used for the
displacement measurement in experimental solid mechanics. In comparison with the
interferometry methods, the DIC technique has been given substantial attention as it does not
require a stringent experimental setup and a complex optical system. Furthermore, the surface
deformation measurement using the DIC technique can be carried out effortlessly since it
requires neither the fringe processing nor the phase analysis. Even though the theoretical
simplicity of the DIC technique is so attractive, the surface deformation and strain
measurements still require a huge computational cost. Therefore, the DIC algorithms have been
gradually modified and improved in the past three decades in order to increase their
computation efficiency and measurement accuracy. Today, numerous successful applications
from different areas can be found in the literature so that a review paper systematically
explaining the development of DIC technique is needed. In 2009, Pan et al. [10] published
a paper which extensively reviews the development of DIC algorithms. In their paper, the
technical information on the DIC technique was presented in an informative way. However,
development of the DIC technique over the years was not presented systematically and
chronologically. A more systematic review of the DIC technique in this way seems to be
desirable for readers to understand the improvement of DIC technique over the years.
Therefore, in this paper a review of the development of the two-dimensional DIC algorithm is
presented in a chronological way. The discussions are focused on two distinct aspects
of improvement of the 2D-DIC algorithms: their computation efficiency and measurement
accuracy. Furthermore, the accuracy analysis of the 2D-DIC is included, followed by a review
of applications of the DIC in the two-dimensional measurement.
2. Fundamental concepts of Two-Dimensional Digital Image Correlation
In general, the term Digital Image Correlation (DIC) refers to a non-contact strain
measurement method that mathematically compares the grey intensity changes of the images
captured at two different states: before and after deformation. This can be achieved by choosing
two subsets (small aperture for pattern matching) from the reference (undeformed) and the
deformed images for correlation. Ideally, the DIC technique is able to correlate many types
of patterns, such as grids, dots, lines and random patterns [11]. Nonetheless, the surface patterns
must exhibit the isotropic behaviour and do not have a preferred orientation as the repeating
textures would lead to problems with faulty registration. Therefore, the random speckle patterns
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Metrol. Meas. Syst., Vol. 23 (2016), No. 3, pp. 461–480.
shown in Fig. 1 are recommended because they are considered to be non-periodic textures.
Although the random speckle patterns look like the laser speckle patterns in nature, in the DIC
technique they directly adhere to the top of object’s surface. Thus, they are being deformed
along with the surface. Theoretically, there are several advantages of using a random speckle
pattern in the DIC technique. For example, the correlations during the image processing will
not be lost even when the object is experiencing large deformations. Besides, the speckle pattern
which contains much information is available everywhere on the entire surface, so that it
permits the use of subsets during the correlation process [12].
Fig. 1. Random speckle patterns.
In the surface deformation measurement using the Two-Dimensional Digital Image
Correlation (2D-DIC) technique, special attention must be given to the arrangement
of specimen, light sources and camera. This is because the accuracy and consistency
of a measurement depends heavily on the imaging system set-up. Fig. 2 shows a schematic
diagram of the experimental set-up for the 2D-DIC system. Basically, the specimen with
random speckle pattern on its surface must be positioned normally to the optical axis of camera
in order to eliminate the out-of-plane displacement. Then, during the entire strain inducing
event, a series of images are being captured before and after deformation, followed by storing
of the digital images in the computer for further processing. Technically, in the 2D-DIC
technique the digital image resolution plays an important role in improving the measurement
accuracy. This is because the image resolution represents the pixels (picture elements) of an
image. In other words, by using a higher spatial-resolution image, a more accurate result can be
obtained since each pixel is representing a more refined quantity of the sample’s surface space.
Fig. 2. A schematic diagram of the experimental set-up for 2D-DIC system.
At the beginning of the image matching process, the Region of Interest (ROI) in the reference
image has to be specified first, followed by determination of the corresponding subsets in the
deformed images. Fig. 3 shows matching of the subsets of the reference and the deformed
images, followed by determination of the displacement vectors which indicate movements
of the correlated subsets. This concept has been successfully applied since the neighbouring
points in the reference image are assumed to remain as the neighbouring points even after
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the deformation took place. In the DIC technique there is no guideline or rule in determining
the optimum size of a subset and therefore it is a very subjective matter. A large subset will
require a longer computation time and gives an average result of the displacement field.
However, a small subset contains an inadequate number of features and hence in the correlation
process it becomes difficult to be distinguished from other subsets. As a consequence,
the correlation may not provide a reliable result [13].
a) b) c)
Fig. 3. Determination of the displacement vectors using the
digital image correlation:
a) the reference image; b) the deformed image; c) the displacement vectors.
Technically, during the image matching process the following correlation criteria are applied
to evaluate similarity between the reference and the deformed subsets: the Cross-Correlation
Criterion (CC), the Sum of Absolute Differences Criterion (SAD) and the Squared Sum
Differences Criterion (SSD). Since the images are captured at two different states, there must
be some changes in the intensity values of digitized images. As a result, a similarity between
the selected subsets from the reference and the deformed images is significantly reduced,
together with the accuracy of the obtained results. Over the years, the correlation algorithms
that compensate the variations of intensity values have been developed. For example, the Zero-
Normalized Cross-Correlation Criterion (ZNCC) and the Zero-Normalized Squared Sum
of Differences Criterion (ZNSSD) have been reported to be the most robust correlation criteria.
This is because the accuracy of the results using the ZNCC and ZNSSD criteria are unaffected
by the offset and scale in lighting. Also, the Normalized Cross-Correlation Criterion (NCC)
and Normalized Squared Sum of Differences Criterion (NSSD) are reported to be unaffected
by the light scale, but be still sensitive to the offset in lighting. The detailed discussion on these
correlation criteria can be found in the literature [10, 14, 15].
In order to determine the average in-plane displacement of the specimen, mapping functions
or shape functions [16] are used to locate an initially square subset in the reference image within
the next captured image under loading conditions. For the rigid body translation, the zero-order
shape functions are used to represent the translation of each point within the selected subset in x
and y-directions. However, the zero-order shape functions are not adequate to represent
the subsets that are undergoing a combination of translation, rotation, normal strain and shear
strain. Therefore, the first-order shape functions are used and expressed in the form of:
y
y
u
x
x
u
u ∆
∂
∂
+∆
∂
∂
+=
1
ζ
, (1)
y
y
v
x
x
v
v ∆
∂
∂
+∆
∂
∂
+=
1
η
, (2)
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Metrol. Meas. Syst., Vol. 23 (2016), No. 3, pp. 461–480.
where:
1
ζ
and
1
η
are the total displacements of the subset; u and v are the translations;
x
u
∂
∂
and
y
v
∂
∂
are the normal strains;
y
u
∂
∂
and
x
v
∂
∂
are the shear strains;
x∆
and
y∆
are the distances from
the subset centre to an arbitrary point within the same subset in x and y-directions, respectively.
Fig. 4 shows the deformation parameters used to represent the average in-plane displacement
of a subset.
Fig. 4. The deformation parameters used to represent the average in-plane displacement of a subset.
If the sub-pixel accuracy is to be achieved in a measurement, the intensity values within
the sub-pixel locations have to be provided since the intensity of images captured with a digital
camera is discrete in nature. This can be achieved using a sub-pixel interpolation scheme which
is employed to represent the grey level values between the sub-pixel locations before starting
the image matching process. For example, bilinear interpolation [17, 18], bi-cubic spline
interpolation [19, 20] and bi-cubic B-spline interpolation [21] have been reported in numerous
papers. Higher-order interpolation schemes are always recommended in the analysis as they
provide results with a higher degree of accuracy. However, the time required for the image
correlation in such schemes is substantially longer than in a lower-order interpolation scheme
[10].
In the early stage, the commonly used coarse-fine searching scheme was the DIC algorithm
employed for determining the deformation parameters of zero-order shape functions [17]. This
algorithm would search for a corresponding subset in the deformed images, which maximizes
the correlation coefficient with the step size of 1 pixel. The step size is further reduced to
0.1 pixel or 0.01 pixel, depending on the sub-pixel accuracy level. Lastly, the DIC algorithm
was used to calculate the displacement parameters. Then, the displacement fields of specimens
were determined. In the last three decades, these algorithms were modified and improved in
order to simplify the iteration process during determination of the displacement parameters, as
well as to better the accuracy of DIC algorithms. The details of the development of DIC
algorithms are discussed in the following section.
3. Development of Two-Dimensional Digital Image Correlation algorithms
The Digital Image Correlation (DIC) was first introduced by Peters and Ranson [22]
in 1980’s for the experimental stress analysis. They proposed a digital imaging technique
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