Experimental Techniques
https://doi.org/10.1007/s40799-021-00447-3

APPLICATIONS PAPER

Uncertainty Quantification for DIC Displacement Measurements
in Industrial Environments
T. Siebert 1 & E. Hack 2 & G. Lampeas 3 & E. A. Patterson 4& K. Splitthof

1

Received: 30 June 2020 / Revised: 13 November 2020 / Accepted: 23 January 2021
# The Author(s) 2021

Abstract
Background: most methods of uncertainty quantification for digital image correlation are orientated towards the research environment and it remains difficult to quantify all of the uncertainty introduced along the measurement chain in an industrial
environment. This gap in capability can become critical when physical tests are required for certification purposes. Objective:
To develop and demonstrate an uncertainty quantification method that was independent of a specific DIC system, easily
integrated with the measurement workflow, applicable at the measurement location and capable of capturing the contributions
from all sources of uncertainty. Methods: an elegant new method utilises the calibration target, commonly used with DIC systems
to evaluate their intrinsic and extrinsic parameters, through reference measurements before and after relative motion between themeasurement system and the object of interest. The method is described and demonstrated for quantifying the field of uncertainty
associated with maps of displacement and deformation in a large-scale industrial component. Results: The fields of uncertainty
associated with measurements, using stereoscopic DIC, of x-, y- and z- displacement components during a compression buckling
test on an aircraft fuselage panel are presented. The derived uncertainty has independently been corroborated along one axis bymoving a calibrated translation stage. Conclusions: A new method has been proposed that allows the quantification of the fields
of uncertainty arising from all sources when DIC measurements are performed on a large-scale object of interest in an industrial
environment. The method requires no additional equipment and can be readily included in the workflow of a measurement
campaign.
Keywords Digital image correlation . Uncertainty quantification . Industrial environment . Uncertainty field

Introduction
In recent years, full-field optical methods for measuring shape,displacement and strain in components have gained in popularity in both research and industry as tools for design anddevelopment. Digital image correlation (DIC) has become
ubiquitous because it requires only grey-scale images that* E. A. Patterson
eann.patterson@liverpool.ac.uk
1

Dantec Dynamics GmbH, Ulm, Germany

2

Empa - Swiss Federal Laboratories for Materials Science andTechnology, Duebendorf, Switzerland

3

Industrial Systems Institute, Athena Research and Innovation Center,
Patras 265 04, Greece

4School of Engineering, University of Liverpool, Liverpool L69 3GH,UK

can be acquired using relatively simple and low-cost equipment and it provides global distributions of the threedimensional components of shape, displacements and deformation [1, 2]. DIC can be used to identify the location andamplitude of the maximum surface strain, to characterise
crack growth behaviour and, via inverse analysis, to evaluate
material properties for both elastic and plastic deformation as
well as to understand the global behaviour of large structures.
However, the quantification of the uncertainty in DIC measurements is less advanced and less widely practised than themeasurement technique. There is a considerable and evolving
literature on the uncertainty in DIC measurements, including
by Reu and his collaborators [e.g. 3, 4], Lavatelli et al. [5] andThai et al. [6]. A number of different approaches have been
investigated including noise floor determination, measurement of rigid body movements, error propagation and using
physical reference materials [3]. However, most of these approaches are orientated towards the use of DIC in a research
environment and it remains difficult to quantify all of theExp Tech

uncertainties introduced along the entire measurement chain,
particularly when measurements in industrial environments
are required. However, the need to quantify measurement uncertainty becomes greater in the industrial environment where
physical tests are often conducted for certification purposes, orto provide data for the validation of computational models thatare used to support decisions with socio-economic consequences. In these circumstances, a knowledge of the measurement uncertainties is required to assess the significance ofdifferences between predictions and measurements [7, 8].
Outside of the controlled environment of a laboratory, theinfluence of conditions in an industrial environment, including
the scale of the object of interest, the ambient lighting conditions and the difficulties associated with creating a suitablespeckle pattern, poses a significant challenge to the quantification of the uncertainties in measurements of a real test object. In practice, these obstacles often lead to quantification of
the uncertainties associated with a DIC system in the laboratory, for instance using a reference material to provide a continuous chain of comparison to a national standard [9, 10],which is assumed to be the minimum uncertainty achievablein measurements made in the industrial environment. This
assumption leads to conservative judgments on the extent towhich predictions represent a physical test and might result in
additional costs when reliable predictions are unnecessarily
rejected. Hence, a need was identified for a straightforward
but reliable assessment of the uncertainty associated withmeasurements acquired using stereoscopic digital image correlation in an industrial environment. Based on advice frompractitioners in industry, the aim was to develop a methodwith the following features: independence from specific DIC
system or manufacturer; ease of integration with workflow in
any measurement process; applicable at the measurement location; and capability to capture the contributions from all
sources of uncertainty [11].
The method was developed in an international collaboration involving a DIC vendor, a major industrial user, twonational laboratories and two university research groups.
And, it is based on a series of measurements of the object ofinterest and the calibration target of the DIC system both before and after a relative rigid body motion between the measurement system and the object of interest. The method and its
application to a 1 m2 panel from the fuselage of an aircraft aredescribed in the following sections. The output from the method are fields of uncertainty for the x-, y- and z- displacement
measurements in the field of view of the DIC system.

Measurement Uncertainty Quantification
The calibration of a stereoscopic DIC system provides the
projection parameters of the DIC system together with anestimate of the uncertainty associated with the reconstructedx-, y-, z-components of the coordinates. However, an uncertainty quantification should be performed in industrial environments with the DIC system located in front of the object ofinterest and set-up to acquire the desired measurements.
The objective of the uncertainty quantification is tocapture the effects of error sources associated with theobject of interest and the environmental conditions. In
addition, some DIC systems may use a different correlation algorithm for determining the positions of the features in the target compared to the one used for correlation of the speckle pattern on an object surface; and this isalso accounted for in the uncertainty quantification. The
uncertainty quantification is performed by introducing arigid body motion between the measurement system andthe object of interest. This motion is the same for theentire region of interest and is compared to the motion
evaluated by the measurement system to yield a field of
deviations which are a direct measure of the deformation
uncertainty. This could be achieved by acquiring imagesof the region of interest on the test object before and after
introducing the relative rigid body motion between themeasurement system and the object; and then, by correlating the images to obtain a field of values that can becompared to the applied relative motion, to obtain thefield of deviations. However, this requires detailed information about the applied motion; and, since it is difficult
to introduce a known rigid-body motion of the required
accuracy, it is preferable to measure the applied rigidbody motion. This is done by fixing the reference target,
Fig. 1, in the field of view of the measurement system infront of the object and acquiring images of it before andafter applying the motion. Consequently, the uncertainty
quantification consists of four measurement steps
sandwiching a physical movement and followed by a correlation step, Fig. 2, namely:
A. Acquire images of the object of interest and use them tocalculate the shape and position of the object;
B. Place the reference target in the field of view in front of
the object of interest and acquire images;
C. Apply a rigid body motion to the measurement system.
The amount and direction should be in the range of the
expected deformation during the test;
D. Acquire images of the reference target in the field of viewin front of the object;
E. Remove the reference target and acquire images of theobject of interest and use them to calculate the shapeand position of the object again;
F. Correlate images from B and D to determine the rigidbody motion relative to the reference target;
G. Transform the object coordinates from step A using therigid-body motion from step F and compare with theobject coordinates from step E.

Exp Tech

Application of Measurement Uncertainty
Quantification
Set‐up of ExperimentFig. 1 Picture of calibration/reference target showing a chessboard
pattern; the corners of the squares provided the reference features in theuncertainty quantification and had been measured by an accredited
laboratory thus providing traceability to the national standard for length

Steps A and E both generate fields of measurements with
x-, y- and z- coordinates of the object of interest and thedifference between them can be compared quantitatively withthe measured value of the rigid body motion from step F toyield fields of deviation for each component of displacementthat are a direct measure of the corresponding uncertainties. In
order to avoid introducing errors, it is important no changes
are made to the DIC system between steps A and B, that thelocation of the calibration target relative to the object of interest must not change between steps B and D, and that the DIC
system and its location relative to the object of interest are notchanged during steps D and E.

The use of the proposed method for quantifying the measurement uncertainty associated with using a stereoscopic DIC
system was demonstrated during a measurement campaign
conducted on a 1 m2 piece of an Airbus A-340 fuselage shownin Fig. 3. The piece of fuselage consisted of the aircraft skinriveted to a framework of stringers and frames. The skin had
transverse and longitudinal joints that were also riveted. The
edges of the panel parallel to the frames (top and bottom in
Fig. 3) were bonded into U-shaped channels, or potting boxes,
in order to allow it to be loaded in compression in an Instron
1346 testing machine, as shown in Fig. 4. The two printed
speckle patterns provided by Airbus and Dantec Dynamics
were respectively pasted to the left and right halves of theoutside face of the fuselage panel. The size of speckle in the
two areas was 2–3 pixels and 3–5 pixels approximately for the
Airbus and Dantec Dynamics patterns, respectively, and themorphology of the patterns was different as shown in Fig. 4.
A commercially available stereoscopic DIC system(Q-400, Dantec Dynamics GmbH) consisting of two cameras(Baumer VCXG-51 M) with 12 mm lenses (Schneider
Kreuznach) and a LED light system was set up to view theouter surface of the panel as shown in Fig. 4. The stand-off
distance of the DIC system from the panel was approximately
1.9 m with a distance of 0.64 m between the cameras giving astereoscopic angle of about 18 degrees. The stereoscopic angle was smaller than the recommended value of 27 degrees[11] due to the constraints imposed by the pillars of the test
machine which would otherwise obstruct the field of view.

Fig. 2 Flowchart for the uncertainty quantification which is conducted in front of the object of interest using a reference/calibration target and rigid body
motion of the DIC system; the steps A to G are described in Measurement Uncertainty Quantification section

Exp Tech

Fig. 3 Inner face of fuselage panel from an Airbus A-340 aircraft
showing the stringers (vertical), frames (horizontal) and both horizontal
and vertical riveted joints

Once the DIC system was set up to view the entire fuselage
panel, a calibration was performed following the proceduredescribed by the manufacturer and using a 50 × 50 cm calibration target with a chessboard pattern that had been engraved by a laser. The values of the calibration parameters
are given in Table 1. The corners of the squares in the chessboard pattern formed the features used in the new method of
uncertainty quantification. Their positions had been measured
by an accredited laboratory with an uncertainty of 2.5 µm forthe x- and y- directions, which defined the plane of the chessboard, and 5 µm for the z-direction, which was normal to thechessboard [12]. The size of these uncertainties is sufficiently
small that they will not introduce a significant error into themethod.
Image correlation of the speckle pattern was performed
using a facet size of 23 × 23 pixels and a pitch of 17 pixels.
No filters or smoothing were used in the calculations of shapeand displacements. The results were presented in a Cartesian
coordinate system with the x-axis along the front horizontal
edge of the lower potting box, the xy-plane defined by a pointon the front edge of the upper potting box, and the z-axis
pointing from the lower potting box towards the DIC system.

Determination of Measurement Uncertainty
After performing the calibration process following the instructions provided by the vendor of the DIC system, a pair ofstereoscopic images (image pair A) was captured of the object

Fig. 4 Set-up for measurement campaign showing panel from A-340
fuselage in test machine arranged for compression test and calibration/reference target in position with stereoscopic DIC system in foreground(top) and speckle patterns on sticky-backed plastic applied to outersurface (bottom) with close-up images of speckle pattern on left
(top close-up) and right (bottom close-up) with the facet size
illustrated (centre close-up)

of interest in its unloaded state with the speckle pattern applied. Then, the reference target, which in this case was thevendor supplied calibration target, was introduced again directly in front of the fuselage panel, and fixed in position. A
pair of stereoscopic images of the reference target (image pairB) were captured without adjusting the DIC system.
Subsequently, the DIC system was moved by a small
amount to introduce a rigid body motion between the measurement system and the object of interest (step C) by moving
its tripod perpendicular to and away from the fuselage panel.
The rigid-body motion was perpendicular to the panel because
the principal direction of deformation of the panel in the compression test was expected to be out-of-plane.
After moving the DIC system, a second pair of stereoscopic
images (image pair D) were acquired of the reference target inits fixed position without adjusting the optical arrangement of
the system. Finally, the reference target was removed from thefield of view without disturbing anything else, a second pair ofstereoscopic images of the fuselage panel (image pair E) were
captured.

Exp Tech
Table 1 Details of calibration
Camera 1

Camera 2

Focal length [px]Principal Point (x, y) [px]Radial Distortion k1
Radial Distortion k2
Tangential Distortion p1

3670.58(1263.2, 1034.4)
0.10310.0820-0.00013

3675.94(1219.9, 1019.0)
0.11980.2370-0.00021

Tangential Distortion p2
Rotation (x, y, z) [rad]Translation (x, y, z) [mm]Calibration residuum [px]Calibration Target ID

0.00015-0.00004(1.9579, 1.9528, 0.3230)(2.1210, 2.1468, -0.0023)(-191.22, 43.98, 1990.34)(-168.29, 43.62, 2029.98)
0.059923577541668913977-125993040-102-1171-verified −102–1171

The applied rigid-body motion of the DIC system was calculated using the two sets of image pairs (B & D) of thereference target captured before and after the motion.
Although the intention had been to move the DIC system ina direction perpendicular to the fuselage panel, the correlationof these image pairs revealed a translation of 4.53 mm in the xdirection (horizontal in-plane), 1.69 mm in the y-direction(vertical in-plane) and − 2.71 mm in the z-direction (positive
away from the panel) with a small rotation of 0.23 degrees
around the z-axis. These movements are of approximately thesame order of magnitude as the expected displacements andhence the in-plane translations should not influence the results
because the principal contributions to the uncertainty are independent of the displacements.
The calculated rigid-body motion, based on image pairs B& D, was applied to the coordinates of the object of interest
which defined its shape as calculated from image pair A.
These translated coordinates of the panel were compared toits measured coordinates obtained from image pair E following the rigid-body motion of the DIC system. The deviation
between the translated and measured coordinates are shown in
Fig. 5 and describe the uncertainty of the measurement system
set-up to perform the measurement campaign, including errors
arising from the DIC system, speckle pattern on the panel andenvironmental influences, such as ambient lighting conditions. The same data is combined in Fig. 6 to show the magnitude of the deviations as a distance from the threedimensional shape of the fuselage panel and also shown in
Fig. 7 as a ‘box and whisker’ plot.
The three-dimensional presentation of the data in Figs. 5
and 6 allow an assessment to be made about whether any
systematic error is present, which does not appear to be thecase in this example. It should be noted that the elevated linesof data running parallel to the x-axis in these figures represent
the potting boxes at the top and bottom of the fuselage panel. It
is clear from Fig. 5 that the fields of deviations for the y- and zdisplacements are larger (absolute means of 0.015 and0.018 mm, respectively) than those for the x-displacement(absolute mean of 0.007 mm). This is likely due to the small
stereo angle in the DIC system which was set up with thecameras on a common line approximately parallel to the xaxis. However, the distributions of deviations are clearer in thebox and whisker plot where it can be seen that mean andmedian values for the x-, y- and z-directions are approximately the same in absolute terms although the x-values are theclosest to zero. However, the scatter in the values for the zdisplacement is substantially larger with an expanded uncertainty [13] (2σ ¼ 42μm ) four times larger than the corresponding intervals for the x- ( 2σ ¼ 8μm ) and ydisplacements (2σ ¼ 12μm ). It is worth noting that the formof the fields of deviations in Fig. 5 is similar to effects causedby heat waves as observed by previous investigators, e.g. [14];however, there is no evidence available from our experiment
to corroborate this observation.
The measurement campaign on the fuselage panel was thenconducted as part of the Horizon 2020 Clean Sky 2 project,
MOTIVATE [15] and a video is available of the process of
capturing the data as described above [16].

Verification of Measurement Uncertainty
In order to verify the outcomes of the procedure described above,
an alternative method was used to evaluate the measurement
uncertainty using a speckled plate mounted on a single-axis
motorised stage whose uncertainty of movement had been previously verified using an interferometer and found to be 8 μm
over a travel of 50 mm with a systematic error of 0.2 μm/mm[12]. The motorised stage (PI 405. DGII, Physik InstrumenteGmbH & Co. KG) was mounted in front of the fuselage panel
with its direction of travel in the negative x-direction. The speckled plate of dimensions 115 × 115 mm was attached to the motorized stage with its plane parallel to the xy-plane and its speckled surface facing the DIC system, as shown in Fig. 8. The stage
was moved in steps of 10 mm up to 40 mm in one direction
followed by an additional 5 mm step in the same direction, before
reversing the direction of motion applying 10 mm steps so that

Exp Tech

Fig. 6 Magnitude of the deviations in microns over the shape of thefuselage panel and potting boxes obtained by comparing the translated
and measured coordinates of the fuselage panel from Fig. 5; the statistical
data provided above the plot relates to: maximum value, minimum value,mean, median, and the standard deviation, all in mm

the steps in the two directions were interlaced, as shown in Fig. 9.
At each step, three pairs of images were captured and the wholeprocess was repeated four times so that a total of 12 image pairs
were acquired at each position of the stage. In Fig. 9, an image isshown, collected at the farthest position, i.e. -45 mm from thestarting position, together with the displacement measured fromthe starting position based on correlation of the images. The
mean value of displacement for the plate obtained from the image
correlation was subtracted from the known position of the stage
to obtain a deviation based on each of the 12 image pairs for eachposition, i.e. 108 (= 12 repeats for 9 positions) values of deviation
in total and these values are plotted in Fig. 10.
The standard deviation is about 4µm for each stage positionin Fig. 10 which is of the same order as the standard deviationfrom the DIC measurements of the object. The data in
Fig. 10 imply that the uncertainty for a 10 mm movement isabout 0.18 µm/mm based on fitting a regression line to all of
the data.

Discussion

Fig. 5 Fields of deviations in millimetres of the x- (top), y- (middle) andz- (bottom) displacements plotted over the shape of the fuselage panel andpotting boxes obtained by comparing the translated and measured
coordinates of the fuselage panel. Above each plot the following
statistical data is provided: maximum value, minimum value, mean,
median, mean of absolute values and the standard deviation

A new method has been described for quantifying the uncertainty in measurements made with a digital image correlation
system in an industrial environment. The main features of themethod are that: it can be easily integrated in the workflow ofa measurement campaign; no additional equipment is required; the uncertainties associated with the whole measurement process are captured, including those arising from theobject of interest and environmental conditions; and it provides values for the uncertainty in the x-, y- and zdisplacements independently and for the entire measured surface of the object. The new method is based on the known

Exp Tech
Fig. 7 Box and whisker plot forthe deviations in x-, y- and zdirection in millimetres including
all of the measurement points ofFig. 5, showing the median (redline), mean (red cross), andintervals of 16–84 % (blue box)
and 2–98 % (black error bars) of
the distribution of deviations

geometric features in the calibration target used in the usualcalibration of a DIC system to establish its projection parameters. A chain of traceability to the national standard for length
can be established by measuring the position of the features in
the calibration target using certified instrumentation; this is an
essential feature when the intention is to establish the uncertainty in a set of measurements. The use of the calibration
target also provides results that are independent of the objectof the measurement campaign which provides a stronger basis
for comparisons between datasets. In addition, the approachallows the full field of view to be considered rather than only
the domain occupied by the test object. These factors will be
important when more than one test object is to be measured
and might not be positioned in precisely the same location in
the field of view. Further, Reu [17] identified the importanceof using a high-quality calibration target in order to reduce
uncertainty in the projection parameters determined throughFig. 8 Motorised stage andspeckled plate set up forverification of the measurement
uncertainty, placed in front of theaircraft panel

the calibration process, and, hence, this approach will complement his recommendations.
Many investigations of errors in DIC measurements haveused rigid-body motions [e.g. 18–21]; however, most of theseinvestigations were laboratory-based and orientated towards enhancing knowledge of uncertainties and their sources. Whereas
the method proposed here is designed to be implemented in anindustrial environment and on a large scale, for example on fullscale tests of aircraft structures [22], and to yield fields of uncertainties for the x-, y- and z-components of displacement measurements. Hence, the new method provides uncertainty values
across the field of view of the DIC system rather than a single
value for the whole field as in previous work based on referencematerials [9, 10] or based on evaluating standard deviations orroot mean square errors (RMSE) in measurements [e.g. 23, 24].
It incorporates error sources from the instrumentation, the environmental conditions and from the object of interest and its

Exp Tech

Fig. 9 Graph (top) showing axial position of motorized stage as afunction of time, stereoscopic pairs of images were acquired of the
speckled plate mounted in the stage at each pause in the motion; anddisplacement (bottom) from initial position at the maximum excursionof -45 mm based on correlation of the images

speckle pattern. The effect of the former has been investigatedextensively [e.g. 3, 4] and the latter was modelled analyticallyand numerically by Lavatelli et al. [5], Su et al. [25] and experimentally by Badadani et al. [26] and Jee et al. [27]. While
recently, Matthews et al. [28] have considered the influence of
external or environmental factors on digital image correlation.
However, the method presented above represents an attempt tocapture the effect of all sources of uncertainty in measurements
made in industrial environments using digital image correlation.

Fig. 10 Deviation in µm of the position of stage from the measured
displacement as function of the set position in mm for 12 repeats

Its applicability in a measurement campaign on a large-scale
panel for the aerospace industry has been successfully
demonstrated.
The method has been designed for use in an industrial
environment where the object of the measurement campaign
is likely to be large and hence it will usually be easier to movethe DIC system rather than the object and calibration target.
However, it is a relative movement that is required and so it isacceptable to move either the DIC system or the object andcalibration target providing that the relative position of theobject and target remain unchanged. The easier option was
adopted in this demonstration, which was to move the DIC
system. The DIC system was moved on its tripod after ensuring that the set-up was secure and rigid so that the calibrationof the system was not disturbed. When a very small relative
movement is required because the expected displacements ofthe test object are small, then it might be appropriate to include
translation stages to ensure very small movements of the DIC
system can be made reliably.
Developing an approach for use in industrial environments
also motivated the choice of the calibration target rather than a‘perfect’ speckled reference plate with a known minimum uncertainty that was substantially less than other sources of uncertainty.
The design of such a speckled plate would be system dependentand necessitate its preparation for each test setup thus rendering it
substantially less practical than a readily available calibration target. While in the demonstration a calibration target was employedwhich had been supplied with the DIC system by the vendor, any
calibration target would suffice providing that the DIC software
can determine the position of the features in the target. As this is a
pre-requisite for every calibration target, it renders the approach
independent of a particular calibration target. It is important thatany errors in the feature positions of the calibration target are
sufficiently small as to have an insignificant influence on themethod; and, this was ensured in the demonstration by measuring
the calibration target in an accredited laboratory which also provided traceability to the international standard for length. It is goodpractice to provide traceability and it will be a requirement for
many measurement campaigns in industry, especially when themeasurements are required to support regulatory cases.
The results from the application of the new method to ameasurement campaign focussed on 1 m2 panel cut from an
A-340 fuselage have been verified by comparison to thoseobtained using a single-axis motorised stage with a flat, speckled plate placed in the field of view of the DIC system. The
results were found to be in good agreement. However, there
are some restrictions associated with the new method, including that there is no relative movement between the measurement system and the object of interest other than the applied
rigid body motion, and that the optical set-up of the measurement system is not altered throughout the process. If theserestrictions are not fulfilled then an offset might be introduced
into the measured uncertainties.

Exp TechConclusions
A new method has been proposed that allows the quantification of the uncertainty arising from all sources when DIC
measurements are to be performed on a large-scale object ofinterest in an industrial environment. The method requires noadditional equipment and can be readily included in theworkflow of a measurement campaign. The method uses thecalibration target employed in the usual calibration of a DIC
system which provides traceability to the national standard forlength, independence from the object of interest and uncertainty for the full field of view. The method has been demonstrated as part of the measurement campaign on a 1 m2 panel
from an aircraft fuselage set up for a compression buckling
test and yielded fields of deviations that characterised the uncertainties in the x-, y- and z-components of displacement
measured over the entire surface of the panel.
Acknowledgements The authors would like to acknowledge helpful discussions with Richard Burguete of the National Physical Laboratory, Ksenija
Dvurecenska of the University of Liverpool and Eszter Szigeti of Airbus
Operations Ltd. This research has received funding from the Clean Sky 2
Joint Undertaking under the European Union’s Horizon 2020 research andinnovation programme under grant agreement No 754660 MOTIVATE andwas supported by the Swiss State Secretariat for Education, Research andInnovation (SERI) under contract number 17.00064.

Declarations
Ethical Statement/Conflict of Interest There are no ethical issues associated with the research reported here and the authors declare that they
have no conflicts of interest. The views expressed are those of the authors
and not the Clean Sky 2 Joint Undertaking.
Open Access This article is licensed under a Creative Commons

Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as
you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were
made. The images or other third party material in this article are includedin the article's Creative Commons licence, unless indicated otherwise in a
credit line to the material. If material is not included in the article's
Creative Commons licence and your intended use is not permitted bystatutory regulation or exceeds the permitted use, you will need to obtain
permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.

4.
5.

6.

7.

8.

9.

10.

11.

12.

13.

14.
15.

16.
17.

18.

19.

20.

21.

References
1.

2.
3.

Lava P, Cooreman S, Debruyne D (2010) Study of systematic errors in strain fields obtained via DIC using heterogeneous deformation generated by plastic FEA. Opt Lasers Eng 48(4):457–468
Sutton MA, Orteu JJ, Schreier H (2009) Image correlation forshape, motion and deformation measurements. Springer, Berlin
Reu PL, Toussaint E, Jones E, Bruck HA, Iadicola M, Balcaen R,
Turner DZ, Siebert T, Lava P, Simonsen M (2018) DIC challenge:

22.

23.

24.

developing images and guidelines for evaluating accuracy and resolution of 2D analyses. Exp Mech 58(7):1067–1099
Fayad SS, Seidl DT, Reu PL (2020) Spatial DIC errors due to patterninduced bias and grey level discretization. Exp Mech 60(2):249–263
Lavatelli A, Balcaen R, Zappa E, Debruyne D (2019) Closed-loop
optimization of DIC speckle patterns based on simulated experiments. IEEE Trans Instrum Meas 68(11):4376–4386
Thai TQ, Hansen RS, Smith AJ, Lambros J, Berke RB (2019)
Importance of exposure time on DIC measurement uncertainty at
extreme temperatures. Exp Tech 43(3):261–271
CEN Workshop Agreement 16779 (2014) Validation of computational solid mechanics models. Comité Européen de Normalisation,
Brussels
Dvurecenska K, Graham S, Patelli E, Patterson EA (2018) A probabilistic metric for the validation of computational models. R Soc
Open Sci 5(11):180687
Patterson EA, Hack E, Brailly P, Burguete RL, Saleem Q, SiebertT, Tomlinson RA, Whelan MP (2007) Calibration and evaluationof optical systems for full-field strain measurement. Opt Lasers Eng
45(5):550–556
Hack E, Lin X, Patterson EA, Sebastian CM (2015) A referencematerial for establishing uncertainties in full-field displacement
measurements. Meas Sci Technol 26(7):075004
International Digital Image Correlation Society, Jones EMC,
Iadicola MA (eds) (2018) A good practices guide for digital image
correlation. https://doi.org/10.32720/idics/gpg.ed1
Crosbie LJ (2018) Quantification of uncertainties in measurements
using Digital Image Correlation (DIC), Master Thesis, Hochschule
Ulm University of Applied Sciences, September 2018
JCGM 100:2008, Evaluation of measurement data — Guide to theexpression of uncertainty in measurement, Joint Committee for
Guides in Metrology (JCGM/WG 1)
Jones E, Reu P (2018) Distortion of Digital Image Correlation (DIC)
displacements and strains from heat waves. Exp Mech 58:1133–1156
MOTIVATE, Matrix optimization for testing by interaction of virtual and test environments, H2020 Grant Agreement No. 754660
and Swiss SERI contract No. 17.00064, see https://www.
engineeringvalidation.org/overview. Accessed 9 Feb 2021
https://youtu.be/YH6uDNPKO0c (Video Showing the process ofUncertainty Quantification). Accessed 9 February 2021
Reu PL (2013) A study of the influence of calibration uncertainty
on the global uncertainty for digital image correlation using aMonte Carlo approach. Exp Mech 53(9):1661–1680
Wattrisse B, Chrysochoos A, Muracciole JM, Némoz-Gaillard M(2001) Analysis of strain localization during tensile tests by digital
image correlation. Exp Mech 41(1):29–39
Schreier HW, Braasch JR, Sutton MA (2000) Systematic errors indigital image correlation caused by intensity interpolation. OptEn
39:2915–2921
Bergonnier S, Hild F, Roux S (2005) Digital image correlation used
for mechanical tests on crimped glass wool samples. J Strain Anal
Eng Des 40(2):185–197
Hild F, Roux S (2006) Digital image correlation: from displacement
measurement to identification of elastic properties–a review. Strain
42(2):69–80
Littell J (2017) Large field digital image correlation used for fullscale aircraft crash testing: methods and results. In: International
Digital Imaging Correlation Society. Springer, Cham, pp 235–239
Reu PL (2013) Uncertainty quantification for 3D digital image
correlation. In: Imaging Methods for Novel Materials andChallenging Applications, Volume 3. Springer, New York,pp 311–317
Zappa E, Hasheminejad N (2017) Digital image correlation technique in dynamic applications on deformable targets. Exp Tech
41(4):377–387

Exp Tech
25.

26.

27.

Su Y, Gao Z, Zhang Q, Wu S (2018) Spatial uncertainty of measurement errors in digital image correlation. Opt Lasers Eng 110:
113–121
Badadani V, Sriranga TS, Srivatsa SR (2018) Analysis of uncertainty in digital image correlation technique for strain measurement.
Mater Today Proc 5(10):20912–20919
Jee C, Salata G, Nobes D, Duke K (2018) Investigating the effect ofa speckle pattern on measurement uncertainty in a threedimensional digital image correlation (3D-Dic) system, CSME
Conference Proceedings. https://doi.org/10.25071/10315/35392

28.

Matthews SJC, Jesson D, Smith P, Heliker M, Beavis L, James B,
Livesey R (2017) Evaluation of external errors relating to portable
use of Digital Image Correlation. In: Proceedings of iDICs 2017
Conference & Workshop. International Digital Image Correlation
Society, Barcelona, Spain, available at https://epubs.surrey.ac.uk/
848765/. Accessed 9th Feb 2021

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.