Politecnico di Milano · Politecnico di Milano Mechanics Department Master of Science in Mechanical...

Politecnico di Milano

Mechanics Department

Master of Science in Mechanical Engineering

Digital Image Correlation Techniques in Dynamic Application

on Deformable Targets

Supervisor: Prof. Emanuele Zappa

Master of Science Thesis by:

Navid Hasheminejad

Matr. N.: 801116

April 2015

شدیم شاد خود ز استادی چندیک شدیم استاد به کودکی به چندیک

شدیم باد چون و برآمدیم آب چو رسید چه مارا که شنو سخن پایان

هـ.ش( 015-724عمر خیام نیشابوری )

With them the seed of Wisdom did I sow,

And with my own hand wrought to make it grow;

And this was all the Harvest that I reap'd--

"I came like Water, and like Wind I go."

Omar Khayyam Neyshaburi (A.D. 1048-1131)

Translated by: Edward FitzGerald

I Table of Contents

Table of Contents Acknowledgment .................................................................................................................... III

List of Figures .......................................................................................................................... IV

List of Tables .......................................................................................................................... VIII

Abstract ................................................................................................................................... IX

1 Introduction and Thesis Outline ....................................................................................... 1

2 State of the Art ................................................................................................................. 4

3 Digital Image Correlation and its Techniques .................................................................. 7

3.1 Digital Image Correlation ......................................................................................... 7

3.2 2D DIC ....................................................................................................................... 7

3.3 Vic-2D ....................................................................................................................... 8

3.4 Time Delay of the Camera ........................................................................................ 9

3.5 Deconvolution Method .......................................................................................... 10

4 First Experiment ............................................................................................................. 11

4.1 Experimental Setup ................................................................................................ 11

4.2 Analysis by Vic-2D .................................................................................................. 14

4.3 Uncertainty Assessment of DIC Method by Vic-2D ................................................ 19

4.4 Deconvolution Analysis .......................................................................................... 25

5 Results of the First Experiment ...................................................................................... 31

5.1 Normal DIC Method for Different Conditions ........................................................ 31

5.2 Vic-2D vs. Deconvolution Method ......................................................................... 40

6 Deconvolution Analysis to Improve DIC Uncertainty ..................................................... 43

6.1 Generation of New Reference Images ................................................................... 44

6.2 Analysis ................................................................................................................... 47

6.3 Results .................................................................................................................... 47

6.3.1 Tests in Which Deconvolution to Create New Reference Images Is Useful ... 47

6.3.2 Tests in Which Deconvolution to Create New Reference Images Is Not Useful

……………………………………………………………………………………………………………………50

7 Second Experiment ........................................................................................................ 53

7.1 Experimental Setup ................................................................................................ 53

II Table of Contents

7.2 Calibration .............................................................................................................. 58

7.3 Beam Profile ........................................................................................................... 59

7.4 Laser Sensor ........................................................................................................... 61

8 Results of the Second Experiment ................................................................................. 67

8.1.1 Effect of Exposure Time on DIC Accuracy ...................................................... 70

8.1.2 Effect of Gain Value on DIC Accuracy ............................................................. 72

8.1.3 Effect of Diaphragm on DIC Accuracy ............................................................ 75

9 Deconvolution Analysis to Improve DIC Uncertainty ..................................................... 77

10 Conclusion .................................................................................................................. 84

10.1 Future Work ........................................................................................................... 85

References .............................................................................................................................. 86

III Aknowledgment

Acknowledgment

First of all, I would like to express my deepest gratitude to my adviser Dr. Emanuele Zappa

for his guidance and encouragement throughout my study and research. It was during his

classes that I got interested in image processing and its applications in Mechanical

Engineering, and it was his support that ended up to this master thesis.

I would also like to express my warm thanks to Dr. Marco Tarabini, Dr. Diego Scaccabarozzi

and other members of the measurement lab for helping me during the experiments.

Thanks also go to all my Professors in Politecnico di Milano and all my friends in Lecco whom

helped me throughout this academic period.

Finally, I would like to thank my parents and my lovely sister Nasim, for their unconditional

love and support during these two years. Without their continuous support and

encouragement, I would not have been able to complete this master program.

IV List of Figures

List of Figures Figure 1: Comparison of capturing images by camera and measuring displacement by laser

sensor in time with same trigger ............................................................................................. 9

Figure 2: Speckled Pattern on a Small Portion of the Beam .................................................. 11

Figure 3: Schematic configuration of the first experiment, front view (up), top view (down)

................................................................................................................................................ 12

Figure 4: Position of the beam, laser and the camera in the first experiment ...................... 13

Figure 5: Beam Profile of test 1 for images 101 to 115 (up) Standard Deviation of test 1 for

photos 101 to 115 (down) ...................................................................................................... 16

Figure 6: Beam Profile of test 1 for images 101 to 115 (up) and Standard Deviation of test 1

for photos 101 to 115 (down), using value sigma to filter the data with low accuracy ........ 17

Figure 7: Motion of a point at the end of the beam for test 1 of the first experiment, using

DIC procedure, without considering sigma ............................................................................ 18

Figure 8: Motion of a point at the end of the beam for test 1 of the first experiment, using

DIC procedure, considering sigma ......................................................................................... 18

Figure 9: Motion of the point in front of laser sensor, obtained by Vic-2D method and Laser

for test 1 ................................................................................................................................. 19

Figure 10: Amplitude and phase diagrams of Transfer function for test 1 ............................ 20

Figure 11: Cross correlation of the motion of a point in front of the beam acquired by laser

and estimated by Vic-2D analysis ........................................................................................... 21

Figure 12: Motion of the point in front of laser obtained by Vic-2D method, and Laser with

and without considering time delay for test 1 ....................................................................... 22

Figure 13: Spectrum of motion of the point in front of laser obtained by camera and laser 23

Figure 14: Spectrum of the motion of the point in front of laser obtained by camera and

laser after applying a hamming window ................................................................................ 24

Figure 15: Coherence for test 1 .............................................................................................. 24

Figure 16: Profile of the beam estimated by Deconvolution analysis, Vic-2D analysis and

position of a point acquired by laser sensor for images 101 to 104 respectively from top to

bottom for test 1 .................................................................................................................... 25

Figure 17: Noise of the profile of the beam across the beam estimated by Deconvolution

analysis, and Vic-2D analysis for images 101 to 104 respectively from top to bottom for test

1 .............................................................................................................................................. 26

Figure 18: Motion of the point in front of laser sensor, obtained by deconvolution method

and Laser for test 1................................................................................................................. 27

Figure 19: Autocorrelation of signals obtained by deconvolution method and laser for test 1

................................................................................................................................................ 27

Figure 20: Phase of Transfer Function and their fitted line to find the time delay for test 1 28

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V List of Figures

Figure 21: Spectrum of the motion estimated by Vic-2D, Deconvolution method and laser

sensor for test 1 ..................................................................................................................... 29

Figure 22: Amplitude and phase of transfer function for test 1 ............................................ 30

Figure 23: Coherence for test 1 .............................................................................................. 30

Figure 24: Peak spectrum error for different tests with different initial displacement of the

beam in constant exposure time (3000 µs) and gain value (0) .............................................. 31

Figure 25: NRMSE for different tests with different initial displacement of the beam in

constant exposure time (3000 µs) and gain value (0) ............................................................ 32

Figure 26: Peak spectrum error for tests with same exposure time (1000 µs), while

increasing gain and initial displacement together ................................................................. 33

Figure 27: NRMSE for tests with same exposure time (1000 µs), while increasing gain and

initial displacement together ................................................................................................. 34

Figure 28: Noise of the motion, estimated by normal DIC for test 9 and 11 ......................... 34

Figure 29: Peak spectrum error for different exposure times and initial displacements, with

gain between 0 and 3 ............................................................................................................. 35

Figure 30: NRMSE for different exposure times and initial displacements, with gain between

0 and 3 .................................................................................................................................... 36

Figure 31: Exposure time of camera multiplied by initial displacement at a point on the

beam in front of the laser for tests of the first experiment ................................................... 38

Figure 32: Peak spectrum error of normal DIC for the tests of the first experiment ............ 38

Figure 33: NRMSE of normal DIC for tests of the first experiment ........................................ 39

Figure 34: Profile of the beam estimated by Deconvolution analysis, Vic-2D analysis and

position of a point acquired by laser sensor for images 101 and 102 respectively from top to

down for test 5 ....................................................................................................................... 40

Figure 35: Noise of the profile of the beam across the beam estimated by Deconvolution

analysis, Vic-2D analysis for images 101 and 102 respectively from top to down for test 5. 41

Figure 36: NRMSE for 6 tests in different settings ................................................................. 42

Figure 37: Multiplication of exposure time and initial displacement for 6 tests of first

experiment ............................................................................................................................. 42

Figure 38: ratio signal and fitted sinc for Test 8, Image 2, w=5.06 ....................................... 44

Figure 39: (a) acquired image number 2 (b) original reference image (c) generated reference

image with w=5.06 for test 8 ................................................................................................. 45

Figure 40: ratio signal and fitted sinc for Test 5, Image 25, w=3.85 ...................................... 45

Figure 41: (a) acquired image number 2 (b) original reference image (c) generated reference

image with w=3.85 for test 5 ................................................................................................. 46

Figure 42: ratio signal and fitted sinc for Test 1, Image 6, w=1.39 ........................................ 46

Figure 43: Motion of the beam in front of the laser calculated by Vic-2D with original

reference image and generated reference images, and measured by a laser sensor as a

reference, for test 8 ............................................................................................................... 48

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VI List of Figures

Figure 44: Error of the motion estimation for test 8 with normal DIC and deconvolution to

generate new reference images, cyan lines mark the images in which Vic-2D could not

calculate the motion .............................................................................................................. 48





generate new reference images, cyan lines mark the images in which Vic-2D could not

calculate the motion .............................................................................................................. 49





generate new reference images ............................................................................................ 50





generate new reference images ............................................................................................ 51

Figure 51: NRMSE for normal DIC and DIC with Deconvolution to generate new reference

images .................................................................................................................................... 52

Figure 52: Photo of the experimental set up of the second experiment ............................... 54

Figure 53: Schematic configuration of the second experiment, front view (top), top view

(down) .................................................................................................................................... 55

Figure 54: Dot grid pattern used for calibration in second experiment ................................ 58


for images 0 to 14 (down) ...................................................................................................... 60


for images 0 to 14 (down) ...................................................................................................... 60

Figure 57: motion in front of laser sensor measured by DIC and Laser ................................. 61

Figure 58: Time delay for different exposure time ................................................................ 62

Figure 59: Motion in front of the laser sensor measured by DIC method and laser sensor

with the sampling rate of the camera, considering the time delay ....................................... 63

Figure 60: Error of the motion in front of the laser by measured DIC ................................... 63

Figure 61: Spectrum of the motion acquired by laser sensor and calculated by DIC method

for test 14 ............................................................................................................................... 64

Figure 62: Aliasing frequency to Real frequency ................................................................... 65

Figure 63: Spectrum of the motion acquired by laser sensor and calculated by DIC method

for integer number of cycles and considering aliasing problem for test 14 .......................... 66

Figure 64: [a]: portion of an image from test 41 [b]: portion of a saturated image .............. 67

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VII List of Figures

Figure 65: Peak spectrum error for tests with constant Diaphragm and Gain value, changing

the exposure time .................................................................................................................. 70

Figure 66: NRMSE for tests with constant Diaphragm and Gain value, changing the exposure

time ........................................................................................................................................ 71

Figure 67: Peak spectrum error over gain for tests with different diaphragm and exposure

times ....................................................................................................................................... 72

Figure 68: NRMSE over gain for tests with different diaphragm and exposure times .......... 73

Figure 69: The magnified diagram of the Peak spectrum error over gain for tests with

different and exposure times ................................................................................................. 74

Figure 70L the magnified diagram of NRMSE over gain for tests with different diaphragm

and exposure times ................................................................................................................ 74

Figure 71: Peak spectrum error over diaphragm for tests with gain equal to 9 and different

exposure times ....................................................................................................................... 75

Figure 72: NRMSE over diaphragm for tests with gain equal to 9 and different exposure

times ....................................................................................................................................... 76

Figure 73: index w for 100 images of test 30 ......................................................................... 77

Figure 74: [a]: One image acquired during the test, [b]: Generated reference image with w=

5.49, [c]: Original reference image ......................................................................................... 78

Figure 75: Displacement estimation for 98 images of test 11 with normal DIC, DIC with

generated reference images and laser sensor ....................................................................... 78

Figure 76: Displacement estimation for 98 images of test 7 with normal DIC, DIC with

generated reference images and laser sensor ....................................................................... 79

Figure 77: Spectrum of motion for test 11 with normal DIC, DIC with generated reference

images and laser sensor ......................................................................................................... 80

Figure 78: Spectrum of motion for test 7 with normal DIC, DIC with generated reference

images and laser sensor ......................................................................................................... 80

Figure 79: Ratio signal and the corresponding fitted sinc function in frequency domain for

the first image of test 24 ........................................................................................................ 81

Figure 80: NRMSE for different configurations of camera, for normal DIC and DIC with

deconvolution method ........................................................................................................... 82

Figure 81: Peak spectrum error for different configuration of camera for normal DIC and DIC

with deconvolution method ................................................................................................... 82

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VIII List of Tables

List of Tables Table 1: Test calender of the first experiment ....................................................................... 14

Table 2: Experimental setup of the first experiment ............................................................. 14

Table 3: Vic-2D Outputs ......................................................................................................... 15

Table 4: NRMSE for tests of the first experiment .................................................................. 37

Table 5: Experimental setup of the second experiment ........................................................ 53

Table 6: Test calendar of the second experiment .................................................................. 56

Table 7: Peak spectrum error for tests 0 to 30 ...................................................................... 68

Table 8: NRMSE for tests 0 to 30 ............................................................................................ 68

Table 9: Peak spectrum error for tests 7 and 11 for normal DIC and DIC using deconvolution

to generate new reference images ........................................................................................ 79

IX Abstract

Abstract

Digital Image Correlation (DIC) is a widely used optical measurement method to track the

motion of an object. Even though a lot of studies have been done on this method, there is

still a lot of improvements possible, especially in case of dynamic conditions. In dynamic

conditions since the target is moving, images acquired during the test have motion effect

(blurring). This blurring can increase the uncertainty of the motion measurement. The

present study aims to investigate the uncertainty of different DIC methods in dynamic

situation and find the variables of the camera and motion that can be effective in the accuracy

of DIC methods. The focus of the study is only on 2D DIC, but similar problems also exist in

3D DIC. Therefore an understanding of two dimensional problems can be helpful for future

studies in 3D conditions too. There were two sets of experiments done in this study. The first

experiment was done in different exposure times and gains of the camera, changing the initial

displacement entered to the tip of the beam. However, the second experiment is much more

extensive, as each variable was changed considering the other variables constant and instead

of applying a random initial displacement to the beam, a shaker was used to create the

motion. Moreover, in the second experimentation, other than exposure time and gain, the

effect of diaphragm aperture of the camera on the uncertainty of the motion was

investigated too. The first method used in the studies was normal DIC method, which was

done analyzing the acquired images in Vic-2D and MATLAB. The second technique was

deconvolution method to find the motion of the beam. Finally, using deconvolution

technique, the motion effect of the images acquired were estimated. Knowing the amount

of motion effect, new reference images with blurring were generated for each image taken

during the motion. Then DIC was applied comparing each image acquired during the test with

its own generated reference image. By this method the effect of blurring in the uncertainty

of the measurement is expected to decrease significantly.

Key words: Image Processing, Digital Image Correlation (DIC), Vibration Measurement,

Vic-2D, Deconvolution Method, Uncertainty, Motion Effect, Exposure Time

1 Introduction and Thesis Outline

Chapter 1


Over the recent years, using vision-based measurement have been a popular method in

experimental mechanics. This is duo to the fact that experimental settings are so much easier

in these methods. To do a vision-based measurement there is only need for a camera, proper

lightening and some pattern or signs on the specimen. These methods could be most useful

when access to the target specimen is not possible, therefore there is not the possibility to

attach sensors to the target.

Digital image correlation is one of the main techniques used in vision-based measurement.

However it has been used mostly in static applications and most of the studies on its

performances have focused on static conditions [1-6]. In recent years the application of DIC

method has been extended to dynamic applications too. The problem of using DIC method

in dynamic conditions is that, dealing with targets in motion cause blurring in the acquired

images. This blurring is an important source of measurement uncertainty in DIC

measurements. To solve this issue, deconvolution method to create new reference images

was suggested. In this method the motion effect that exists in the acquired images is

estimated by deconvolution method. Then this motion is used to simulate the estimated

motion effect on a reference image. This way the reference image has the same blurring that

the acquired image has. Therefore this could be an effective method to increase the DIC

accuracy in dynamic conditions [7, 8].

It is known that in static condition the measuring uncertainty of a vision-based measurement

system is dependent to image resolution, contrast, processing algorithm, noise, etc. but in

dynamic condition there are also other factors like exposure time of the camera or relative

motion between the camera and the object [9]. Therefore, setup of a camera and choosing

its parameters can be important for a DIC analysis in dynamic condition.

This study consist two sets of experiments and analysis of these experiments to find out the

important parameters of the camera that can affect the uncertainty of the DIC method.

Moreover, uncertainty of three different method to estimate the motion of the beam was

investigated.

The first experiment is done on a cantilever beam, with different initial displacement applied

to its tip. The parameters of the camera such as exposure time and gain are changed in

different tests. First, a normal DIC analysis is done on the images by help of Vic-2D and


MATLAB. Then the amount of influence of the variables such as initial displacement entered

to beam, exposure time and gain index of the camera on the accuracy of the DIC analysis is

investigated. Afterwards, the motion of the beam is estimated by another method named

deconvolution and the results are compared between the two methods. Lastly,

deconvolution method is used on the acquired images to generate new reference images.

Again a DIC analysis is done on the images considering the new reference images and

performance of this method is also compared with the normal DIC method.

The second experiment consists more tests in different conditions. Moreover, to investigate

the effect of camera’s parameters on the uncertainty of analysis more accurately the beam

is mounted on a shaker. The shaker applies a harmonic motion with fixed frequency and

amplitude to the beam. Besides, other than exposure time and gain index, the diaphragm

aperture of the camera is changed for different tests too. Like the first experiment a normal

DIC analysis is done on the images and the influence of exposure time, gain index, and

diaphragm aperture is investigated on the uncertainty of the analysis. Afterward, DIC analysis

with generated reference images with the help of deconvolution is done on the images and

the capability of the improvements done by this method is studied.

The main body of the work is organized as below:

Chapter 2 is state of the art of the study. It consist the researches that have been

done on DIC in both static and dynamic applications, and the uncertainty assessment

of DIC method in both cases and effect of camera parameters on DIC method for

dynamic conditions.

Chapter 3 explains the DIC method, Vic-2D software and deconvolution method that

was used in this research.

Chapter 4 contains the first experiment that was done and the analysis of the images

by two methods: normal DIC by Vic-2D and MATLAB, and deconvolution with

MATLAB. The procedure of analyzing the results for one test is explained and two

parameters named peak spectrum error and NRMSE are defined to compare the

uncertainty of the analysis for different tests and methods.

In Chapter 5 the analysis explained in previous chapter is done for all the tests, the

results are compared and the effect of different parameters in uncertainty of the

motion estimation is investigated. Furthermore, normal DIC and deconvolution

method are compared with each other.

Chapter 6 uses the deconvolution method to generate new reference images with

proper blurring to eliminate the uncertainty that is caused by the motion effect of

the images.

In Chapter 7 the second experiment is explained and the same procedure of

chapter 4 is done on the images acquired from this experiment.


Chapter 8 is comparison of the results of the second experiment. The peak spectrum

error and NRMSE is calculated for different conditions and effect of different

parameters of camera on DIC analysis is studied thoroughly.

Chapter 9 is again using deconvolution method to create new reference images for

acquired images of the second experiment and comparison of the results of this

method with normal DIC and investigation of the proper condition to use each

method.

Chapter 10 contains the conclusion of the study and suggestions for future works.

4 State of the Art

Chapter 2

2 State of the Art

DIC in Static Applications

Two-dimensional (2D) Digital Image Correlation (DIC) technique was first developed in the

1980s by several groups of researchers: Yamaguchi [10], Peter et al. [11] and Sutton et al. [12].

In the past few years, the DIC technique had been significantly improved through the

reduction of the computation's complexity, advancements in computers and imaging devices,

achievement of high accuracy contour/deformation measurement and expansion of its range

of application. The available literature in case of static DIC application is wide and a lot of

studies have been done to investigate the uncertainties of this method [1-4]. In 2002, the

symmetric errors that arise from the use of under matched shape function, i.e., shape

functions of lower order than the actual displacement field was analyzed by

H. W. Schreier et al. [5]. In 2009, M. Bornert et al. [6] proposed a general procedure to

evaluate DIC displacement measurements errors. It uses synthetic speckle pattern images

undergoing spatially fluctuating sinusoidal displacement fields. They evaluated the RMS error

of displacement obtained with various DIC formulations for different subset sizes, speckle

sizes and other parameters. But using the DIC method is not limited to static conditions. It

can also be applied to the specimens in the movement. But using it in dynamic condition arise

the motion effect in the acquired images. Therefore, the application of DIC in dynamic

application should be investigated too.

Implementing DIC in Dynamic Applications

Although, DIC uncertainty studies were mostly concentrated on static cases, its application

expanded to the dynamic conditions too. Some dynamic application of DIC that have been

studied recently are mode shape recognition [13-16] and vibration analysis [17, 18]. In 2003

an advance 3D image correlation photogrammetry was applied on two dynamic applications

by T. Schemidt et al. [19]. The first application was using short duration white light pulses to

study an automobile tire on road with up to 240 km/h speed. And the second study was using

a pulsed laser to study a flywheel.

5 State of the Art

In 2007, a DIC methodology was used to investigate the dynamic crack growth of a polymeric

beam, subjected to impact loading by M.S. Kirugulige et al. [20]. In 2009, DIC method was

used for shape recognition of a circular plate by W. Wang et al. [16]. In the same year, T.

Siebert et al. [21] showed the applications of DIC to measure the different mode shapes in

case of harmonic vibration, a shock phenomenon and noise excitation. In another research,

in 2009, DIC approach was performed on vibration analysis of a membrane for an impact test

and an excitation of a circuit board using white noise [18]. At the same time, M. N. Helfrick

et al. [22] investigated the possibility to use three-dimensional DIC for detecting damages

through curvature methods.

Later, in 2011, vibration mode shapes of a composite panel were measured by a DIC system

and the results were used to modify and update a FE model to predict the structural

responses by W. Wang et al. [14]. In another work, M. N. Helfrick et al. [17] measured the

vibration of a metal base dryer cabinet by DIC approach along with traditional acidometers

and a scanning laser vibrometer and then compared the results with a finite element model.

Uncertainty in General Dynamic Applications Dealing with a target in movement can cause motion effect on the acquired images. This

motion effect is an important source of measurement uncertainty in DIC technique. Unlike

DIC in static condition, there are not many studies on DIC uncertainties in dynamic condition.

In 2007, a new approach was followed by E. A. Patterson et al. [23] to establish a reference

material as an international standard to access the uncertainty of a full-field optical system

suitable for measuring static, in plane strain distributions. Reference materials provide a

simple definition of the measuring quantity that can be traced to an international standard

and can be used to assess the uncertainty associated with a measuring system. Efforts are

now underway to extend this idea to a system measuring 3D deformations or in dynamic

motion. Primary design for a reference material have been completed and are being

evaluated now [24, 25].

In 2013, E. Zappa et al. [8] investigated the uncertainty of DIC method in case of translating

target in dynamic conditions. The focus of the study was on 2D DIC. The study was done in

two parts. First part was proposing two different method to simulate the motion effect on a

reference image and the validation of these methods. With these methods, motion effect of

the acquired images can be simulated on the reference images. The second part of the study

suggests a numerical technique, to estimate the motion effect of an acquired image. With

this method the uncertainty of the normal DIC can be predicted from the motion effect that

exists in the acquired image. Using this predicted motion effect, the performances of DIC

method in dynamic application can improve. In another study, a method to simulate the

6 State of the Art

motion effect on a reference image is proposed. This method is applied on a real dynamic

test and the uncertainty of DIC measurement with this method is estimated [26].

Variable Parameters of the Camera for DIC Method in Dynamic Conditions Using a camera as a displacement transducer has been an interesting subject in the recent

years. Advances in computers and digital imaging technology have allowed the scientists to

use the cameras as displacement transducers. The main advantage in this kind of

measurement is that with only one camera, each pixel of the image can be considered as a

transducer itself. Moreover, the measurement set up is easy since only one camera, some

targets and a computer is needed, and the measurement in this method is contactless. The

vision-based measurement was first proposed in almost-static applications, where the

targets move slowly with respect to exposure time of the camera, so the motion effect can

be neglected. But later on, with the improvement of technology, the application of cameras

as transducers was applied to dynamic applications too. The literature in uncertainty analysis

of vision-based measuring devises in static applications is so strong, but there is still a needs

for further analysis in case of dynamic motions. The most recent study on performance

evaluation of cameras in dynamic measurements has been done by G. Busca et al. [9] in 2014.

In this research, some indexes are suggested to qualify the measurement uncertainty of an

imaging device used in dynamic measurement. These indexes are E2PR index which shows

the most important parameter of a camera for dynamic tests is exposure time, SFR_s index

which qualifies the measurement uncertainty in case there is no priory information available

about the acquisition conditions and MI index that reveals information about the whole

quality of the test and if it is reliable or not.

To the best of our knowledge, no research have focused on different methods of DIC in

dynamic applications, specially applying deconvolution method to generate new reference

images with blurring, and influence of different parameters of the camera on the uncertainty

of these methods.

7 Digital Image Correlation and its Techniques

Chapter 3


3.1 Digital Image Correlation

Digital Image Correlation (DIC) is an image analysis method, based on grey value of the digital

images that allows determination of the contour and surface displacements of an object

under mechanical or thermal load in three dimensions. Due to rapid new developments of

high resolution digital cameras and computer technology, the applications for these

measurement methods have increased. Since the system determines the absolute position

and displacement of the object in space, deformation measurements with very high

resolution are possible even under the presence of large deformation amplitudes and

macroscopic rigid body movements.

The technique used in this research is DIC method. In principle, DIC is an optical metrology

based on digital image processing and numerical computing. During the past few years, the

DIC method has been significantly improved for reducing computation complexity, achieving

high accuracy deformation measurement and expanding application range. For example, the

two-dimensional (2D) DIC method using a single fixed camera is limited to in-plane

deformation measurement of the planar object surface. To obtain reliable measurements,

some requirements on the measuring system must be met. If the test object is of a curved

surface, or three-dimensional (3D) deformation occurs after loading, the 2D DIC method is

no longer applicable. To overcome this disadvantage of 2D DIC, 3D DIC based on the principle

of binocular stereovision was developed. Besides, the digital volume correlation (DVC)

method, as a direct 3D extension of a 2D DIC method, has also been proposed by Bay and

Smith et al [27], which provides the internal deformation of solid objects by tracking the

movement of volume unit within digital image volumes of the object.

3.2 2D DIC

Compared with the interferometric optical techniques used for in-plane deformation

measurement, the 2D DIC method has both advantages and disadvantages. The advantages

of this method are as following:


Firstly, DIC method needs simple experimental setup and specimen preparation. To do a DIC

analysis, only one fixed CCD camera is needed to record the digital images of the test

specimen surface before and after deformation. Specimen preparation only consist of making

a random gray intensity distribution on the surface, by a spray paint.

Secondly, 2D DIC does not need much requirements in measurement environment. Specially,

there is no need to use a lot of sensors in this method. A white light source or natural light

can be used for illumination during loading. Thus, it is suitable for both laboratory and field

applications.

Finally, it has a wide range of measurement sensitivity and resolution. The 2D DIC method

deals with digital images, therefore, digital images acquired by different devices can be

analyzed by this method. For instance, 2D DIC can be coupled with optical microscopy, laser

scanning confocal microscope (LSCM), scanning tunneling microscope (STM), scanning

electron microscopy (SEM) and atomic force microscopy (AFM) to calculate microscale to

nanoscale deformation measurement. Similarly, deformation can be measured by analyzing

the dynamic sequence of digital images recorded with high-speed digital image recording

equipment using the 2D DIC method [28].

There are also some disadvantages in using 2D DIC method. For instance, the object surface

must have a random gray intensity distribution on it. Furthermore, the accuracy of

measurement is heavily dependent on the quality of the imaging system. Also, at present,

the strain measurement accuracy in this method is lower than that of interferometric

techniques.

In general, doing a 2D DIC analysis have three consecutive steps.

1- Specimen and experimental preparations

2- Recording images of the planer specimen surface before and after loading

3- Processing the acquired images by a computer program to obtain the displacement

and strain of the specimen

3.3 Vic-2D

Vic-2D is a software developed by Correlated Solutions Incorporation. Vic-2D uses some

optimized correlation algorithms to provide full-field displacement and strain data for

mechanical testing on planar specimens. Using this software, actual, in-plane movement can

be determined for every point within the measurement area, as well as the Lagrangian strain

tensor. Vic-2D can measure in-plane displacements and strains for specimen sizes ranging

from lower than 1mm to higher than 10m. Setup of the software is simple, and specimen


preparation only requires the application of a random speckle pattern on the surface of the

specimen. No special illumination or lasers are required.

3.4 Time Delay of the Camera

An important point in using a camera during the experiments and comparing its results with

the measurements done by a laser sensor, is the exact time that a camera is acquiring an

image. Exposure time of the laser sensor is not zero, but it can be neglected with respect to

that of the camera. Therefore, as it is can be observed in Error! Reference source not found.,

data number n is corresponding to time n*∆t. In the other hand, each data saved by the

camera is being acquired in a time interval equal to exposure time. Therefore the same

assumption is not correct for the camera. The image number n is taken between time interval

n*∆T and n*∆T + exposure time. Consequently, it is considered that each photo is captured

at the middle of the exposure time. This way, data acquired by camera is in time delay equal

to exposure time divided by two, with respect to the data acquired by laser sensor.

Figure 1: Comparison of capturing images by camera and measuring displacement by laser sensor in time with same trigger


3.5 Deconvolution Method

One method to estimate the displacement and motion effect present in acquired images is

to perform a deconvolution analysis. This analysis is done by determining the square pulse

which could be convolved with the reference image in static condition, to recreate the

acquired image with motion effect. Once the square pulse is determined, the corresponding

width would be an estimation of motion effect (w) and the shift would represent the net

displacement (a).

After finding out value of motion effect w by deconvolution, this motion can be added to the

reference image. The new generated image would be the reference image with added motion

effect, the same amount of the motion effect present in the acquired image. Now if this

generated image be considered as the new reference image, it is expected to be able to

decrease the contribution of motion effect (i.e. blurring) in the final uncertainty of

displacement estimation.

Deconvolution technique could be performed through few simple steps:

1) The Discrete Fourier Transform (DFT) of a row (in the case of horizontal motion) or a

column (in the case of vertical motion) should be calculated.

2) The ratio of the obtained matrix to the DFT of the same row number (or column number)

in the reference image needs to be found.

3) Repeat this procedure for all the rows (or columns) and average these results. Keep in mind

that, this ratio signal is in frequency domain. (This ratio is supposed to be equivalent with the

DFT of the desired square pulse)

4) Considering the fact that the Fourier transform of a square pulse is a sinc function,

determining the desired square pulse would be easier in frequency domain. Therefore, the

fourth step would be finding a sinc function in frequency domain which matches the best to

the obtained ratio signal.

5) Once the sinc function is known, the parameters of the corresponding square pulse (width

and offset) can be easily determined.

11 First Experiment

Chapter 4

4 First Experiment

The first experiment was designed in order to investigate the ability of the camera to estimate

the vibration of a beam with a reasonable accuracy. The experiment was done in 11 different

conditions. The changing variables were, the exposure time and gain of the camera, and also

the initial displacement of the beam. Two methods were used to calculate the motion of the

beam in this chapter. First method is normal DIC using Vic-2D software and the second way

is using deconvolution to estimate the motion.

4.1 Experimental Setup

First, a speckled pattern shown in Figure 2 was painted on one side of the beam. The speckle

pattern was painted by a frame with circle shape holes with 1.2 mm diameter. This diameter

was chosen 4 px, as the speckle pattern should be at least a 3 by 3 pixels square [29].

Figure 2: Speckled Pattern on a Small Portion of the Beam

12 First Experiment

Afterwards, the beam and the camera were positioned as shown in Figure 3. The camera is

in a proper distance to have the total length of the beam in its field of view. It is also

positioned perpendicular and exactly in front of a point at the middle of the beam. The

thickness of the beam is not so much, so the vertical resolution size of the camera is reduced

from top and down sides as much as possible, in order to increase the frame rate of the

camera.

Figure 3: Schematic configuration of the first experiment, front view (up), top view (down)

13 First Experiment

The experiment was done near a window in front of the natural light and some fluorescent

lamps. There was also a small lightening device close to the tip of the beam, which can be

observed in Figure 4.

Before starting the vibration, a photo was taken from the beam in static condition to be

considered as the reference image in Vic-2D software. Finally, the end of the beam was pulled

down and freed, so that the beam starts to vibrate. Target’s motion was recorded by a digital

camera with frame rate of 50 fps. The shutter speed of the camera was changed from 1000 µs

to 2000 µs, 3000 µs, 4000 µs and 5000 µs. Meanwhile, the gain was 0, 3, 6 and 9 depending

on the camera’s shutter speed as represented in Table 1. The vertical displacement of the

beam, on 800 mm from the fixed point, was measured simultaneously with a laser. In order

to have a synchronized images and laser data, both laser sensor and the camera have the

same trigger. The specification of the experimental setup are reported in Table 2.

Figure 4: Position of the beam, laser and the camera in the first experiment

Camera

Laser Sensor

Speckled Beam

14 First Experiment

Table 1: Test calender of the first experiment

Test Number Shutter Speed (µs) Gain

1 , 2 , 3 3000 0

4 , 5 4000 0

6 2000 0

7 2000 3

8 5000 0

9 1000 0

10 1000 6

11 1000 9

Table 2: Experimental setup of the first experiment

Device Brand and Type Specifications

1 Camera Allied Vision Technologies – GX3300

Resolution = 3296 * 2472 Sensor type : CCD

Progressive Max frame rate at full

resolution = 17 fps

2 Beam Material : Aluminum Length from the fixed

point = 993 mm

3 Laser Sensor Micro Optronic – ILD 1400-50(00) Max output = 1mW

4.2 Analysis by Vic-2D

In this section the images acquired during the experiment were analyzed by Vic-2D software.

To do the analysis in Vic-2D first a reference image and all the deformed images were loaded.

The reference image is the photo taken in the static situation and deformed images are the

ones taken during the test. Then, a rectangular Aoi, area of interest, was chosen on the

reference image. The Aoi should cover the whole surface of the speckled beam and also a

little bit of its surrounding. Afterward, a seed point was chosen inside the Aoi. The seed point

should be close to an area with low displacement, and also somewhere which black speckles

are easy to be identified. In this case, it was set near the fixed position of the beam. Finally,

the subset size and step were set equal to 15 and 3 pixels respectively. By performing DIC

15 First Experiment

analysis on the images, the value “v”, the raw Y-axis displacement between the reference

image and a given image, for every subset on the beam was obtained. Output values of Vic-2D

software used in the project, are presented in Table 3.

Table 3: Vic-2D Outputs

Output Variable

Unit Description

x pixel The X location, in the raw image, of the data point

y pixel The Y location, in the raw image, of the data point

v pixel The raw Y-axis displacement between the reference image and a given

image

Sigma pixel The 1-standard deviation confidence in the match. 0 indicates a perfect

match; higher numbers indicate a noise, excessive gradients, or possibly a failed match.

After finishing the analysis in Vic-2D, the outputs were loaded in Matlab. Matrix “v” is a matrix

containing the displacement of the beam at different positions, coordinated by matrices “x”

and “y”. To plot the profile of the beam as a line each column of the “v” was averaged. This

operation gives a vector for each image which shows position of different points on beam

corresponding with a row of matrix “x”. Moreover, to have an idea of the variation of the

measured displacement in each column of the beam, standard deviation for each column of

matrix “v” was calculated. Also, it should be mentioned that to be able to compare the results

with the data acquired by the laser sensor, as discussed in the next section, all values of this

new vector were subtracted by its mean.

The result of this procedure for images number 101 to 115 of test 1 are reported in Figure 5,

in terms of mean displacement and standard deviation. As represented in this figure, a high

value of standard deviation and some obvious errors in the beam profile, especially near the

position of the laser, are observed.

Hence, another value named “Sigma”, standard deviation confidence in the match, was used

to reduce this error. Value of sigma is high for points with low accuracy, which mostly

happens near the edge of the beam or position of the laser. High values for sigma near the

position of the laser is because the laser base had nearly the same color as the beam itself,

therefor it causes difficulties in analysis of Vic-2D.

16 First Experiment

Therefore, values of matrix “v” were filtered with a proper sigma limit. Sigma limit in test 1 is

0.02 for the first 498 pixels from tip of the beam, and 0.01 for the rest of the beam. Two

values of sigma limit were chosen for the beam since the error and consequently the sigma

are higher at the tip of the beam and near the position of the laser. As represented in Figure

6, when sigma is considered for test 1, beam profile for the same 15 images is much

smoother. Moreover, standard deviation has decreased from maximum of 9 pix in Figure 5

to less than 0.03 pix in Figure 6.

Figure 5: Beam Profile of test 1 for images 101 to 115 (up) Standard Deviation of test 1 for photos 101 to 115 (down)

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

Position [pix]

Dis

pla

ce

me

nt

[pix

]

0 500 1000 1500 2000 2500 3000 35000

5

10

Position [pix]

Std

[p

ix]

17 First Experiment

Figure 6: Beam Profile of test 1 for images 101 to 115 (up) and Standard Deviation of test 1 for photos 101 to 115 (down), using value sigma to filter the data with low accuracy

The motions of the beam at any point can be calculated with putting together the results

obtained above. Figure 7 shows the motion at the end of the beam without considering

sigma. The trend of the diagram shows an unacceptable amount of error in the analysis. As

represented in Figure 8, considering sigma improves the results significantly and shows a sine

wave with damping as expected.

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

Position [pix]

dis

pla

ce

me

nt

[pix

]

0 500 1000 1500 2000 2500 3000 35000

0.01

0.02

0.03

Position [pix]

Std

[p

ix]

18 First Experiment

Figure 7: Motion of a point at the end of the beam for test 1 of the first experiment, using DIC procedure, without considering sigma

Figure 8: Motion of a point at the end of the beam for test 1 of the first experiment, using DIC procedure, considering sigma

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

4

time [s]

dis

pla

cem

ent

[mm

]

0 1 2 3 4 5 6 7 8 9 10-4

-3

-2

-1

0

1

2

3

4

time [s]

dis

pla

cem

ent

[mm

]

19 First Experiment

4.3 Uncertainty Assessment of DIC Method by Vic-2D

To discuss the accuracy of the test, motion of the beam at 800 mm from its fixed position was

measured with a laser sensor described in Table 2. As this measurement is relative, the mean

value of the data was subtracted from it. As a result, data measured by laser has the same

average as the data acquired by camera and this way they are comparable. Figure 9

represents the motion of the beam for the first second of test 1, measured by both laser and

camera.

Figure 9: Motion of the point in front of laser sensor, obtained by Vic-2D method and Laser for test 1

As explained in section 3.4, there is a time delay between the data obtained by laser and the

camera. Therefore, the first goal is to find out the time delay between the two signals plotted

above. There are two methods for this purpose.

First method is to plot the phase diagram of the transfer function and calculate the slope of

the fitted line. To estimate the transfer function in MATLAB, the two signals should have the

same length. However, as the sampling frequencies of the camera and laser were 50 and

2048 Hz respectively, the two signals have different number of samples. Consequently, the

data obtained by the laser was down sampled and then the transfer function was calculated.

The amplitude and phase diagram of the transfer function can be seen in Figure 10. The slope

of the red fitted line in the phase diagram is 0.02126, therefore, the time delay is 0.0034 s for

test 1 calculated by this formula:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-3

-2

-1

0

1

2

3

Time [s]

Dis

pla

cem

ent

[mm

]

by DIC

by Laser

20 First Experiment

𝑇𝑖𝑚𝑒 𝑑𝑒𝑙𝑎𝑦 =𝑆𝑙𝑜𝑝𝑒

2 ∗ 𝑝𝑖

Figure 10: Amplitude and phase diagrams of Transfer function for test 1

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency [Hz]

Am

plit

ud

0 5 10 15 20 25-2

-1

0

1

2

3

Frequency [Hz]

Phase [

rad]

21 First Experiment

The second way to find the time delay is to plot the cross correlation diagram. This time, to

have a higher time resolution, instead of down sampling the data acquired by the laser

sensor, the signal obtained by camera was up sampled. Figure 11 represent the

cross correlation between the data acquired by laser sensor and up sampled data of the

camera. The time delay of the camera calculated by this method for test 1 is equal to

0.003418 s. It can be seen that the time delay calculated by both methods has the same value.

Figure 11: Cross correlation of the motion of a point in front of the beam acquired by laser and estimated by Vic-2D analysis

Once the time delay is estimated, diagram plotted by laser was shifted 0.003418 s to the left

side so it can be compared with the diagram plotted by camera’s data without having a time

delay. Figure 12 shows the motion of the point in front of the laser obtained by Vic-2D

analysis, by laser without considering the time delay and by laser after applying the time shift.

It can be seen that the motion obtained by laser and shifted to the left side equal to the time

delay, overlaps the motion plotted by Vic-2D analysis much better.

-3 -2 -1 0 1 2 3

-2

-1

0

1

2

x 104

X: 0.003418

Y: 2.08e+04

Time [s]

Am

plit

ude

22 First Experiment

Figure 12: Motion of the point in front of laser obtained by Vic-2D method, and Laser with and without considering time delay for test 1

In order to compare the motion estimated by DIC method with the motion measured by the

laser sensor and calculate the error for each test, the root mean square error is used. If the

motion measured by the laser sensor is A(i) and the motion estimated by DIC method is

named B(i) then RMSE and normalized root mean square error (NRMSE) are defined as

following:

RMSE = √∑[A(i) – B(i)]2

𝑁

𝑁

𝑖=1

NRMSE =𝑅𝑀𝑆𝐸

max(𝐴(𝑖)) − min(𝐴(𝑖))

The maximum of the signal A(i) was considered equal to the peak of the spectrum of this

signal. And the minimum of it was also considered equal to negative of this value. Therefore,

the denominator of the NRMSE is equal to 2 multiplied by peak of the spectrum of A(i).

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-3

-2

-1

0

1

2

3

Time [s]

Dis

pla

ce

me

nt

[mm

]

by DIC

by Laser

by Laser considering delay of the camera

23 First Experiment

Another method to compare the signals acquired by the camera and the laser, is to plot their

spectrum diagrams (Figure 13). As it can be seen, the maximum amplitude for both diagrams

exist at the same frequency equal to 7.615 Hz.

Figure 13: Spectrum of motion of the point in front of laser obtained by camera and laser

The diagram of spectrum for these signal has a high amount of leakage, therefore to

overcome this issue a hamming window was used. Figure 14 represents the spectrum of the

two motion after applying a hamming window on them. The peak spectrum error of the two

signals is equal to 1.17 present for test 1 as calculated bellow.

(0.6653 − 0.6574)

0.6653∗ 100 = 1.17%

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 80

0.2

0.4

0.6

0.8

1

1.2

1.4

X: 7.615

Y: 1.266

Frequency [Hz]

Am

plit

ude [

mm

]

X: 7.615

Y: 1.278 by Camera

by Laser

24 First Experiment

Figure 14: Spectrum of the motion of the point in front of laser obtained by camera and laser after applying a hamming window

Furthermore, the coherence diagram of the signals is plotted in Figure 15. From the

coherence diagram and the diagram of the amplitude of the transfer function plotted in

Figure 10, it can be noticed that between frequencies 1 Hz to 9 Hz the value is close to 1,

which means the motion estimated by Vic-2D have the same amplitude as motion calculated

by laser in those frequencies.

Figure 15: Coherence for test 1

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X: 7.615

Y: 0.6574

Frequency [Hz]

Am

plit

ude [

mm

]

X: 7.615

Y: 0.6653by Camera

by Laser

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Co

here

nce

25 First Experiment

4.4 Deconvolution Analysis

In this section the images acquired by camera are analyzed by deconvolution method. As it

was discussed earlier in section 3.5, parameter ‘a’ represents the net displacement of the

target with respect to the reference image. Thus, to calculate the vertical motion of the beam

at each point, the length of the beam was divided to portions with 16 pixels width. Motion of

each portion was considered equal to displacement of its center. Finally, the profile of the

beam for each photo was estimated. Profile of the beam for photos number 101 to 104 are

plotted in Figure 16.

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

Dis

pla

cem

ent

[pix

]

Deconvolution

Vic-2d

Laser

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

Dis

pla

cem

ent

[pix

]

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

Dis

pla

cem

ent

[pix

]

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

Position [pix]

Dis

pla

ce

me

nt

[pix

]

Figure 16: Profile of the beam estimated by Deconvolution analysis, Vic-2D analysis and position of a point acquired by laser

sensor for images 101 to 104 respectively from top to bottom for test 1

26 First Experiment

Afterwards, a curve is fitted to the profile of the beam estimated by deconvolution. Then the

value of the displacement from the fitted curve along the beam is subtracted from the

original profile of the beam obtained by deconvolution. The same procedure is done on the

profile estimated by Vic-2D method and both noise diagrams are plotted at Figure 17.

Figure 17: Noise of the profile of the beam across the beam estimated by Deconvolution analysis, and Vic-2D analysis for images 101 to 104 respectively from top to bottom for test 1

0 500 1000 1500 2000 2500 3000 3500-0.2

-0.1

0

0.1

0.2

No

ise

[p

ix]

Deconvolution

Vic-2d

missing point of Vic-2d

0 500 1000 1500 2000 2500 3000 3500-0.2

-0.1

0

0.1

0.2

No

ise

[p

ix]

0 500 1000 1500 2000 2500 3000 3500-0.2

-0.1

0

0.1

0.2

No

ise

[p

ix]

0 500 1000 1500 2000 2500 3000 3500-0.2

-0.1

0

0.1

0.2

Position [pix]

Nois

e [

pix

]

27 First Experiment

Figure 18 shows motion of a point in front of the laser sensor by normal DIC, deconvolution

method and laser sensor as a reference. As explained before, the time delay of the signal

obtained by data of the camera can be calculated by autocorrelation or phase of the transfer

function. Figure 19 shows the autocorrelation of two signals obtained by deconvolution and

laser sensor. The time delay calculated by autocorrelation is 3.42 ms.

Figure 18: Motion of the point in front of laser sensor, obtained by deconvolution method and Laser for test 1

Figure 19: Autocorrelation of signals obtained by deconvolution method and laser for test 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-3

-2

-1

0

1

2

3

Time [s]

Dis

pla

cem

ent

[mm

]

Deconvolution

Laser

Vic-2d

-3 -2 -1 0 1 2 3

-2

-1

0

1

2

x 104

X: 0.003418

Y: 2.063e+04

Time [s]

Am

plit

ude

28 First Experiment

Furthermore, Figure 20 represents phase of the transfer function of the two signals. The

equation of the fitted line is x=0.02162 * y, therefore the time delay is calculated 3.4 ms as

following:

𝑇𝑖𝑚𝑒 𝑑𝑒𝑙𝑎𝑦 =𝑆𝑙𝑜𝑝𝑒

2 ∗ 𝑝𝑖=

0.02162

2 ∗ 𝑝𝑖= 0.0034 𝑠

Figure 20: Phase of Transfer Function and their fitted line to find the time delay for test 1

0 2 4 6 8 10 12

-1

0

1

2

3

Frequency [Hz]

Phase [

rad]

data

fitted line

29 First Experiment

The spectrum of the signals of the motion are again plotted after applying a windows to the

signals. The natural frequency of the motion obtained by laser sensor and deconvolution

method are equal to 7.615 Hz (Figure 21).

Moreover, the peak spectrum error for deconvolution method is calculated as following for

test 1:

(0.6653 − 0.6574)

0.6653∗ 100 = 1.19%

Figure 21: Spectrum of the motion estimated by Vic-2D, Deconvolution method and laser sensor for test 1

7.2 7.3 7.4 7.5 7.6 7.7 7.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X: 7.615

Y: 0.6574

Frequency [Hz]

Am

plit

ud

e [

mm

]

Spectrum

X: 7.615

Y: 0.6527

X: 7.615

Y: 0.6653

Deconvolution

Laser

Vic-2d

30 First Experiment

Finally, diagrams of amplitude and phase of transfer function and the coherence are plotted

in Figure 22 and Figure 23. It can be seen that between frequencies 2 Hz to 8 Hz the amplitude

of transfer function and coherence are higher than 0.9, which means there is a reasonable

correlation between the motions measured by deconvolution method and laser sensor.

Figure 22: Amplitude and phase of transfer function for test 1

Figure 23: Coherence for test 1

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Cohere

nce

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency [Hz]

Am

plit

ud

0 5 10 15 20 25-3

-2

-1

0

1

2

3

4

Frequency [Hz]

Ph

ase

[ra

d]

31 Results of the First Experiment

Chapter 5


5.1 Normal DIC Method for Different Conditions

Test number 1, 2 and 3 have the same exposure time and gain value. The only difference

between these tests is the initial displacement applied to the beam. As the initial

displacement increases, the speed of the beam when passing the horizontal axis increases

too. Therefore, the blurring effect decreases the accuracy of the DIC method. Consequently,

peak spectrum error and NRMSE increase from test 1 to test 3, as shown in Figure 24 and

Figure 25. This growth in error is more significant from test 2 to 3 when the initial

displacement of the beam is increasing from 5 mm to 9.3mm.

Figure 24: Peak spectrum error for different tests with different initial displacement of the beam in constant exposure time (3000 µs) and gain value (0)

0

0.5

1

1.5

2

2.5

3

2.8 5 9.3

Pea

k sp

ectr

um

err

or

[%]

Initial displacement of laser point [mm](Test 1) (Test 2) (Test 3)


Figure 25: NRMSE for different tests with different initial displacement of the beam in constant exposure time (3000 µs) and gain value (0)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

2.8 5 9.3

NR

MSE

Initial displacement of laser point [mm](Test 1) (Test 2) (Test 3)


Test 9, 10, and 11 have the same exposure time equal to 1000 µs but the gain is 0, 3 and 9

respectively and the initial displacement of the point in front of laser sensor is increasing from

5.1 mm to 7.8 mm and 12.8 mm. Increasing the initial displacement of the beam, increases

the amount of motion effect in the images. Therefore the amount of peak spectrum error

increased from test 9 to 11 (Figure 26).

Figure 26: Peak spectrum error for tests with same exposure time (1000 µs), while increasing gain and initial displacement together

The same trend of peak spectrum error (Figure 26) is expected for NRMSE (Figure 27), but it

can be seen that NRMSE is higher in case of test 9 than the other two tests. This is duo to the

fact that, in 1000 µs the acquired images are too dark. Therefore, the estimated motion of

the beam is going to be noisy. But, as the gain of the camera increases the images are getting

brighter and DIC analysis is getting less noisy. The peak spectrum error, is just consideration

of the peaks of the spectrums, and noise of the signal is not affecting it much. However,

NRMSE is the error between each point of the motion in time history. So NRMSE is more

affected by the noise of the signal. As shown in Figure 28, the noise of the motion in test 9 is

higher than the noise of the motion in test 11, therefore the NRMSE for test 9 is higher too.

0

1

2

3

4

5

6

7

8

9

10

Test_09 Test_10 Test_11

Pea

k Sp

ectr

um

Err

or

[%]

Test Number

G : 0In. di. : 5.1

G : 3In. di. : 7.8

G : 9In. di. : 12.8


0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Test_09 Test_10 Test_11

NR

MSE

Test Number

G : 0In. di. : 5.1

G : 9In. di. : 12.8

G : 3In. di. : 7.8

0 50 100 150 200 250 300 350 400 450 500-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Err

or

[%]

Image Number

test 9

test 11

Figure 27: NRMSE for tests with same exposure time (1000 µs), while increasing gain and initial displacement together

Figure 28: Noise of the motion, estimated by normal DIC for test 9 and 11


To investigate the effect of the exposure time of the camera on the accuracy of the DIC

method, Tests 3, 5, 7, 8 and 9 are considered. All these tests have a gain between 0 to 3 and

approximately close initial displacement. From Figure 29 it can be seen that, the peak

spectrum error increases when the exposure time goes up. The effect of exposure time is

most important when it goes up from 4000 µs to 5000 µs as the error increases from less

than 8 % to higher than 18 %.

Figure 29: Peak spectrum error for different exposure times and initial displacements, with gain between 0 and 3

0

2

4

6

8

10

12

14

16

18

20

1000 2000 3000 4000 5000

Pea

k Sp

ectr

um

Err

or

[%]

Exposure time [µs]

G : 0In. di. = 5.1

G : 3In. di. = 6.2

G : 0In. di. = 9.3 G : 0

In. di. = 8.9

G : 0In. di. = 7.1


Figure 30 shows NRMSE is slightly changing before 4000 µs and is less than 2 in all situations.

But, it suddenly arise to higher than 3.5 for exposure time 5000 µs in which the motion effect

is much stronger.

Figure 30: NRMSE for different exposure times and initial displacements, with gain between 0 and 3

0

0.5

1

1.5

2

2.5

3

3.5

4

1000 2000 3000 4000 5000

NR

MSE

Exposure time [µs]

G : 0In. di. = 5.1

G : 3In. di. = 6.2

G : 0In. di. = 9.3

G : 0In. di. = 8.9

G : 0In. di. = 7.1


Table 4 signifies that, Tests 4 and 8 are in the worst condition. The exposure time for test 4 is

4000 µs and the initial displacement of the beam is 13.2 mm in front of the laser sensor which

is the second highest between the tests. This causes a high amount of blurring in the images

and a lot of missing points in the analysis of Vic-2D. Therefore there is no error defined for

this test in Matlab. On the other hand, Test 8 has a low initial displacement, but the exposure

time of the camera in this test is 5000 µs. Even though Vic-2D analyzes the images of this test,

the error is so high because of the blurring effect.

The lowest NRMSE is for tests 6, 10 and 11. This means that for exposure time lower than

1000 µs the blurring effect is lower and the accuracy of DIC method is higher.

Table 4: NRMSE for tests of the first experiment

Initial

displacement of laser point

exposure time [µs]

gain NRMSE

Test_01 2.8 3000 0 0.033077

Test_02 5 3000 0 0.049216

Test_03 9.3 3000 0 0.11798

Test_04 13.2 4000 0 -

Test_05 8.9 4000 0 0.11842

Test_06 14.4 2000 0 0.025959

Test_07 6.2 2000 3 0.044109

Test_08 7.1 5000 0 0.24763

Test_09 5.1 1000 0 0.082245

Test_10 7.8 1000 6 0.025626

Test_11 12.8 1000 9 0.024825

From the results it can be concluded that the errors depend on both exposure time and the

amplitude of the motion. To show this relation, in Figure 31 the value of exposure time

multiplied by the initial displacement of the point in front of the laser is calculated for each

tests. Also, peak spectrum error and NRMSE for each test are plotted in Figure 32 and Figure

33. It can be seen that all the diagrams have almost the same trend. For higher values of the

exposure time multiplied by initial displacement, the errors are higher because of the motion

effect in the images and vice versa.

However there are some irregularities that shows other conditions like the gain of the camera

and the diaphragm are also important. The second experiment concentrates on these

parameters too.


0

10000

20000

30000

40000

50000

60000Ex

po

sure

tim

e *

Iniit

ial d

is.

Test number

0

2

4

6

8

10

12

14

16

Pea

k Sp

ectr

um

Err

or

[%]

Test number

Figure 31: Exposure time of camera multiplied by initial displacement at a point on the beam in front of the laser for tests of the first experiment

Figure 32: Peak spectrum error of normal DIC for the tests of the first experiment


0

0.05

0.1

0.15

0.2

0.25

0.3N

RM

SE

Test number

Figure 33: NRMSE of normal DIC for tests of the first experiment


5.2 Vic-2D vs. Deconvolution Method

The second method to estimate the profile of the beam and motion was deconvolution.

Figure 16 and Figure 17 from section 4.4 show, even though the profile of the beam seems

smooth and reasonable with both methods, the noise for the profile with deconvolution

method is higher than that of with normal DIC for test 1.

However, plotting the same diagrams for test 5 with higher exposure time and initial

displacement which can cause to motion blurring, shows that deconvolution method can

estimate the displacement much better and less noisy in case of having motion effect in the

images (Figure 34 and Figure 35).

0 500 1000 1500 2000 2500 3000 3500-5

0

5

10

15

20

Dis

pla

ce

me

nt[

pix

]

Deconvolution

Vic-2d

Laser

0 500 1000 1500 2000 2500 3000 3500-6

-4

-2

0

2

4

Position [pix]

Dis

pla

ce

me

nt[

pix

]

Figure 34: Profile of the beam estimated by Deconvolution analysis, Vic-2D analysis and position of a point acquired by laser sensor for images 101 and 102 respectively from top to down for test

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