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thesis entitled

DIGITAL IMAGE PROCESSING ALGORITHMS FOR

ELECTRONIC SPECKLE PATTERN INTERFEROMETRY

presented by

Soonsung Hong

has been accepted towards fulfillment
of the requirements for

Master's degree in Mechanics

 

 

 

Major professor

Date May 5, 1997

 

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Michigan State
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MSU in An Affirmatiw Action/Equal Opportmity institution
Wane-M

DIGITAL IMAGE PROCESSING ALGORITHMS FOR
ELECTRONIC SPECKLE PATTERN INTERFEROMETRY

By

Soonsung Hong

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Materials Science and Mechanics

1997

ABSTRACT

DIGITAL IMAGE PROCESSING ALGORITHMS OF
ELECTRONIC SPECKLE PATTERN INTERFEROMETRY

By

Soonsung Hong

Digital image processing algorithms for two electronic speckle pattern
interferometry (ESPI) techniques were developed. A real-time image processing
algorithm for correlation ESPI was implemented with look-up table (LUT) operations in
order to achieve a fast, non-destructive inspection method with qualitative displacement
measurement capability. Also, a precise whole-field displacement and strain
measurement technique was achieved by using phase-shifting ESPI. Image processing
algorithms were developed for phase calculation with a four-step phase-shifting method,
noise reduction with local phase unwrapping, and strain calculation using least square
surface fitting. Experimental results for the displacement and strain measurement of a
pin-loaded plate problem show a good agreement with numerical analysis results. This
technique has been proved to be well suited for the typical applications, in terms of speed,

accuracy, and ease of use.

Copyright by
Soonsung Hong

1997

ACKNOWLEDGEMENT

The author wishes to offer his sincerest appreciation and gratitude to his academic
advisor Dr. Gary Lee Cloud for his continuous and valuable guidance during the course
of this work. He also wishes to thank his committee, Dr. Robert Hubbard and Dr. Dahsin
Liu for their interest in this research. The author extends his gratitude to Henry Wede,
Francesco Lanza di Scalea, and Emad Zidan for their helpful assistance and discussion.

Finally, the author would like to thank his parents for their encouragement and support

iv

TABLE OF CONTENTS

LIST OF FIGURES ....................................................................................... vi
1. INTRODUCTION ...................................................................................... 1
1.1 INTRODUCTION ............................................................................................. l
1.2 OBJECTIVE AND SCOPE ................................................................................. 2
1.3 RELEVANT LITERATURE ............................................................................... 2
2. SPECKLE METROLOGY TECHNIQUE ................................................. 4
2.1 LASER SPECKLE EFFECT ............................................................................... 4
2.2 SPECKLE PATTERN INTERFEROMETRY ......................................................... 6
2.3 ELECTRONIC SPECKLE PATTERN INTERFEROMETRY ................................... 9
3. DIGITAL IMAGE PROCESSING ........................................................... 11
3.1 BITMAPIMAGE ................ 11
3.2 LOOK UP TABLE (LUT) .............................................................................. 12
3.3 IMAGE FILTERING ....................................................................................... 16
4. CORRELATION ESPI ............................................................................. 19
4.1 THEORY OF CORRELATION ESPI ................................................................ 19
4.2 ALGORITHM FOR CORRELATION ESPI ....................................................... 22

4.3 APPLICATION To NON-DESTRUCTIVE INSPECTION OF PRESSURE VESSEL 29

5. PHASE SHIFTING ESPI ......................................................................... 32
5.1 THEORY OF PHASE SHIFTING ESPI ............................................................. 32

5.2 ALGORITHM FOR PHASE SHIFTING ESPI .................................................... 35
5.2.1 Computation of Relative Phase Map .......................................................... 35

5.2.2 Phase Change Map ..................................................................................... 38

5.2.3 Noise reduction and Fringe smoothing using Local unwrapping method..40

5.2.4 Strain Calculation using Least Square Surface Fitting ............................... 45

5.2.5 Sensitivity and Spatial Resolution of ESPI ................................................ 48

5.3 APPLICATION TO STRAIN ANALYSIS OF PIN-LOADED PLATE ..................... 50
5.3.1 Experimental procedure .............................................................................. 50

5.3.2 Results and Discussion ............................................................................... 53

6. CONCLUSIONS ...................................................................................... 62

LIST OF FIGURES

Figure 1 Formation of laser speckle effect ........................................................................... 5
(a) Objective speckle
(b) Subjective speckle

Figure 2 Typical speckle pattern interferometers ................................................................ 8
(a) Out-of-plane sensitive setup

(b) In-plane sensitive setup

Figure 3 Notation for M x N bitmap image matrix ......................................................... 12
Figure 4 Illustration of a homogeneous point operation using LUT ................................. 14
Figure 5 Block diagram of a typical image processing system .......................................... 15
Figure 6 Typical smoothing window operatiOns ............................................................... 17

(a) 3x3 low-pass convolution filtering

(b) 3x3 median filtering
Figure 7 Relationship between intensity change and phase change .................................. 21
Figure 8 Input LUT’S for combining two images .............................................................. 24
Figure 9 Output LUT for real-time subtraction ................................................................. 25
Figure 10 Algorithm of real-time subtraction .................................................................... 26

Figure 11 A combined image of two speckle interference patterns

from specimen tilting ........................................................................................ 27

Figure 12 Correlation ESPI fringes representing contours of constant out-of-plane

displacement ...................................................................................................... 28

Figure 13 Out-of-plane sensitive correlation ESPI setup for non-destructive inspection of

composite pressure vessel (M= mirror, BS= beam splitter, SF= spatial filter).30

Figure 14 Correlation ESPI pattern obtained by pressurizing the composite pressure

vessel which has an impact damage .................................................................. 31

vi

Figure 15 Sensitivity vector relation .................................................................................. 34

Figure 16 3D plot of two-argument arctangent function ................................................... 36
Figure 17 Random phase map ¢(x,y) ................................................................................. 37
Figure 18 Raw phase change map A¢(x,y) from out-of-plane sensitive setup ................... 39
Figure 19 Flow chart of the image smoothing with local unwrapping .............................. 41

Figure 20 Smooth phase change map obtained by using local unwrapping algorithm ...... 43

Figure 21 Line profile of horizontal section in the raw phase change map (0) and the

filtered phase change map (0) ........................................................................... 44
Figure 22 The least square surface fitting of displacement map ........................................ 46
Figure 23 Dimensions and loading condition of specimen (unit in mm) .......................... 51

Figure 24 Dual-beam illumination setup of phase shifting ESPI (M= mirror, BS= beam
splitter, SF = spatial filter, CL= collirnating lens) ............................................. 52

Figure 25 Raw phase change map of pin-loaded plate ...................................................... 54

Figure 26 Displacement map showing contours of the constant in-plane displacement uy

obtained by (a) ESPI and by (b) FEM .............................................................. 55

Figure 27 Strain map of ayy obtained by (a) ESPI and (b) FEM ....................................... 57

Figure 28 Normal strain concentration factor «Sn/6* along the net-section of the plate:

comparison between ESPI and FEM ................................................................. 59

Figure 29 Normal strain concentration factor 8”]6" along the axis of symmetry of the
plate: comparison between ESPI and FEM ....................................................... 60

vii

1. INTRODUCTION

1.1 Introduction

With the advance of electronics and computer technology, many new
measurement techniques are being introduced to various scientific and engineering fields,
especially in mechanics. Although numerous analytical and numerical design techniques
have been developed to predict the mechanical response of a structure under certain
loading conditions, experimental measurement is essential for the validation of different
design techniques as well as the evaluation of the final product. Among the various
experimental mechanics approaches, several optical measurement techniques have been
developed to obtain whole-field measurement of stress or strain; these include
photoelasticity, moire interferometry and holographic interferometry. The combination of
electronics and laser optics provides a new and precise displacement measurement
technique that is known as Electronic Speckle Pattern Interferometry (ESPI). ESPI has
many unique advantages derived from the characteristics of its main components, which
are a computer and a laser. First, electronic data acquisition and digital processing
provide a fast and convenient way of optical data acquisition, processing, storage and
analysis as compared with other optical measurement techniques. Next the characteristics
of the laser optics give high sensitivity and high spatial resolution for non-contacting,
whole-field measurement. In spite of its relatively short history, ESPI is becoming a
promising measurement tool for mechanics applied to materials science and
manufacturing. Currently, the major research trends in ESPI include wide applications for

many diverse areas, as well as the modification of ESPI setups and the development of

improved image processing algorithms. In this work, the focus is on the implementation
of rapid and efficient image processing algorithms for non-destructive inspection and for

whole-field strain analysis based on displacement measurements using ESPI.
1.2 Objective and Scope

This work consists of a comprehensive study of ESPI techniques based on well-
established optical theories and a development of digital image processing algorithms for
real-time ESPI and for a quantitative strain analysis.

This chapter is an introduction which describes the background of ESPI and
outlines this study. Chapter Two deals with the basic metrology techniques using the
laser speckle effect, which is the origin of ESPI. Chapter Three introduces digital image
processing which enables ESPI to become a useful measurement tool. Chapter Four
presents the optical theory of correlation ESPI technique, the implementation of real-time
image processing algorithms, and the application to non-destructive inspection (NDI) of a
pressure vessel. Chapter Five covers the theories of phase shifting ESPI, the step-by-step
image processing algorithms for quantitative strain analysis, and an application to the

strain measurement of a pin-loaded plate.

1.3 Relevant Literature

Since the first electronic version of Speckle pattern interferometry technique was
demonstrated by Butters and Leendertz (1971) and independently by Macovski, et a1.
(1971), many improvements have been made in this area by Biedermann and Bk (1975)
and Lokberg and Hogmoen (1976). The developments of ESPI were reviewed by Jones

and Wykes (1989). The quantitative phase measurement using phase shifting by Creath

(1985) was a notable improvement in ESPI. Consequently, the more complicated image
processing algorithms for phase calculation and speckle noise reduction for automated
fringe analysis were develOped by Vrooman and Maas (1991) and by Ritter, et al. (1997).
Recent developments and extensive applications of phase Shifting ESPI methods were
reviewed by Joenathan (1990) and Cloud(1995). Also, the algorithms of whole-field
strain calculation using phase shifting ESPI were obtained with numerical differentiation
techniques by Jia and Shah (1991), and by Moore et a1. (1996). ESPI has already been
applied in many areas including material testing of concrete (Jia and Shah 1994), and
composite (V ikhagen 1990), as well as the non-destructive inspection of composite
materials (Chen, 1995). In addition, another type of speckle metrology technique, which
is known as “speckle shearography”, was employed by Nakadate, et a1. (1980) to directly

measure the spatial derivative of displacement.

2. SPECKLE METROLOGY TECHNIQUE

2.1 Laser Speckle Effect

When an optically rough surface is illuminated with a laser, each point on the
surface reacts as a point source of a spherical wavefi'ont of scattered light. Considering a
imaging plane which has a distance L from the illuminated object surface in Figure 1 (a),
the intensity at each point on the plane is contributed by the interference of scattered light
rays from every point of the whole illuminated area. Since the illuminated object surface
is optically rough in the scale of the wavelength, each scattered light ray has a random
phase that is dependent on the height of the scattering surface point on the object.
Consequently, the resultant intensity I(x, y) from the interference of the scattered light rays
has also random variance. This explains the speckle effect, which has random intensity
distribution from 0 to maximum. This type of speckle effect is called ‘objective’ Speckle.

From statistical analyses of the random speckle, the average diameter S0,,j of the speckle

is dependent on the wavelength A of the laser, the distance L between the illuminated
object surface and the imaging plane, and the diameter D of the illuminated area on the

object surface (Cloud, 1995).

L
50,]. =1.223A , (1)

Likewise, an image of a surface that is illuminated with a laser also has a similar
Speckle appearance. When an image of a surface illuminated with a laser is formed by
using an imaging system which consists of imaging lens and aperture as in Figure 1 (b),

the intensity I(x, y) at one point in the imaging plane is determined by the scattered laser

 

 

illuminating
beam

 
   

 

 

 

 

 

 

 

 

 

 

 

> z
I(x,y)
imaging
object plane
surface
(a)
x
A illuminating
/ beam
A, z
>
I(w)
system imaging
object plane
surface

 

(b)
Figure 1 Formation of laser speckle effect

(a) Objective speckle
(b) Subjective speckle

 

light from a corresponding point on the object surface. However, due to the diffraction
limit of imaging system, the resultant intensity at one point on the imaging plane is
contributed to by the corresponding circular region on the scattering object surface. Thus,
the intensity at one point is determined by the interference of random phases fi'om the
corresponding region (Jones and Wykes, 1989). This type of speckle is called ‘subjective’
speckle, because the size of the speckle depends on the imaging system. The average

speckle size on the imaging plane is

S

3qu = 1.22(1+ M)AF (2)
where F is aperture ratio (F = f/a = focal length/aperture) and M is magnification of lens

(Cloud, 1995). This subjective speckle is used in most speckle metrology techniques.

2.2 Speckle Pattern Interferometry

The random distribution of intensity in a speckle pattern contains the
characteristic roughness information of the corresponding region on the surface. Since the
speckle moves with the point on the surface, we can measure the displacement of each
point by tracing the movement of Speckle. From this speckle characteristic, the “speckle
photography” method was developed to measure the in—plane movement of speckle by
double exposure technique using photographic recording media. The sensitivity of the
speckle photography is dependent on the speckle Size.

In order to increase the sensitivity of measurement to the wavelength scale,
interferometry techniques that use speckle were developed. When the laser speckle

pattern is combined with another coherent laser beam which has a Speckle pattern or a

smooth wavefront, the image obtained from the interference also has a random Speckle
appearance known as a “speckle interference pattern”. The resultant intensity of the

speckle interference pattern at any image point can be expressed as
II=IR+IO+2 Iklocoso (3)
where I R and 10 are the intensities of the reference and object beams, and d) is the phase

difference between reference and object beam (Cloud, 1995). In Equation (3), the
intensity of the speckle interference pattern depends on the relative phase 4» between the
two laser beams as well as the intensities of the two laser beams. Since the displacement
of object surface causes a change of the relative phase due to the optical path length
change, the intensity after deformation becomes

12 =IR+IO+2 [RIO cos(¢+A¢) (4)
where Ad) is change of relative phase.

Considering the correlation of II and 12, the phase change Ail) can be determined
with “correlation speckle pattern interferometry”. When the negative photographic film of
the first speckle interference pattern is superimposed with the second pattern, fringes are
obtained corresponding to the changes of the degree of correlation between the two
speckle interference patterns. Each fringe spacing in correlation interferometry represents
27: phase change due to the displacement on the surface (Jones and Wykes, 1989).

Two typical speckle interferometers are shown in Figure 2. Figure 2 (a) is an out-
of-plane sensitive arrangement of speckle interferometer which has an in-line smooth
reference wavefront. The fringes obtained from this speckle pattern interferometer

represents in-plane as well as out-of-plane displacement. However, as long as the angle of

 

 

illuminating
beam

   

smooth
reference
beam

INK

 

 

 

 

 

 

 

  
  

 

 

 

 

 

% b
V k 2
imaging
system imaging
object plane
surface
(a)
illuminating
x A beam
> V a z
imaging
system imaging
object plane
surface illuminating
beam
(b)

Figure 2 Typical speckle pattern interferometers
(a) Out-of-plane sensitive setup

(b) In-plane sensitive setup

 

 

illuminating beam from the viewing direction is smaller than 15°, the relationship

between out-of-plane displacement and phase change may be approximated by
A4) = 330 + cosO) uz 5 3; uz (5)

where A4) is the phase change and uz is out-of-plane displacement (Chen, 1995). The

arrangement shown in Figure 2 (b) uses two coherent speckle patterns to make a new
Speckle interference pattern without a smooth reference beam. This setup gives fiinges
which are sensitive to in-plane displacement. Symmetry of the two illuminating beams
allows observation of in—plane displacement in the presence of out-of-plane
displacement. The relationship between the phase change A4) and in-plane displacement

uis

M = 4?“ sine u, (6)

where 9 is the illuminating angle from the object surface normal (Cloud, 1995).

2.3 Electronic Speckle Pattern Interferometry

Since it is necessary to resolve only the speckle interference pattern, the resolution
requirement of the recording media for speckle pattern interferometry is relatively low
compared with the requirement for holographic interferometry. Thus, digital image
acquisition and processing with a CCD camera and computer may be applied to the
speckle pattern interferometry technique. This electronic version of Speckle pattern

interferometry, known as Electronic Speckle Pattern Interferometry (ESPI), allows fast

10

measurement of surface displacement without any photographic processing or plate
relocation.

In addition to correlation ESPI, another ESPI technique which can measure the
optical path length change quantitatively by measuring the exact phase value through
phase shifting became possible with the advent of powerful computers and improved
digital image processing techniques. With this phase shifting ESPI technique, there is no
need to count fringes and interpolate between them. Moreover, the speed and

convenience of data processing and storage makes this technique promising.

3. DIGITAL IMAGE PROCESSING

Owing to the advance of electronic and computer technology, digital image
processing has become a powerful tool for various scientific areas (Russ, 1992),
especially for the optical metrology field. To present the electronic version of speckle
pattern interferometry, a basic understanding of digital image processing is essential.
Therefore, the fimdamental ideas of digital image processing will be discussed in this

chapter.

3.1 Bitmap Image

In digital image processing, the image is usually acquired with a CCD (charge
coupled device) array and a frame grabber board inserted into a computer. A CCD camera
consists of a large number of photosensitive semiconductor elements in a 2D matrix.
During the acquisition of one image, each element collects the electric charges generated
by absorbed photons. These electric charges in each element are converted to an analog
voltage signal proportional to the intensity at each pixel, and sequentially transferred to
the frame grabber at the speed of 10 million pixels per second which is 30 frames/second
in US standard RS-170. The sampling frequency of the frame grabber is synchronized to
this voltage signal in order to digitize it to 8-bit digital data and to store the digitized
image into the frame buffer of the frame grabber, or into the main memory of the
computer. These digitized values at every pixel construct a bitmap image in a large
matrix form. The position of a pixel in a bitmap image is given in the common notation
for matrices. The indices m, n denote the position of the row and the column in the

M x N image matrix, as illustrated in Figure 3.

11

12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3 Notation for M x N bitmap image matrix

3.2 Look Up Table (LUT)

The most basic operation of digital image processing is a homogeneous point
operation using a look-up table (LUT). Intensity values at individual pixels are modified
depending on the intensity value using one argument function. Such an operation is

expressed by

1;... = f0...) (7)
It is important to note that the result of a point operation does not depend on the
neighboring pixels or the position of pixel. This homogeneous point operation is
commonly used to perform the following simple image processing tasks:

1. Correction and optimization of the brightness and contrast of a whole image

2. Compensation of non-linear CCD camera response

3. Highlighting of an image part with a certain range of gray level

13

Direct computation of a homogeneous point operation is inefficient for a complicated
function like a logarithmic or trigonometric function. A precalculated table which has 256
elements for all 256 possible gray values can be used for this homogeneous point
operation, because the definition range of any point operation consists of only few gray
values, typically 256 for 8-bit image processing. Then the computation of the point
operation is reduced to a replacement of the gray value by the element in the table with an
index corresponding to the input gray value. Such a table is called a look-up table or
LUT. An illustration of an LUT operation is shown in Figure 4.

Fig 5. Shows a block diagram of a typical image processing system which
includes the hardware level implementation of the LUT operations. An input LUT located
between the analog-digital converter and the flame buffer is used to perform a point
operation before the image is stored in frame buffer. Another output LUT is located
between the frame buffer and the digital-analog converter for output of image in the form
of an analog video signal. With this output LUT, a point operation can be performed and
observed interactively without modifying the stored image. Point operations are the most
simple class of operations which are commonly used for image enhancement. More

advanced applications of LUT will be discussed in the chapter on correlation ESPI.

l4

LUT

 

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31

 

62

 

 

32

 

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Figure 4 Illustration of a homogeneous point operation using LUT

 

[78
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It

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Main
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Output LUT
_ Data
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i
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Control Signal

 

Figure 5 Block diagram of a typical image processing system

16

3.3 Image Filtering

Another class of image operation is a window operation that uses neighboring
pixels to find a filtered gray value for a pixel in a new output image. Various window
operations may be distinguished by the way of combining the gray values of neighboring
pixels, or by the goal of each operation. The most elementary window operation is a
convolution filtering which multiplies every pixel in the filtering window with the
corresponding weighting factors of the filtering mask, adds up the products, and writes
the result to the position of the window center pixel in the output image. This operation is
performed for every pixel in the image by sliding the filtering window. The mathematical

expression of the convolution filtering using N x N filtering mask (Jahne, 1991) is,

[rim = Z: Zfltjlm+tn+j (8)

i=-rj=-r

where H”. is a filtering mask and r = (£751) with N being an odd number.

This convolution filtering with a filtering mask can be characterized by weighting and
summing up. As an example, Figure 6 (a) shows a low-pass convolution filtering for
simple image smoothing.

Unlike this linear operation, another way of combining the pixels in a window is a
rank value filter which may be characterized as comparing and selecting. This type of
window operation sorts the gray values of the pixels in a window, chooses one value
ranked in the sorted list, and writes the value into the center pixel of the window. As an
example, a median smoothing filter is Shown in Figure 6 (b). The median value of a

sorted list is selected as a result for the center pixel. The median filtering is useful to

 

  

 

average

 

 

 

 

 

 

 

(a)

sorted list

median m

 

(b)

Figure 6 Typical smoothing window operations
(a) 3x3 low-pass convolution filtering

(b) 3x3 median filtering

18

remove impulsive noises in images and to preserve edges without any arithmetic
operation (Lim, 1990). More complicated window operations will be discussed in the

chapter on phase shifting ESPI.

4. CORRELATION ESPI

4.1 Theory of Correlation ESPI

The intensity of a speckle interference pattern at one detector point is written as,
I,=IR+10+2 IRIOcoscb (9)
where IR and 10 are the intensities of the reference and object beams, and (1) is the phase
difference between reference and object beam. After the deformation of the object, the

intensity at the same point will change because of the change of the phase difference due

to the displacement of surface point. The new intensity is,
12=1R+IO+2 [RIO cos(¢+A¢) ‘ (10)
where Ad) is the change of the phase difference due to the object movement. Even though
intensity is the only variable that we can measure with a CCD camera, the phase change
information can be derived from intensity change. Thus, the intensity change can give us
displacement information for each pixel. The intensity change may be expressed as,
AI = 12 — II
= 2 1R10(cos(¢+A¢)—cos¢) (11)
. A . A

= 4 1 R10 sm(¢ + Di) 314—29)
Since the intensity change AI depends on the random phase difference 4) as well as the
deformation-induced phase change A4), a statistical consideration is required to find a

relationship between intensity change AI and phase change A¢ during deformation. A root

mean square of the intensity change with respect to the random phase difference can be

19

20

derived from the integration of square of the intensity change from 0 to Zn random phase

difference.

((1302) = 51; fi“(AI)2d¢ = 81,10 an???) (12)

$4329” (13)

The ensemble average of the absolute intensity change is proportional to the absolute sine

<wu>=m

 

function of half the phase change. In order to compare this result with absolute values of
Equation (11), Figure 7 shows the relationship between absolute intensity change [All
and phase change Ad). This result explains the low fringe visibility of correlation ESPI at
the region of minimum correlation which has a large intensity change. After all, the only
calculation to be implemented for correlation ESPI fiinges is the absolute value of the

difference between two Speckle interference patterns.

Intensity change IAI IN IR 10

 

21

 

5 = o
4 - /
. <|AI I> W4
3 — __________ ¢=1r/2
.. I” \\ ¢=3fl7l4
1 —
O i ' i I I r l
0 It 2n
Phase change Aq)

Figure 7 Relationship between intensity change and phase change

22

4.2 Algorithm for Correlation ESPI

In order to implement speckle correlation interferometry with digital image
processing, the absolute value of subtraction between two frames of speckle interference
patterns should be obtained at every pixel in a bitmap image. However, direct pixel-by-
pixel calculation is not appropriate because of large computational load and time delay
during calculation. Thus, a real-time subtraction algorithm was developed for correlation
ESPI by using LUT operations.

In order to achieve a real-time correlation ESPI algorithm, a special consideration
is needed to split the bit planes of a frame buffer into two parts to store the two speckle
interference patterns with half the intensity resolution; for example, 4-bit = 16 gray
values, instead of 8-bit = 256 gray values. More advanced applications of LUT operations
are employed to construct this frame which contains both undeforrned and deformed
speckle interference patterns. First, a speckle interference pattern fi'om the ESPI setup is
digitized into one bitmap image which has a sensitivity of 8-bit = 256 gray scale. This
digitized image is read into a frame buffer via an input look-up table (LUT). The input
LUT allows a fast homogeneous point operation at hardware level before the pixels are
stored in the frame buffer. Thus, a special input LUT is used to acquire the first speckle
interference pattern of the undefonned state. This LUT is designed to transform an 8-bit
image into a 4-bit image, and to store it into the higher 4-bit planes of one frame buffer.

The transformation function to generate this input LUT (ILUT) is
1;", = ILUT1(I,,m) = int(1,,,,, /16) x 16 (14)

The higher 4-bit planes in the frame buffer should be protected with a protective mask

23

before overwriting the second image into the lower 4-bit planes. Next, the second speckle
interference pattern of deformed specimen is acquired and stored into the lower 4-bit
planes with another input LUT. The second input LUT is expressed by

1;," = ILUT2(1,,,,,) = int(1,,,,, /16) (15)
Figure 8 shows the plots of the two input LUT’S used to combine the two speckle
interference patterns. The input LUT operations mentioned above are well suited to
combine two Speckle interference patterns of undeformed and deformed specimen into
one 8-bit image.

Next, another application of LUT operation was developed to obtain a real-time
subtraction algorithm without any modification of the stored image. A pixel in an image
only has one of the 256 possible combinations of two 16-level gray values. Considering
an LUT as a precalculated table of 256 possible cases, we can use it as a two-argument
function operator. Equation (16) shows the implementation of the output LUT (OLUT)
operation for the absolute subtraction as

1;," = OLUT(1,,,,,) = |1l — 1,| (16)
= |int(1,,,,, /16) x 16— mod(1m,16)x16l

The plot of this output LUT is shown Figure 9. This output LUT transforms the combined

image into a subtracted image on the CRT display. Actual pixel-by-pixel calculation is

not involved in this real-time subtraction algorithm. An advantage of this approach is that

we can observe the real-time correlation ESPI fringes on the screen at 30 frame/sec,

which is the frame rate of US television standard.

24

 

 

 

 

 

 

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,+_-_:128— —
.9 ._
<1- - _
YEP 64L .—

I . _

0 m,,....
0 64 128 192 256
Input intensity
(8)

256

£192.

(I)

a .

8 a

15128.3

.9 I

V- a

E 64—

A _

0——1—1-1=T—. . . I . .

 

 

 

 

0 64 128 192 256
Input intensity
(b)

Figure 8 Input LUT’S for combining two images

25

256

 

p—t
\O
N

I J_l l l l

 

Output intensity
5
00

 

O\
.5

L111

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O '*I"'I'T"I'i'
0 64 128 192 256

Bitmap intensity

Figure 9 Output LUT for real-time subtraction

A schematic diagram of the algorithm for correlation ESPI fringes is shown in
Figure 10. As an example, Figure 11 and Figure 12 show a combined image of the two
speckle interference patterns and the correlation ESPI fringes obtained with specimen

tilting in the out-of-plane sensitive setup.

26

 

 

I110|fll|0|0|1|0| 01111L0|0|1|1|1|

 

 

I,=178 I= 103
_LUT#1 _LUT#2

1*: 176 1* =96
Illolllllolllllol
I,2=182

 

 

OLUT

1*,2=80
|0l1|0|1|0|0|0|0l

IAII

 

 

Figure 10 Algorithm of real-time subtraction

27

 

Figure 11 A combined image of two speckle interference patterns

from specimen tilting

28

 

Figure 12 Correlation ESPI fringes representing contours of

constant out-of-plane displacement

29

4.3 Application to Non-Destructive Inspection of Pressure Vessel

Non-destructive evaluation is potentially one of the major applications of
electronic speckle pattern interferometry (Nokes and Cloud 1993; Vikhagen 1991). The
real-time correlation ESPI algorithm developed in this work was applied to find a defect
on a composite pressure vessel in a non-contacting way. Due to the high strength-to-
weight ratio, composite pressure vessels have been used in the aerospace industry and
have a good potential to be used for fuel tanks of natural gas vehicles. However, the
reliability and safety are the biggest concerns for this application. Thus, it is imperative
to detect flaws on tanks during or prior to use. Those defects may be caused by improper
manufacturing process or by impact damage during a service period. Screening with non-
destructive inspection is a principal application of real-time correlation ESPI.

Figure 13 shows the experimental setup for out-of-plane displacement
measurement. During pressurizing, a defect-free pressure vessel will expand uniformly
and show parallel ESPI fringes. However, if there is a flaw in the tank, the ESPI fringes
will show anomalous out-of-plane displacement contours. Figure 14 shows the “bull’s
eye” shape of correlation ESPI fringe patterns representing non-uniform deformation due
to a defect. The selection criteria of the NDI application can be established by calibrating

with intentionally induced damages.

30

 

Control
Monitor

A

 

 

Computer
Frame Grabber

V

Pressure EFD Display

Vessel M I Monitor

4‘ ! Laser I
M

 

 

 

 

 

 

 

 

 

 

 

 

Figure 13 Out-of-plane sensitive correlation ESPI setup for non-destructive inspection

of composite pressure vessel (M= mirror, BS= beam splitter, SF= spatial filter)

31

 

Figure 14 Correlation ESPI pattern obtained by pressurizing the composite pressure

vessel which has an impact damage

5. PHASE SHIFTING ESPI

5.1 Theory of Phase Shifting ESPI

Although correlation ESPI provides a fast and convenient displacement
measurement technique, it still has some limitations that make it unsatisfactory for
quantitative displacement measurement. Like many other optical measurement
techniques, correlation ESPI can measure displacement using an absolute sine function of
phase change. Thus, the trigonometric function introduces a sign ambiguity and requires
further data reduction that consists of locating the center of each fuzzy fiinge, numbering
the fiinge order, and interpolating between them.

However, phase shifting ESPI prOvides another speckle pattern interferometry
technique which can determine the displacement field on the specimen surface
quantitatively by measuring exact phase change at each pixel. In order to calculate the
change of optical path length, the relative phases between reference beam and object
beam must be obtained both before and after deformation. Then, the change of the
relative phase is directly related to the displacement by sensitivity vector calculation.

The phase shifting technique has been widely used for this phase measuring
purpose. The phase shifting ESPI method introduces some known amount of phase shift
to the reference beam by means of, for example, a mirror mounted on a piezo-electric
transducer (PZT). Various phase measuring algorithms for the phase shifting method
have been developed in the past; these include the three-step, four-step, and Carre

techniques which have been developed by various researchers and which are summarized

by Cloud (1995).

32

33

The intensity of the speckle interference pattern at one detector point is written as

 

I(x,y) = 1,(x,y) + 10(x,y) + 2J1.(x,y)10<x,y) cos¢(x.y) (17)
Since there are three unknowns in Equation (1 7), namely the reference beam intensity I R ,

the object beam intensity 10 , and the relative phase d) between the reference beam and

the object beam, a minimum of three speckle interference patterns are needed to
determine the exact phase value. The four-step phase shifting method is commonly used
because of simplicity and ease of calculation. The intensity distributions of speckle

interference patterns obtained by four-step phase shifting can be expressed as

 

I, (x,y) = [R (x,y) + 10(x,y) + 2J1R(x,y)10(x,y) cos(¢(x,y)+a,) (18)
where IR = intensity of reference beam
10 = intensity of object beam

4) = original phase difference between reference and object beam
. 1t 31:
(ink: known phase shift (0, —2— , 7t and 7) when k=1, 2, 3 and 4

Now, we can calculate the phase difference (I) at every point from the four intensity

values at phase shifting steps by using following equation.

 

14(xay)_lz(x’y)) (19)

¢(x,y) = tan"[
11(x,y)-13(x,y)
Because of the nature of the random speckle, the phase difference map in a speckle

interference pattern has a random distribution; thus, the phase difference map does not

show any useful information. However, the change of phase diflerence during

34

deformation corresponds to the change of optical path length caused by the displacement
on the object surface,

A¢(x,y) = ¢..,...(x,y) -¢..,.,.(x,y) (20)
Once the phase change is determined, the corresponding displacement can be calculated
by the following sensitivity vector relationship (Cloud, 1995).

A4) = K 0L
(21)
= (R2 "' k1) ' L
where K is sensitivity vector, L is the displacement vector, and k1 and k2 are the

propagation vectors of viewing direction and illuminating direction, respectively, as

illustrated in Figure 15.

 

 

 

 

 

 

Figure 15 Sensitivity vector relation

35

5.2 Algorithm for Phase shifting ESPI

5.2.1 Computation of Relative Phase Map

In order to obtain the relative phase map, four images of speckle interference
patterns are acquired with the four-step phase-shifting method, using a calibrated piezo-
electric transducer (PZT) to produce the phase shift. The PZT phase shifter may be
calibrated with real-time correlation ESPI fringes. Four intensity values at each pixel in

the four images are inserted into the following equation.

 

_ -l [4(x9y)_12(x’y)
¢(x’y)_tan (I(x,y)-130M) (22)

This equation yields a value of the phase ¢(x, y) in phase modulo 1t which has uncertainty
of mt. In order to obtain a phase value in modulo 2n, several techniques have been
employed, including consideration of the signs of the numerator and denominator by
Creath (1985), or by using a 2D look-up table by Vrooman and Mass (1991). In the
present research, the modulo 21: was found by using the two-argument arctangent
function (function ATAN2 in some computer languages), where the signs of the
numerator and denominator in Equation (22) are taken into account,

¢ = atan2( (1, — 1,),(1, — 1,)) (23)
Figure 16 shows a 3D surface plot of the two-argument arctangent function. The
calculated phase value «b which has modulo 2n from -1t to 1t, is mapped into the 8-bit gray
level.

Because of the asymptotic behavior of the arctangent function at the origin, under-

modulated pixels, which have near-zero values of both denominator and numerator in

36

Equation (22), can introduce significant amount of phase measurement error. This low
modulation happens in regions of insufficient illumination or wherever there is
correlation loss. In addition, the pixels which have zero or maximum intensity values are
another source of phase measurement error. Thus, special considerations must be
implemented in the phase measuring algorithm to recognize and discard these under-
modulated and erroneous pixels. The invalid pixels are detected and marked as zero gray
level in the 8-bit image of the phase map. Consequently, the valid pixels in the completed
phase map have gray levels ranging from 1 to 255 corresponding to the phase modulo 21:
from -7t to 1:. Figure 17 shows an example of a random phase map ¢(x,y). Invalid pixels

comprise 14% of pixels.

6
I
I

a .

s“““
‘\\\\\‘

 

Figure 16 3D plot of two-argument arctangent function

isfifigl‘l"
“"dr ’ 'f
. "2);;

4’
4.
A

a

\
.<,\ z

a

 

Figure 17 Random phase map ¢(x,y)

38

5.2.2 Phase Change Map
In order to obtain the phase change map, pixel-by-pixel subtractions between two

phase maps are needed.
A¢(x’y) =¢afl¢r(x’y)—¢b¢fore(x9y) (25)

The subtracted results of the phase values are again mapped into the 8-bit gray-level
range, which has a range from 1 to 255, considering the Zn phase ambiguity. During this
subtraction stage, the pixels that have either one of the two phase values marked as
invalid should remain invalid. This phase change map A¢(x, y) yields a wrapped
displacement contour map for the specimen surface. Figure 18 shows an example of the
phase-change map obtained from the out-of-plane sensitive interferometer.

The amount of displacement corresponding to each fringe can be calculated with
sensitivity vector analysis, which in turn depends on the optical geometry of the system.
The out-of-plane sensitive speckle interferometer in Figure 2 (a) has the following

relationship between out-of-plane displacement uz and phase change Ad).

I.
u, — 21r(1+ c056) Ad) (26)

 

Equation (27) shows a relationship between in—plane displacement u, and phase change
Ad) in the in-plane sensitive setup in Figure 2 (b).

A
u, = ,
4n srnG

 

(27)

However, the invalid pixels and systematic noises make it difficult to resolve the fiinges

and to perform strain calculation. A post-processing procedure for noise reduction and

39

 

tup

rve SC

it

Figure 18 Raw phase change map A¢(x,y) from out-of-plane sens

40

fiinge smoothing is required in order to obtain high fiinge visibility and smooth data for

further analysis.

5.2.3 Noise reduction and Fringe smoothing using Local unwrapping method

The raw phase change map obtained from the phase subtraction contains two
types of phase measurement error; these are the invalid pixels caused by the low
modulation, and the scattering of the phase values due to the slight decorrelation of
speckles between exposures before and after deformation. Special image filtering
algorithms are required to replace the invalid pixels with valid neighboring pixels and to
smooth the wrapped phase change map. Owing to the presence of Zn phase edges and
under-modulated invalid pixels, the convolution averaging filter is not appropriate for this
raw phase change map. Several image processing techniques have been employed in the
past for noise removal and fringe smoothing. A combination of median filtering and out-
range pixel smoothing (Lim 1990) was employed by Creath (1985). Also, another
filtering technique was employed using transformation to sine and cosine domains,
simple smoothing, and retransformation to the phase domain by Ritter (1997).

In this research, a local unwrapping algorithm was developed as a preprocessing
step for image filtering of a wrapped phase map. The flow chart for smooth filtering using
the local unwrapping algorithm is shown in Figure 19. First, two upper- and lower-
threshold values are chosen to count the number of upper-thresholded pixels and the
number of lower-thresholded pixels in a filtering window. Then, invalid pixels in the

window are counted. If the number of upper-thresholded pixels is larger than that of

41

 

 

Aq), (i,j=1...n)

 

 

 

 

N = # of upper px

upper

N = # of lower px

lower

N = # of invalid px

invalid

 

 

 

 

 

 

 

 

13¢lower'qu)lower_i-21lc Ad) =A¢upper-Z1lc

upper

 

 

 

 

 

 

 

 

 

 

Ad), (i,j=1...n) 4

 

 

 

     
  

N < n2/2 NO

invalid

 

  

 

 

 

_ _ 22 Alps
Ad) — ("z-Mmalid)

 

51-) = invalid

 

 

 

 

 

 

Figure 19 Flow chart of the image smoothing with local unwrapping

42

lower-thresholded pixels, the lower-thresholded pixels are unwrapped by adding 21:.
Otherwise, the upper-thresholded pixels are unwrapped by subtracting 21:. The 21: phase
discontinuity in the window is thereby eliminated by the local phase unwrapping.

These unwrapped phase values in the window can be used for any image filtering
operation. In this section, the simple averaging filter was applied to the locally
unwrapped window for smoothing of the wrapped phase change map without blurring at
21: phase edges.

However, the phase values in the window still contain invalid pixels. In order to
remove the invalid pixels in the valid region as well as the valid pixels in the invalid
region, half of the number of all pixels in the window are chosen as another threshold for
the decision. If the number of invalid pixels in a window is lower than this threshold, the
window is considered as a valid region, and the center pixel in the window is replaced
with the average of valid phase values in the window. If not, the center pixel is marked as
an invalid pixel. An advantage of this method is that it provides a smooth phase change
map in which the sharp 21: phase edges are preserved. Figure 20 shows the result of the
smoothing of the wrapped phase change map in Figure 18 by using this local unwrapping
algorithm. The line profiles of a horizontal section are shown in Figure 21. This local
unwrapping technique may be employed to calculate the strain map directly from the

wrapped displacement map.

43

 

Figure 20 Smooth phase change map obtained by using local unwrapping algorithm

44

 

   

 

 

256
0 % o
_z+_ <9 1:. _ n0
‘E‘ 192 9’ o 0 upper threshold
3 0% 000 6 °5°
8 o O 0
Cl
9 fl
—q
0)
>
O)
—-4
53‘
H
(D

 

 

 

O 128 256 384 512
Position (pixel)

Figure 21 Line profile of horizontal section in the raw phase change map (0)

and the filtered phase change map (0)

45

5.2.4 Strain Calculation using Least Square Surface Fitting

In order to determine the strain field, the first spatial derivatives of the
displacement map with respect to the x- and y-axis have to be calculated. The least square
fitting method has been widely used for the data smoothing and the approximate
differentiation of discrete data. The basic idea of the least square fitting method is to find
a polynomial fitting function which minimizes the summation of squares of differences
from the given data.

In this study, the least square surface fitting algorithm was implemented to obtain
the strain field. The n x n neighboring pixels around each pixel in the displacement map

have discrete displacement values u”. and positions (x y”. ), where i, j=1 ...n. The strain

0'!

calculation procedure consists of finding a fitting plane of u(x, y) = ax +by+ c in Figure

22, which minimizes the following expression of the sum of square error.

S:::(u(xij,y,j)—u,.j)2=::(ax,j+byij+c--u,.j)2 (28)

i=1 jsl i=1 j=l
The values of a and b represent the slopes of the fitting plane with respect to x and y
directions, respectively. In order to find the minimum of the previous expression, the

partial derivatives have to be set to zero, yielding:

68

—— =2 2211c. ax..+b ..+c—u..

6a g( y yy U) (29,3)
=2 (a ZZxU2+bZnyyy+cZXxU-22xyuy) =0

6S

_ =222 .. ax..+b ..+c-u--

= 2 (a 232va +b 22y,2 + c 22y, - smug.) = 0

46

Fitting plane

M y u(x,y)=ax+by+c

 

 

y, __

 

 

 

 

 

 

Figure 22 The least square surface fitting of displacement map

47

as
—=222 ..+b..+ —..
ac W" y” c u”) (29.c)

=2 (a 22x, +122sz +an —>:2u,.j) =0

where 222 = :2": .

i=1 j=l

These three equations can be expressed in the following matrix form.

2
Six. zzxyy, 22x, a 2279,11,.

'1

2
7.1ny. ya. 22y”. ZZyU b = ZZyUuy. (3 0)
Six. 22y”. n2 c ZZu.

1} :1

Considering a local coordinate system which has its origin at the center pixel of the
window in Figure 22, the following terms in Equation (30) vanish because of the regular
distribution of the discrete data and the symmetric shape of the window.

221x”. = 22y”. = 227:ny = O (31)
Finally, solving Equation(30) yields

_ Znyug. b _ ZEyUuij _ ZZuij

 

 

a — , — , c — 32
22x; 22y; n2 ( )
The denominators of Equation (32) are simply related to the size n of the window as
2228—32—1 2 21 33
1' " yy- ‘6" (n - ) ( )

The strain calculation from the displacement map is reduced to the application of a
convolution filter. As an example, a and b fi'om Equation (32) for a 5x5 window can be

written as

48

 

 

 

 

_-2 '1 O 1 2‘ Full ”12 "13 “14 “151
'2 ‘1 0 l 2 ”21 ”22 “23 “24 “25
a = 516 —2 —1 0 1 2 um 1:32 1133 u34 u35 (34,a)
—2 -1 O 1 2 u41 u42 u43 u44 u45
_-2 '1 O 1 2, _u51 “52 “53 “54 “55 J
P 2 2 2 2‘ Fun “12 “13 “I4 ”15-
1 1 1 1 “21 “22 ”23 “24 “25
b = 56 0 0 0 0 O : 113, 1432 u33 u34 u35 (34,b)
‘1 ’1 "'1 "1 ‘1 “41 “42 “43 “44 “45
_-2 —2 —2 —2 —2_ _u5, 1152 u53 us4 u55 _

 

 

 

 

where A:B = :2": A1311

i=1 j=l

From Equation (34), it is obvious that the spatial derivative of the displacement
map obtained with the least-square surface fitting is the average of the slopes obtained
with the least-square line fitting in the window. In order to get the strain map directly
from the wrapped displacement map, the local phase unwrapping algorithm previously

discussed is combined with this convolution filter instead of the average filter.

5.2.5 Sensitivity and Spatial Resolution of ESPI

The sensitivity and the spatial resolution of measurement are important
parameters for the choice of experimental measurement technique. In general, many other
optical measurement techniques, including correlation ESPI, can measure displacement
only with fiinges representing constant displacement contour. The sensitivity of these
measurement techniques is defined as a displacement between neighboring fringe lines.

For example, the measurement sensitivity of in-plane sensitive correlation ESPI which

49

has the illuminating angle 9=30° corresponds to the wavelength of laser 9: E 0.633pm.
However, the sensitivity of measurement of phase sifting ESPI depends on the intensity
resolution limit of the image processing system. For 8-bit image processing, the 256 gray
levels represent a wavelength of displacement. Consequently, the measurement
sensitivity of the phase shifiing ESPI is U256 .2. 2.5mm in theory. For the practical
application of ESPI, experiment calibration using a precise translating device, for
example, a rotating disc (Cloud 1995), is required to obtain the actual sensitivity of
measurement.

In addition, the spatial resolution of displacement measurement of an ESPI system
depends on the spatial resolution of the image processing system, which is the size of the
bitmap image matrix. The maximum number of resolvable correlation fiinges in a full
screen was found to be about 50 (Chen, 1995). Thus, the spatial resolution of a
correlation ESPI system using 512><512 pixels can be at least 10 pixels. Although the
phase shifting ESPI provides spatial resolution of one pixel owing to the pixel-by-pixel
measurement capability, the practical spatial resolution limit of phase shifting ESPI is
determined by the size of smooth filtering window (V ikhagen, 1991). Likewise, the
spatial resolution of strain measurement, that is the strain gage size, is equal to the size of
the convolution filter derived in previous section for the strain calculation. Because the
practical spatial resolution of ESPI system depends on the magnification of the imaging
lens as well as the resolution of the bitmap image, an experimental spatial calibration
procedure using a scale is needed to transform the pixel domain of the bitmap image into

the spatial domain of the specimen surface.

50

5.3 Application to Strain Analysis of Pin-loaded Plate

The strain field in an epoxy plate loaded in tension with a steel pin is determined
using phase shifting ESPI and the strain calculation algorithm developed in this work.
5.3.1 Experimental procedure

Dimensions and loading condition of the specimen tested are shown in Figure 23.
The schematic diagram of the in—plane sensitive phase shifting ESPI setup which has two
illuminating beams is shown in Figure 24. The piezo-electric transducer used to perform
the phase shifting is controlled by a DT2815 12-bit D/A converter by Data Translation
inserted into a PC. The imaging system consists of an imaging lens and a monochrome
CCD camera connected to a DT2851 512x512x8-bit frame grabber by Data Translation.
The algorithms for the four-step phase shifting ESPI and the strain calculation were
implemented into menu-driven software using C language and DT-IRIS subroutine

library (Data Translation 1988).

51

“ I I I “ P=63.6N

 

L=l40

 

 

pin load, P e=39

 

 

 

 

 

 

w=45

Figure 23 Dimensions and loading condition of specimen (unit in mm)

 

 

Control
Monitor

A

Computer
———————— — — Frame Grabber
——————— — — — D/A Converter

V

V

 

 

 

 

 

Display
Monitor

 

 

 

 

 

 

 

 

 

B\S§—<—| Laser J

Figure 24 Dual-beam illumination setup of phase shifting ESPI (M= mirror,
BS= beam splitter, SF= spatial filter, CL= collirnating lens)

53

5.3.2 Results and Discussion

Figure 25 shows a raw phase change map of the pin-loaded plate obtained using
the four-step phase-shifting ESPI algorithm by Lanza di Scalea (1996). The wrapped map
of the displacement u obtained after employing the noise reduction and smoothing
procedure previously presented is shown in Figure 26 (a) as 16 gray levels for a
41><41mm2 area of the plate. Each fiinge represents a displacement u20.675p.m. The
pattern exhibits good symmetry with respect to the vertical axis of the plate. The u-
displacement contour plot obtained by the FEM analysis (Lanza di Scalea et al., 1997) is
shown in Figure 26 (b) for comparison with the ESPI results. The eyy strain maps
obtained by ESPI and FEM are shown in Figure 27 (a) and Figure 27 (b). The
experimental results in Figure 27 (a) are mapped into a 16 gray level contour plot, and
show good symmetry.

Good agreement between ESPI and FEM is observed in the overall shape of the
maps in Figure 26 and Figure 27. Nearly zero strain at the upper edge of the hole reveals
separation of the pin from the plate due to the applied load, and the highly negative strain
at the lower edge of the hole shows the compressive bearing effect induced by the pin.
Zero strain also occurs at an angle of about 45° from the bottom of the hole.

Figure 28 and Figure 29 show the line profiles of the normal strain concentration

factor eye“ along two critical directions of the plate, namely the net-section at y=0, and
the axis of symmetry at x=0. Both experimental and numerical results are presented. The

far field reference strain 8* was measured at a point positioned at x=0 and y=6r, r being

54

. c.4‘
5 (ef’cl ’
A:“~‘I"K'q’
r, "wk”,

 

Figure 25 Raw phase change map of pin-loaded plate

55

m§m_1n5¢ e:c.~.r.~--~=_»=w.v~v.w~ «114;; ;.»

 

(a)

Figure 26 Displacement map showing contours of the constant in-plane displacement uy

obtained by (a) ESPI and by (b) FEM (Continued overleaf)

56

14W]

--
_ 15.35

=
- step=0.675

 

(b)

Figure 26 (Continued)

57

ew|]onfin]
-400

-200

-100

100

200

300

 

400

(a)

Figure 27 Strain map of 8,, obtained by (a) ESPI and (b) FEM (Continued overleaf)

58

 

(b)

Figure 27 (Continued)

59

 

1111

 

net-section

 

 

 

 

 

 

 

x/r (r = pin radius)

Figure 28 Normal strain concentration factor eyy/e“ along the net-section of the plate:
comparison between ESPI and FEM.

60

 

 

 

 

 

 

 

 

 

 

 

 

 

2
j
'4 d “‘1‘ 3'; axis\of symmetry
'5 i — — ESPI
‘6 ‘ ---------- FEM
'7 l l l l I 1 l I l l
-6-5-4-3-2-10123456

y/r (r = pin radius)

Figure 29 Normal strain concentration factor (Zn/8* along the axis of symmetry of the
plate: comparison between ESPI and FEM.

61

the radius of the pin. A high strain gradient is observed near the hole, the strain
decreasing to a nearly constant value at a small distance from the discontinuity.

The small-scale fluctuations observed in the experimental plots appear to be the
effect of local inhomogeneity in the specimen. Two portions of the ESPI plot in Figure 29
have been purposely represented as dotted lines. The first portion (between about 3r and
4r distance from the center of the hole) shows a large fluctuation of the results caused by
a localized anomaly of the light scattering properties of the surface of the specimen. The
second portion (close to the edge of the hole) shows a decrease in strain values which can
be partly explained by: 1) the effect of friction at the pin/hole interface, and 2)
mathematical approximations affecting the strain calculation near the edges of the
specimen, even though these approximations are limited to at most two pixels from the
edge for the 5x5 convolution filtering window used in this analysis.

Besides the obvious approximations affecting any numerical result, a possible
reason for the discrepancy between ESPI and FEM results in Figure 27 and Figure 28 is
the presence of residual stress and/or mechanical damage around the hole of the specimen
caused by the drilling. Additionally, the coefficient of fiiction used in the numerical
simulation might not have precisely represented the actual pin/hole contact condition in
the specimen. The general trend and shape of the experimental and numerical plots in

Figure 28 and Figure 29 show good correlation.

6. CONCLUSIONS

This work is composed of two parts: (1) a comprehensive study of speckle
metrology techniques and related digital image processing, and (2) developments and
applications of the digital image processing algorithms for electronic speckle pattern
interferometry. In the study of speckle metrology, the basic optics theories of the laser
speckle effect and its applications to displacement measurement are described. Also,
fundamental digital image processing ideas are studied as essential tools of ESPI. A real-
time image processing algorithm for the correlation ESPI technique is developed and
applied to the non-destructive inspection of a composite pressure vessel. In addition, a
special image filtering technique using local phase unwrapping is designed for the
filtering of a wrapped phase change map from phase shifting ESPI. Finally, a whole-field
strain calculation algorithm is derived from least-square surface fitting.

The major conclusions of this work are:

(1) Electronic speckle pattern interferometry provides a powerful non-contacting whole
field displacement and strain measurement tool for various engineering fields.

(2) Real-time correlation ESPI is suitable for the non-destructive inspection of
intermediate or final products with fast and qualitative displacement measurement
capability.

(3) The local unwrapping method developed in this study is useful to enable image
filtering for the wrapped phase change map obtained from various phase measurement

techniques.

62

63

(4) The phase-shifting ESPI and strain calculation algorithms provide a precise whole-

field displacement and strain measurement tool which has displacement sensitivity of

1/256 of a wavelength and an equivalent strain gage size of 0.4mm.

Possible future research areas of ESPI are:

1.

Design of a new optical setup to measure three displacement components
simultaneously.

Modification of the optical setup to provide a vibration-tolerant, flexible and compact
arrangement with optical fibers and a diode laser

Further development of a user-friendly and automated ESPI software

Development of a standard calibration method using a rigid and precise loading frame
for comparing analytical and numerical results.

Investigation of applicable engineering problems and modification of the optical

setup for industrial applications.

List of References

64

List of References

Biedermann, K. and Ek, L. “A recording and display system for hologram interferometry
with low resolution imaging devices,” Journal of Physics E: Scientific Instruments, 8,

571-576,(1975).

Butters, J .N. and Leendertz, J .A., “Holographic and video techniques applied to

engineering measurement,” Measurement and Control, 4 (12), 349-354, (1971).

Chen, X. Electronic Speckle Pattern Interferomet_ry, Electronic Shearoggaphy, and Their
Applications, Ph.D. Dissertation, Michigan State University, (1995).

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