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thesis entitled
Electronic Speckle Pattern
Interferometry and Applications In

Engineering Mechanics
presented by

Xiaolu Chen

has been accepted towards fulfillment
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ELECTRONIC SPECKLE PATTERN
INTERFEROMETRY AND APPLICATIONS IN
ENGINEERING MECHANICS

By
Xiaolu Chen

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

1992

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ABSTRACT

ELECTRONIC SPECKLE PATTERN
INTERFEROMETRY AND APPLICATIONS IN
ENGINEERING MECHANICS

By

Xiaolu Chen

Holographic interferometry (HI) techniques have been brought to near perfection and
have solved a wide variety of practical problems. The techniques have, however, not
received the general acceptance in industry as their potential should indicate. The major
reluctance stems from the cumbersome and slow process of film recording and

development, and from the method’s sensitivity to environmental disturbances.

This paper describes the calibration and use of an Electronic Speckle Pattern
Interferometry (BSPI) system which is a combination of holography, video recording,
signal processing and computer technology. The major advantages of ESPI are fast
recording (1/30 s), real time correlation fringe display, and computer controlled speckle
pattern image processing with displacement calculation. ESPI also can display real time
modal shape of a vibrating object. The theory of speckle pattern decor-relation and actual
measurements obtained from ESPI are discussed in detail. Some results of using ESPI as
a nondestructive test tool for composite material are presented. Conclusions and

recommendations are presented.

To My Parents

ACKNOWLEDGMENTS

The author wishes to express his sincerest appreciation and gratitude to his academic
advisor and major professor Gary Lee Cloud for his valuable guidance and encouragement
during the course of this research.

The author also wishes to thank his wife Jianzhen Xie and newborn son Louie Chen for
their patience, understanding, help and encouragement.

TABLE OF CONTENTS

Page

LIST OF TABLES ............................................................................................................ vi
LIST OF FIGURES ......................................................................................................... vii
INTRODUCTION .............................................................................................................. 1
CHAPTER 1 LASER SPECKLE AND ITS ROLE IN ESPI ....................................... 6
1.1 Speckle and Its Origins ...................................................................................... 6

1.2 Size of Speckle ................................................................................................. 9

1.2.1 Objective Speckle Size ............................................................................ 9

1.2.2 Subjective Speckle Size ......................................................................... 10

1.3 The Brightness Distribution of Speckles ........................................................ 11

1.4 Coherent Combination of Speckle and Uniform Fields .................................. 13

1.4.1 Size .......................................................................................................... 13

1.4.2 Brightness Distribution ......................................................................... 13

1.5 Coherent and Incoherent Combination of No Speckle Fields ....................... 14

1.6 Polarization Efi‘ects .......................................................................................... 16

1.7 Speckle Pattern Decorrelation ......................................................................... 17

1.7.1 Out-of-plane Translation ....................................................................... 19

1.7.2 In-plane Translation ....... ‘. ....................................................................... 20

1.7.3 Out-of-plane Rotation ............................................................................ 21

1.7.4 In-plane Rotation .................................................................................... 21

CHAPTER 2 DISPLACEMENT ANALYSIS AND OPTICAL SETUPS ................. 22

2.1 Sensitivity Vector ............................................................................................ 22
2.2 Out-of-plane Displacement Sensitive Optical Setup ..................................... 26
2.3 In-plane Displacement Sensitive Optical Setup .............................................. 27
2.4 Two Special Cases ........................................................................................... 32
2.4.1 Pure Out-of-plane Displacement. .......................................................... 32
2.4.2 Pure In—plane Displacement. .................................................................. 34

2.5 Limitations of ESPI .......................................................................................... 35
2.5.1 Measurement Sensitivity .......................................................................... 35
2.5.2 Object Size Limitations ............................................................................ 36
2.5.3 Depth of Field ........................................................................................... 37
2.5.4 Surface Condition ..................................................................................... 37
2.6 Practical Optical Setups for ESPI .................................................................... 38
~ CHAPTER 3 ESPI SYSTEM ........................................................................................ 41
3.1 Introduction ...................................................................................................... 41
3.2 Video System and Other Electronics in ESPI ................................................ 41
3.3 Speckle Correlation Fringe Formation by Video Signal Subtraction ............. 44
3.4 Speckle Correlation Fringe Formation by Video Signal Addition ................. 46
3.5 The Measurement of Real Time Vibration Pattern ........................................ 48
3.6 The Measurement of Dynamic Displacement ............................................... 51
3.7 The Optimization of Light Intensity in ESPI .................................................. 51
3.7.1 Two Speckle Beam Case ........................................................................ 52
3.7.2 Smooth Reference Beam Case .............................................................. 52

3.8 Spatial Resolution of the Video System and Its Effect on ESPI .................... 52
3.8.1 Spatial Resolution (two-speckled—beam case) ..................................... 55

3.8.2 Spatial Resolution (smooth reference beam case) ................................ 56

iv

3.8.3 General Conclusion ................................................................................ 60

3.9 Error Sources ................................................................................................... 60

3.10 Displacement Measurement Using Phase Information ................................. 62

3.10.1 Principal Phase Determinationn .......................................................... 62

3.10.2 Phase Measurement ............................................................................ 62

3.10.3 Means of Phase Shifting ..................................................................... 64

3.10.4 Phase-measurement Algorithms ......................................................... 65

3.10.5 Comparison of Phase Measurement Techniques ................................ 74

3.10.6 Phase Unwrapping ............................................................................... 75

3.10.7 From Phase Change to Displacement. ................................................. 77
CHAPTER 4 NONDESTRUCTIVE TEST OF COMPOSITE USING ESPI .......... 78
4.1 Stressing Techniques ........................................................................................ 78

4.1.1 Mechanical Stressing ................................................................................ 78

4.1.2 Thermal Stressing .................................................................................... 79

4.1.3 Pressure Stressing ................................................................................... 80

4.1.4 Acoustic Stressing .................................................................................... 81

4.1.5 Vibration Excitation .................................................................................. 81

4.1.6 Microwave Excitation ............................................................................... 81

4.2 NDT Results of Composite using ESPI ............................................................ 82

4.2.1 Using Thermal Stressing .......................................................................... 82

4.2.2 Using Gravity (creeping) .......................................................................... 95

4.2.3 Using Vibration ......................................................................................... 97
CONCLUSIONS AND RECOMENDATIONS ........................................................... 115
REFERENCES ............................................................................................................... 116

LIST OF TABLES

Table Page

1.1 Fringe order N vs vibration amplitude

in time-average ESPI mode ..................................................................................... 50

1.2 Determination of the phase modulo 21c ..................................................................... 76

LIST OF FIGURES

Figure Page

1.0

1.1
1.2
1.3
1.4

1.5
1.6
1.7
2.1
2.2

2.3

2.4

2.5

2.6

2.7

2.8

Step by step comparison between (A) real time

image holography and (B) ESPI system .................................................................... 4
A typical image plane speckle pattern ........................................................................ 7
Formation of objective speckle .......................................................... 9
Formation of subjective speckle ................................................................................ 10
Probability density functions of the brightness

distribution of a fully-developed speckle feild ......................................................... 12
Coherent combination of speckle field and uniform field ......................................... 14
Incoherent combination of two speckle fields ........................................................... l6
Diagram for speckle decorrelation analysis ............................................................... 18
Position and propagation vectors .............................................................................. 22
The variation of 535': resulting from the change

of illuminating and viewing angle ............................................................................ 25
Out-of-plane sensitive ESPI optical setup

using uniform reference beam .................................................................................. 26
ESPI with reduced out-of-plane displacement sensitivity ......................................... 27
The optical arrangement for in-plane displacement sensitive setup .......................... 28
An alternative optical setup of in-plane displacement measurement ........................ 30
A practical optical setup of an in-plane

displacement sensitive ESPI system. .................................... . .................................. 31
Pure out-of-plane displacement. ................................................................................ 32

2.9

2.10
2.11

2.12

2.13

3.1

3.2

3.3

3.4

3.5

4.1
4.2

4.3
4.4
4.5

The relationship between (1," and d to illumination
angle 0 in pure out-of-plane case ............................................................................ 33
Pure in-plane displacement. .............. 34
The relationship between rim and d to illumination
angle 0 in pure in-plane case ................................................................................. 35
A smooth, in-linc reference beam interferometer Which
uses a beam splitter to combine the object and reference beams ......................... 39
A smooth, in-line reference beam interferometer based on i
the hole-in-mirror principle .................................................................................... 40
The block diagram of ESPI system ............................................................................ 42
The first few cycles of the 1?, distribution which defines the
intensity distribution of time-averaged speckle fringes for a
sinusoidally vibrating surface .................................................................................. 50
The general geometry of a smooth
reference beam interferometer ................................................................................. 57
Schematic for measuring phase using a PZT mirror as the phase
shifter and sending data to a computer for the phase calculation ............................ 63
(1) CCD may with finite-sized detector element. (2) Detector
element much smaller than speckle size. (3) The size of
the detector element and speckle are almost equal. (4) Speckle
size is much smaller than the detector element. ...................................................... 67
The ESPI system ........................................................................................................ 83
Impact damaged composite (glass/epoxy) specimens used
in NDT using ESPI gravity and thermal stressing tech niques ............................... 84
Setup for NDT of composite using ESPI thermal (resistor) method ......................... 86
Setup for NDT of composite using ESPI thermal (steamer) method ........................ 87
Fringe pattern obtained when composite plate #7 is .‘point heated’

viii

4.6

4.7

4.8

4.9
4.10

4.11

4.12
4.13

4.14

4.15

4.16

4.17

4.18

4.19
4.20

at the center using a resistor heating device and then with

the heater removed. ................................................................................................ 88..
Fringe pattern obtained when composite plate #7 is heated
at the upper right comer using a resistor heating device

and then the heater is removed ................................................................................ 89
Fringe pattern obtained when composite plate #7 is in free

expansion at AT about 8 °C (23-15) with At about 5 seconds ............................... 90
Fringe pattern of plate #9 when heated at the upper right

comer and then with the heater removed ................................................................. 91
The 3D plot of Figure 4.8 .......................................................................................... 92
The 2D plot of Figure 4.8 of the section where the

damage spot is locate! - -- - - -- - -_ .............................................. 93

 

The 2D plot of Figure 4.8 of a arbitrary section

away from the damaged spot .................................................................................. 94
Setup for NDT of composite using ESPI by gravity creeping method ..................... 96
Plate #3 creeping at room temperature with
fringe accumulation time At = 5 sec ....................................................................... 98
Plate #9 creeping at room temperature with fringe
accumulation time At = 30 sec ................................................... , ............................. 99
Plate #7 creeping at room temperature with fringe
accumulation time At = 30 sec .............................................................................. 100

Impact damaged composite (glass/epoxy) specimens used in NDT

using ESPI time-average mode, speaker was used for excitation ....................... 101
Setup for vibration test using a speaker ................................................................. 102
Plate #1 vibrating at 173 Hz, (a) before impact, (b) after impact ........................... 103
Plate #1 vibrating at 707 Hz, (a) before impact, (b) after impact. .......................... 104
Plate #1 vibrating at 942 Hz, (a) before impact, (b) after impact ........................... 105

4.21
4.22
4.23
4.24
4.25
4.26
4.27

4.28

4.29

Plate #6 vibrating at 100 Hz, (a) before impact, (b) after impact ........................... 106

Plate #6 vibrating at 300 Hz, (a) before impact, (b) after impact ........................... 107
Plate #6 vibrating at 388 Hz, (a) before impact, (b) after impact ........................... 108
Plate #6 vibrating at 451 Hz, (a) before impact, (b) after impact ........................... 109
Plate #6 vibrating at 761 Hz, (a) before impact, (b) after impact ........................... 110
Plate #6 vibrating at 805 Hz, (a) before impact, (b) after impact ........................... 111

Experimental setup for nondestructive inspection using ESPI’s
time-average vibration mode. The composite being tested

is A s-4/828 mPDA, 18 plies, the depth of cut is 9 plies ..................................... 112
The carbon fiber plate vibrating at 2057 Hz,

(a) plate without cuts, (b) plate with cuts ............................................................ 1 13
The carbon fiber plate vibrating at 8150 Hz,

(a) plate without cuts, (b) plate with cuts ............................................................ 114

INTRODUCTION

Vlfrth the advent of the laser in 1960 and the holographic recording process, a unique
technique which is called holographic interferometry (HI) was created to perform
interferometric measurements on objects. H] was first demonstrated by Powell and
Stetson [1] for vibration study. HI has many advantages as a measuring technique; as the
wavelength of the laser light serves as the measuring unit, it is a noncontact,
nondestructive method with very high sensitivity. In addition, the information is
presented as a three-dimensional image of the test object which is covered with a fringe
pattern. From the appearance of this pattem one can quickly determine the overall
deformation and the location of stress concentrations. HI applications have been
demonstrated by many authors[2-6]. In spite of these obvious advantages, industry in
general has been slow to accept this new technique. HI has been mostly confined to
research laboratories with some notable exceptions, e. g. Rolls-Royce [7] in England,
Brown Boveri in Switzerland and in the tire quality inspection area. The reasons for this,
apart from the usual distrust towards new unfamiliar techniques, are in two aspects. First,
the stability requirement in holography is not readily compatible with industry
environments unless pulsed lasers are used. Second, the photographic recording process
and subsequent development introduce an annoying time delay which prevents on-line
inspection. Although self-developing and reusable recording media have been
developed, there still remains a time delay between the recording and observation of the
fringe pattern, and direct computer data processing is not applicable. In addition, the cost

for consumable material is fairly high.

The essential of a hologram interferometer is that it records the complete pattern of
waves emanating from the object, both in amplitude and phase, by combining it with a
so-called reference beam. To measure deformation, wave patterns are recorded when the
object surface is in its original and deformed states, and these are combined to give an
interference fi'inge pattern related to the deformation that has taken place. The
holographic process is used here only as an intermediate step in the acquisition of this
fringe data, and unnecessary information relating to the three-dimensional shape and the
surface reflectance of the object are included. The hologram stores far more information

about the surfaces than is really necessary for measuring surface displacement.

For this reason it is natural to investigate the use of television systems to replace
photographic recording materials and to use electronic signal processing and computer
techniques to generate interference fringe patterns. This technique is called Electronic
Speckle Pattern Interferometry (ESPI). The basic principle of ESPI was developed
almost simultaneously by Macovski et a1 (1971) [8] in the United States, Schwomma
(1972) [9] in Austria, and Butters and Leendertz (1971) [10] in England. The last group
especially has pursued the development of the ESPI technique vigorously in both
theoretical and practical directions. Later, another group in Norway headed by Ole

Lokberg also started successful research and development in ESPI.

For speckle pattern interferometry, the resolution of the recording medium used need
not be that high compared with that required for holography, since it is only necessary that
the speckle pattern be resolved, and not the very fine fringes formed by the interference of
object and holographic reference beam. The minimum speckle size is typically in the
range 5 to 100 um, and it can be varied to some extent to suit the resolution limits of a TV
camera without losing phase information about the surface position, so that a standard
television camera may be used to record the speckle pattern. Thus, video processing may

be used to generate correlation fringes equivalent to those obtained photographically.

The major feature of ESPI is that it enables real-time correlation fringes to be displayed
directly upon a television monitor without recourse to any form of photographic
processing and plate relocation. Furthermore, the vibration isolation is relaxed (only need
1/30 s to record a frame of speckle pattern) and no dark room is needed. A computer is
used to control the entire process, to calculate the displacement and present results in

graphical form. The advantages can be summarized as follows:

1. Does not require the highly stable environment necessary for conventional

holographic interferometry.
2. System can be used in brightly lighted conditions, no dark room is needed.

3. Since no film and the processing of the film are needed, the material cost per

experiment is very low.

4. People with little background in optics can operate the system.

5. The safety hazard is significantly lowered.

6. Expanded experimental capability.

7. High efficiency, automatic data processing, real-time result presentation.
Comparison of ESPI and HI

ESPI and image HI are compared step by step in Figure 1. The recording mechanism
in holography is a film grain exposure which, after development, results in a proportional
amplitude transmittance of the reconstruction wave. In ESPI the equivalence consists of
a charge buildup which subsequently is transformed by the TV scan into a current
proportional to the exposure. After first exposure, for H1 one simply places the

developed film ( hologram) back into the reference wave. The interference pattern

 

 

Deflection

 

 

 

 

 

 

 

 

 

 

Deflection

Ar
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Film processing I I Frame grabbing
Reconstruction Reconstruction
optically electronically

Quantitative 3D displace-
. I III fringes mentp10t
Fringe pattern formed
FEA data base
(A) Image holography (B) ESPI 57593“)

Fig. 1.0

Step by step comparison between (A) real time image holography

and (B) ESPI system.

 

stored in the hologram now acts as a complex grating sending some of the light into a side
order wave which is identical to the original object wave. Therefore we see a
reconstructed image of the object which, upon deformation of the object, will create an
interference fringe pattern. In ESPI we have to simulate the optical reconstruction by
electronic processing of the video signal. Correlation fringes are obtained by electronic
subtraction or addition and displayed on a TV monitor where we see the object covered
with exactly the same bright and dark fringes as in holography, except that the image looks
more coarse. Moreover, ESPI can calculate phase and displacement information and

present the results in computer graphics very rapidly.

Chapter 1

Laser Speckle and Its Role in ESPI

Laser speckle is used as the phase information canier in an ESPI system. Knowledge

of its properties are very important for a good understanding of ESPI.
1.1 Speckle and Its Origins

Operation of the first continuous wave (cw) He-Ne laser in 1960 revealed an
unexpected phenomenon; objects viewed in highly coherent light acquire a peculiar
granular appearance. As illustrated in Figure 1.1, the detailed structure of this granularity
bears no obvious relationship to the macroscopic properties of the illuminated object, but
rather it appears chaotic and unordered, with an irregular pattern that is best described by
the methods of probability and statistics [11].

The physical origin of the observed granularity, which we now know as “laser
speckle”, was quickly recognized by the early workers in the field [12-13]. The surfaces
of most materials are extremely rough on the scale of an optical wavelength (0.6 microns).
This includes most surfaces other than those which are polished to high optical quality.
Speckle can also be produced by transmission through scattering objects such as ground
glass, opal glass or particles in liquid. When laser light is reflected or scattered from such
a surface, the optical wave arriving at any moderately distant point consists of many
coherent components or wavelets, each arising from a different microscopic element of
the surface. The distances travelled by these various wavelets may differ by several or
many wavelengths if the surface is very rough. Interference of the dephased but coherent

wavelets results in the granular pattern of intensity that is called speckle.

 

Fig 1.1

A typical image plane speckle pattern.

When the geometry is that of an imaging system, rather than the free-space
propagation, the explanation must incorporate diffraction as well as interference. Even
for a perfectly corrected (aberration-free) imaging system, the intensity at a given image
point can result fi'om the coherent addition of contributions from many independent
surface areas. It is necessary only that the diffraction limited (amplitude) point-spread
function of the imaging system be broad in comparison with the microscopic surface
variations to assure that many de-phased coherent contributions add at each image point.

Thus speckle can arise either from free-space propagation or from an imaging operation.

In this paper the speckle considered is “Gaussian speckle”. The terminology
“Gaussian speckle” is derived from the fact that, as a result of the rough surface
approximation and the central limit theorem, the complex amplitude is a circular complex
Gaussian process. This results in a negative exponential probability density function for
the intensity. “Within the limits of the necessary conditions, the statistics of a Gaussian
speckle pattern are independent of the nature of the scattering medium; in particular, the
surface roughness does not influence the statistics provided that the surface roughness is
greater than the wavelength and that a large number (N) of scatterers contribute to the
intensity at any image point (patch). For most practical applications this is generally the

C386.

On the other hand, if only a few independent scatterin g areas are present, then the
speckle statistics do contain information about the scattering medium. Such “small-N”
speckle usually has non-Gaussian statistics and hence the probability density function of

intensity is usually not of the negative exponential type.

In the experimental measurement of the intensity in a speckle pattern, the detector
aperture must of necessity be of finite size. Hence the measured intensity is always a

somewhat smoothed or integrated version of the ideal point-intensity, and the statistics of

the measured speckle will be somewhat different than the ideal statistics of the speckle

pattern.
1.2 Size of Speckle
1.2.1 Objective Speckle Size

The size of laser speckles, a statistical average of the distance between adjacent
regions of maximum and minimum brightness, is always related to the apertureangle that
the radiation subtends at the plane defining the speckle field. Thus, for example, the size
(diameter) Sobj of the ‘objective’ speckles formed on a screen H at distance L by
scattering of coherent light from a circular region of diameter D , see Figure 1.2, is given

by [14.15].
53,33. = 1.22%). (1.1)

where I. is the wavelength of the laser light.

. er Source

 

 

 

 

H
Observation Plane

Fig. 1.2 -
Formation of Objective Speckle

10
1.2.2 Subjective Speckle Size

Alternatively, if the speckle field is formed by collecting the scattered radiation field
with a lens and focusing it onto the screen (Figure 1.3) a ‘subjective’ speckle pattern is
formed. The size Ssub of the individual speckles in this case is then related to the aperture
ratio F of the lens (the f/number) and the magnification M of the lens. The speckle size in

the image is then [16,17],
S ~1.22(1+M)IF, (1.2)

sub =

From simple lens theory, the speckle size on the scattering surface (object) is given by

sub =

0 ~ F
l.22(1+M)l—M , (1.3)

This is defined as the resolution element on object. Subjective speckle is the type that is

used in ESPI and most other speckle metrology methods.

Lase Source

 

 

 

Object
Image Plane

Fig. 1.3
Formation of subjective speckle

11
1.3 The Brightness Distribution of Speckles

The speckle is itself an interference phenomenon. There are two different speckle
patterns. One called the ‘fully-developed’ speckle pattern develops only from interference
of light that is all polarized in the same manner. The speckle field itself will then be
similarly polarized. Surfaces at which polarized light is singly scattered, such as lightly
abraded metal, generally give rise to polarized speckle fields, as do also lightly—scattering
transmission elements such as ground glass. On the other hand, matte white paint
surfaces or opal glass, into which the light penetrates and is multiply scattered, depolarize
the light and thus do not generate a fully developed speckle pattern. The brighmess

distributions of the two speckle patterns are markedly different from each other.

The distribution of brightness of a fully-developed speckle pattern is governed by the

negative exponential relationship [18]

p(I) = (imxp “l“ . “-4)
I0 Io

where p(I) is the probability that a speckle has brightness between the values I and

(1+ dI) , and 10 is the average brightness. This relationship is plotted in Figure 1.4, and
it shows that the most probable brightness for a speckle is zero, i.e. there are more dark
speckles in the field than speckles of any other brightness. It is this property that is of the
greatest importance in distinguishing a fully-developed speckle pattern from one which is
partially-developed.

DO)

12

 

0.8-

0.5-

0.4-

 

J.

 

0 . 5 1 1 . 5 2 2 . 5
IO

Fig 1.4
Probability density functions of the brightness

distribution of a fully-developed speckle field

 

13

1.4 Coherent Combination of Speckle and Uniform Fields

In a typical ESPI system, a uniformly bright field of coherent radiation, which is the so
called reference beam, is added to the speckle field. The addition of the reference field
will affect both the size and the brightness distribution of the speckle field.

1.4.1 Size

When a reference beam is introduced the size of a speckle will approximately double.
The reason for this involves the interference effect of adding a uniform strong wave to the
speckle pattern in the direction of the optical axis. The size of a speckle without the
addition of the reference beam corresponds roughly to the spacing of the interference
fringes generated by waves coming from the opposite ends of a diameter of the
speckle-forming pupil if an imaging system is used. When the Strong reference wave is
introduced, the principal interference effects will take place with respect to this central
strong ray, so that the maximum angle between interfering rays is halved. The

interference fringe spacing is doubled as is the size of the speckle.
1.4.2 Brightness Distribution

Burch [19] has considered the statistical distribution of brightness when the uniform
field is added to the speckle pattern in varying proportions. A typical curve is shown in
Figure 1.5, which shows the distribution when the average speckle brightness is equal to

the reference field brightness. The mathematical relationship is expressed by

1
2 1 1 5
3(1) _ (17))exp[-(l+21—0)]Jo[2(21—0) ] (1.5)

14

where Jo is the Bessel function of zero order with imaginary argument. The important
feature of this curve is that it does not differ greatly from the distribution curve for the

speckle pattern alone; in particular, the most probable brightness is still zero.

P(I)

 

 

 

 

 

Fig 1.5

Coherent Combination of speckle field and uniform field

1.5 Coherent and Incoherent Combination of Two Speckle Fields

An important class of speckle interferometers, particularly those for measuring
in-plane surface displacement, operate by the interference of two independent speckle

patterns. When this occurs, the size of the speckles does not change appreciably, but their

15

brightness distribution may. In the case where the two original speckle fields are brought
together coherently, the result will be a third speckle pattern, differing in detail from its
two constituent patterns, but whose size and statistical brightness distribution remains the
same. However, if the two original speckle fields are combined incoherently, the

brightness distribution follows the equation [20],

pa) = 4 l expt—zi). (1.6)
I2 [o

0

This relationship is plotted in Figure 1.6. It is seen that now there is a very low
probability of a dark speckle occurring. Conceptually, this is not surprising, since when
two intensity speckle patters are overlaid physically, there is a high probability that the
bright areas of one pattern will be superimposed on to the dark areas of the other.
Surfaces that completely depolarize the light will give a speckle pattern having a
brightness distribution that agrees with the above equation, since any two orthogonally

polarized components of the scattered light are incoherent with one another.

Although there is a striking statistical difference between the brightness distributions
of coherently and incoherently summed speckle patterns, in practice it is not easy to

distinguish the two visually.

16

13(1)

 

 

 

 

 

Fig. 1.6

Incoherent combination of two speckle fields.

1.6 Polarization Effects

Since phase information relies upon the formation of interferometric fringes formed by
the construCtive and destructive interference between the object and reference beams, the

light in the two beams should have the same polarization. Laser beams polarized

l7

orthogonally to each other will not interfere. Most lasers are linearly polarized and this
can, in some instances, cause problems in recording speckle patterns. Although both
beams are derived from the same source, polarization changes can occur as a result of
reflections. Fortunately, most diffuse objects scatter light in randomly polarized fashion,
and there will always be components having the same polarization as the reference beam.
For example, in the study on composites (carbon fiber and glass/epoxy), we found that
they do not depolarize light; the light scattered has the same polarization as the reference
light. Light scattered from white carton board will be partially depolarized. If a

polarization problem exists, it can be rectified by the following methods.

(1) Changing the surface properties of the object (e. g. paint it or spray with aluminum

paint).

(2) Rotating the plane of polarization in the reference or object beams to match each
other by inserting a half-wave plate into either beam and rotating it until the extinction

angle is the same for each beam when tested with a polarizing filter.

(3) Circularly polarizing the light as it emerges from the laser by orienting a quarter-wave

plate in the laser output beam.
1.7 Speckle Pattern Decorrelation

In the following discussion it is assumed that the illumination direction and the viewing
direction are parallel with the normal of the object surface . This assumption is close to

the real ESPI case. Refer to Figure 1.7 for the configuration used in this section.

In speckle pattern correlation interferometry, it is assumed that neither the
displacements which give rise to the phase variation causing the fringes nor other
displacements not contributing to this phase variation significantly alter the random phase

and amplitude of the speckle pattern in the fringe observation plane. This is, however, an

18

Imaging system
- l I

2 d l "
I Detector

plane"

 

 

 

Fig. 1.7
Diagram for speckle decorrelation analysis.

approximation which is valid only when the displacements involved are less than some
minimum value which depends on the kind of displacement involved and the viewing
geometry. For example, in the case of in-plane displacement interferometry, a body may
undergo in-plane strain together with out-of-plane rotation. The effect of the latter will be
to reduce the contrast of the plane-strain fiinges when the magnitude is sufficient to cause
speckle pattern decorrelation. Another important factor which should be noted is that
when the object deforms the resolution elements also move. If this movement is big
enough to move across the detector element, it will ‘lose the memory’ of the speckle
which contains the displacement information. Consider here the case in which the
speckle and the detector element have the same size. The criterion to judge if there is

decorrelation is as follows:

19

(1) When the phase change across the resolution element is equal to or bigger than 21c, the

speckle will be totally decorrelated.

(2) When the resolution element moves across and out of the detector element, the
detector will lose the memory of the displacement (phase) information carried by the

speckles.

(3) If the phase change or memory loss in either case is less than about one tenth of a
corresponding critical values, the speckle is not decorrelated and no ‘memory loss

9

occurs .

Four different cases are considered below in order to determine which factor is

dominant for each.
1.7.1 Out-of-plane Translation

As the object is displaced along the viewing direction, the relative phase of the
components of light scattered from a resolution element will also change. It can be
shown that the maximum value of this phase change is 21c across the resolution element
when the object moves by an amount Azl given by (neglect the small quantities of second

order)

Mau2

” 1.22(1+M)fx ' (1'7)

 

Azl

Here u is the object-to-lens distance, a is the aperture diameter, f is the focal length, M is

the magnification of the imaging system.

It also can be shown that when the translation is

fu7t

A2231.22(1+M)'b4—'ax9

(1.8)

20

the detector will lose memory of the corresponding resolution element, which means the

resolution element will move out of the detector element.

If M=1 / 15, u= 500 mm, f/a = 16 (typical numerical aperture used in ESPI), for x =

50 m we will have
Az1 ~= 16009ttm, and A22 = 1976ttm .

So, in this case the ‘memory loss’ is more important, and we also can see that ESPI has
large tolerance in the z direction. It will be shown in Chapter 3 that the tolerance above is

more than enough in using an ESPI system.
1.7.2 In-plane Translation

When a body moves in its plane, the speckle pattern in the image plane also moves in
proportion to the magnification of the viewing system. If the amount of the movement is
small compared with the resolution element size, the change in the speckle pattern at a
given point in the image plane is also small. It can be shown that the speckle pattern at a

point is decorrelated when the object is translated by an amount Ax 1 , given by

Mau

A"1'""1.22(1+1t4)f‘

(1.9)

 

The detector element will lose memory when

m2~1.22(1+M)%3 . (1.10)

As the object is translated in its plane, the speckle pattern is translated; it does not
remain identical in form because the light scattered from a given point in the object is
incident on the viewing lens at a difierent angle so that the displaced speckle pattern is not
identical in form to the original pattern. When Axl = a, the displaced speckle pattern is

totally decorrelated with respect to the original pattern.

21
IfM=1/15, u =500mm,x=50mmandf/a = l6weget
Ax] = 1601p.m, M2 = 198nm
again ‘memory loss’ is more sensitive.
1.7.3 Out-of-plane Rotation

When the resolution element is rotated by an angle 0 about an axis lying in the object

plane, the speckle pattern is decorrelated when 0 is given by

9:5 Ma

q=1.22(1+M)f (1'11)

 

where q is the resolution element diameter. For M = 1 / 15, f/a = 16, we obtain
9 = 0.180.
1.7.4 In-plane Rotation

An in-plane rotation of the object gives rise to an equivalent rotation of the speckle
pattern. A point at a distance R from the center of rotation moves by Ra, where a is the

angle of rotation; thus the speckle pattern is decorrelated when

.. q _ 7if
on»i _ 1.22(1+M)———33MR, (1.12)

for M =1/15, f/a =16, we obtain

a = 023°.

From the above analysis, we conclude that the "memory loss" effect is more important

than the decorrelation effect.

Chapter 2

Displacement Analysis and Optical Setups

This chapter discusses quantitative measurements using an ESPI system and some

practical ESPI optical setups.
2.1 Sensitivity Vector

The sensitivity of ESPI measurement is governed by the orientation relation between
three vecrors, namely, the illumination vector, the displacement vector and the viewing
vector [21]. In Figure 2.1, the object is illuminated by a point source located at 0. Light
is scattered by an object point P to an observer or viewing plane at point Q. When the
object is displaced, so that the point P is displaced by L to P’, the optical path from the
source 0 to a point in the viewing plane via a given point P in the object is altered. The
change in phase associated with this change in optical path is the basis of holographic and

speckle correlation techniques for measuring surface displacements.

 

Fig. 2.1 Position and propagation vectors

22

23

Let 5 represents the phase shift of light scattered by point P on the object in a particular
direction. In Figure 2.1, several vectors are defined for use in determining the relation
between 8 and L. Vectors R and r1 lie in the plane defined by points 0, P, and Q; and
RI and k2 are the propagation vectors of the light illuminating P and the light scattered
toward the viewing plane, respectively. Since the magnitude of a propagation vector is

2
7:! , the phases of the two light rays which reach the viewing plane are as follows:

¢1=k10r1+k20(R-r1)+¢0 (2.1)

¢2=k30r3+k40(R—r3)+¢0 (2.2)

Here 61 is the phase of the light scattered by P before diSplacement, (1)2 is the phase of the
light scattered by P after displacement; and (to is the arbitrary phase assigned to these rays

at the point source 0. The phase difference measured at the viewing plane is

8 = ¢2-¢1 . (2.3)

After displacement of P, the propagation vectors in the illumination and viewing
directions are R3 and k4. Define the small changes, AR] and Ak2_ , in these propagation

vectors by
k3 = k1+Akl, It4 = k2+Ak2. (2.4)
Combining the preceding equations gives
5:(kz—k1)o(rl-r3)+Akl-r3+Ak20(R—r3) , (2.5)

In practical situations the magnitudes of r1 and r3 are much larger than L = I r3-r1i; so,
for practical purposes, Akl .L r 3 and Aid .1. (R - r3). Because of these relations, the

last two scalar products in equation (2.5) vanish, and the phase difference becomes

5: (k2—k1)0L, (Z6)

24

This relation forms the basis of quantitative interpretation of the fringes of ESPI.
It is convenient to define the sensitivity vector K by,
K = k2 - k1 (2.7)
so that,
8 = K 0 L. (2.8)

Thus, the phase change is

21:

21:
238:7-(K-L). (2.9)

Ad):

In general the fringe pattern represents in-plane as well as out-of-plane displacement.
When illumination and viewing angle are small (less than 15°) to the normal of the object

surface, we can write, to a very good approximation, that
211‘. '
A6 = T (c0503. + cosOv) dz (2.10)

where 03. is the angle of object illumination to surface-normal, 033 is the angle of viewing
direction to surface-normal, and dz is the displacement vector oriented within 03. and 03.
We can see here the phase is not only a function of displacement but also a function of ii-
lumination angle and viewing angle. Therefore, it is not possible to calculate the exact

actual displacement in ESPI. For NDT applications this is not a concern.

Let d", be the measured (calculated) displacement, we should have

dm c0803. + cos 633

71— = 2 (2.11)

 

25

The approximation relationship of dm vs (12 is graphically illustrated in Figure 2.2.

0. 992

0.99

0.988

0.988

0.984

0.982
0

 

 

 

 

 

15

Fig. 2.2
The variation of ( d," / dz) resulting from the change of

illuminating and viewing angle

26

2.2 Out-of-plane Displacement Sensitive Optical Setup

A practical arrangement for out-of-plane sensitive measurement is shown in Figure 2.3

 

Illuminating ggggence
Beam I
/ (l \
Imaging I

Beam 5 litter
System p

 

Fig. 2.3
Out-of-plane sensitive ESPI optical setup

Here the object is illuminated by the object beam at an angle 93. to the surface normal and
an image is formed by the lens L at image plane H. A diverging spherical reference wave
is added to the image by the beam splitter B. When the object is displaced, the change in
the phase of the object beam relative to the reference beam is given by equation (2.10)

with 033 = 0, so that this setup is sensitive to out-of-plane displacement. ESPI is based on

this setup but with a diverging illuminating beam.

Reduced out-of-plane displacement sensitivity may be obtained using the optical

arrangement shown in Figure 2.4. The correlation phase factor is now given by

2
A6 = T“ (c059i1 - coseiz)dz (2.11)

27

  
  

4 X Illuminating & Reference

111,911

  

Beams

 

 

System DCICC ti118

Fig. 2.4

ESPI with reduced out-of-plane displacement sensitivity

where 0i 3 and 032 are the angles of inclination of the two illuminating wavefronts In and
In to the surface normal of the object. Viewing is in the normal direction. When the
difference between 0i 3 and 032 are small, (cos Oil - cos 03 2) becomes small and contours
of out-of-plane displacement fringes, typically of the order of 10 um, may be observed.
Displacements of this magnitude may cause speckle pattern decorrelation, and this fact

limits the degree of desensitization.
2.3 In-plane Displacement Sensitive Optical Setup

The arrangement shown in Figure 2.5 gives fringes which are sensitive to in-plane
displacement. Here the object lies in the x, y plane and is illuminated by two plane
wavefronts, I“ and 112 inclined at equal and opposite angles, 0, to the x-axis
surface-normal. The positive y-axis points out of the page and the center of the viewing

lens aperture lies on the z-axis.

28

Imaging
I Plane
2

, ll
U L l
Imagin

System

 

Fig. 2.5

The optical arrangement for in-plane displacement sensitive measurement

When an element is displaced by a distance d(dx, dy, dz) the relative phase change of

the two beams is given by

At) = ¥dx sine. (2.12)

The relative phase of In and I12 is constant over planes lying parallel to the yz-plane so
that the displacement components dy and dz lying in those planes will not introduce a
relative phase change. This form of interferometer therefore allows in-plane displacement

distributions to be observed independently in the presence of out-of-plane displacements.

Similarly, y-axis illumination geometry in which the object is illuminated at equal

angles to the y-axis will form a fringe pattern where

4
A6 = {Edysine (2.13)

29

In order to determine all the components of the plane strain tensor, the fringe spacing

measurements must be taken from both illumination geometry fringe patterns.

A third in-plane displacement sensitive geometry may be used. In this setup the object
lies in the xy-plane and is illuminated by plane wave-fronts In and 112 propagating in the
xz-plane and yz-planes at equal angles 0 to the surface-normal. Viewing is in the normal

z-direction. This is referred to as the orthogonal arrangement and it can be shown that

11¢ = 4T"(c133+dy)sine . (2.14)

In practice it is difficult to utilize the in-plane measurement described above. The
reason is that large optical components are needed in order to study sizeable objects.

Two practical in-plane sensitive setups are illustrated in Figure 2.6 and Figure 2.7.

30

Laser beam

Beam expansion

Beam collimation

Mirror 2 Mirror 1

A

U i
1/ -'
Irnagrng system

Object surface

 

 

 

 

   

 

Fig. 2.6
An alternative optical setup of in-plane displacement

sensitive ESPI system

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2.4 Two Special Cases

In order to get more understanding about what an ESPI system really measures, we
analyze two special cases -- pure out-of-plane and pure in-plane. In this analysis,

diverging spherical illumination and viewing parallel with surface normal are used.

2.4.1 Pure Out-of-plane Displacement

In this case, the displacement vector is parallel with the viewing vector (Figure 2.8).

 

 

Fig. 2.8

Pure out-of-plane displacement

Here dis the displacement vector and K ( k2 - k1 ) is the sensitivity vector, where k2 is
the viewing vector, k1 is the illuminating vector and kl’ is parallel with k1. kl, kl’ and
[(2 are unit vectors.

Now the question. is how the angle 0 affects the measured displacement 1d,". From

Figure 2.8, we can derive a relationship between the measured displacement and the

actual displacement. This is given by

33

1+ 9
(cos)d

dm=d0K= 2 ,

(2.15)

here (I is the actual displacement. The relationship between dm and d for angle 6 less
than 15° is plotted in Figure 2.9. We can see there is a good approximation when 9 is

small.

 

“ls“

0.995

0.99

0.985

 

 

 

0.98

 

0 5 10 9 15

Fig. 2.9
The relationship between dm and d to illumination angle 0

in pure out-of-plane case

34

2.4.2 Pure In-plane Displacement

' Here, the displacement vector is normal to the viewing vector k2 (Figure 2.10)

 

 

 

 

 

 

Fig. 2.10

Pure in-plane displacement

In this case, the relation between measured and actual displacement is given by

dm = do K = (sin0)d. (2.16)

Note that the setup is a typical out-of-plane ESPI. For a pure in-plane displacement, only
a small portion of the displacement will be sensed. The relationship between the

measured displacement dm and the actual displacement d for .6 less than 15° is plotted

in Figure 2.11.

35

 

 

 

 

dm

7
0.14
0.12 - a
0.1 r r
0.08 r a
0.05 - -;
0.04 - -
0.02/- -

0 4 4

0 5 10 9 15

Fig. 2.11

The relationship between dm and d to illumination
angle 6 in pure in-plane case

2.5 Limitations of ESPI

The main factors which limit the range of measurements that can be made using the

various ESPI methods are discussed below.
2.5.1 Measurement Sensitivity

ESPI can be used to give fringes which represent lines of either in-plane or out-of-plane
displacement. The fringe sensitivity for an in-plane interferometer is calculated from
equation (2.12) to be I/(Zsin 0 ) , where 71 is the wavelength of the light used and 0 is the
angle of incidence of the illuminating beams. Out-of-plane interferometers may give

fringes representing constant displacements at intervals of the order of £1, or they may be

36

desensitized up to about hundreds of microns. It is not possible to detect less than one
hinge accurately with a conventional ESPI system, so that this value represents the

maximum sensitivity of the system.

We shall show in chapter 3 that the fringe spacing on the TV camera must be less than
l/120 of the screen width; this restriction limits the displacement gradient and also the
total displacement which can be observed. The visibility of the fringes obtained using
time-averaged ESPI to observe out-of-plane vibrations falls off rapidly with increasing

vibration amplitude unless stroboscopic illumination or other techniques are used.

2.5.2 Object Size Limitations

The maximum area which can be inspected in one view is limited by the laser power
available and the camera sensitivity. There is no reason why a larger area can not be
inspected if sufiicient laser power is available, but the mechanical stability of the system

and the coherence of the laser also limit the performance of the system.

When in-plane measurements are being made, the illuminating wave-fronts must be
plane if fiinges of uniform sensitivity are to be obtained. Unless a large collimating lens
is used for large areas, the fringe pattem interpretation will be rather difficult. When the

surface of the object being inspected is not flat, it can be shown that the fringes may have

sensitivity to out-of-plane movements.

In order to observe fringes on a small area, a relatively large deforming force must be
applied, and this is likely to give rise to rigid body translations, which cause speckle
decorrelation and hence a reduction in fringe visibility. The same applies to displacements
to which the interferometer does not have fringe sensitivity or has little sensitivity.
Decorrelation and memory loss (essentially decorrelation) due to in-plane translations and
rotations increase as the magnification of the viewing system is increased. Thus,

decorrelation of the speckle, causing a reduction in fringe visibility, is likely when ESPI is

 

37

used at high magnification. Fringes have been observed on an area of 0.05 mm2 in an

out-of-plane ESPI system [21]
2.5.3 Depth of Field

Because the ESPI system must use a high F-number (small aperture) viewing system,
the depth of field of the system is high, so the depth of field is generally not a restriction in
ESPI.

2.5.4 Surface Condition

It has been assumed throughout this discussion that the surface under examination does
not alter microscopically during the course of the measurement. If it does so, through
oxidation, recrystallization, or other factors, de—correlation of the speckle will result.

Additionally, the nature of the scattering surface itself can lead to a much greater
dependence of the speckle pattern upon a tilt of the surface. For surfaces like abraded
metal, the scattering from the surface is ‘two-dimensional’(only scattered once). When

the light penetrates to some extent into the ‘surface’ the light is then scattered three-
dimensionally within the material, so that path changes resulting from a small tilt of the
surface will vary in a random fashion from point to point. This occurs for such materials
as paints, paper and cardboard, and many organic substances. The net effect is that the
tolerance on the allowable tilt is much narrower when a multiple-scattering surface is

being studied than when the light is only scattered once.

Another consideration of practical importance relates to the type of surface required for
measurement of in-plane displacement using double illumination interferometry. Due to
the high an glcs of incidence of the two illuminating beams, it is evident that the surface
being studied must be totally diffusing, with no enhanced scattering in the specular

direction. For this reason the object very often has to be coated with a matt white paint.

 

38

2.6 Practical Optical Setups for ESPI

There are two basic ways of combining the object and reference beams in an ESPI

system for out-of-plane measurement. These are shown in Figures 2.12 and 2.13

respectively.

In Figure 2.12, the unexpended input reference beam is filtered and expanded by a
spatial filter to remove extraneous optical noise and create a spherical wavefront. This
well conditioned beam is particularly important for use in the addition mode (explained

in chapter 3). The reference beam then is reflected onto the TV camera target by a

small-angle wedge (about 1°) beam splitter. The rear face of the beam splitter is
The point of divergence

anti-reflection coated in order to suppress secondary reflections.
of the reference wave-fiont is made conjugate with the mid-point of the maximum focal

range to take care of the two extreme focal conditions. Light scattered from the object is

collected by the viewing lens and an image is formed in the plane of the TV camera’s
This system suffers from the

target where it interferes with the reference wavefront.
disadvantage that dust particles which tend to collect upon the beam splitter, together with

any small blemishes due to imperfect cleaning, act as light scattering centers. These

cause reference beam noise and hence degrade the quality of addition fringes. In the
subtraction mode of ESPI, this is not a serious problem.

Another arrangement which considerably reduces the reference beam noise is shown in

Figure 2.13. The unexpended reference beam is pre-expanded by lens L1 and focussed
down through a mirror-with-pinhole. The reference beam is aligned by translating the
lens 1Q so that its focal point coincides with the pinhole. The small hole in the mirror

does not degrade the image quality unless a significant fraction of the light transmitted by
the viewing lens is incident on the hole. The point of divergence of the reference beam

and the center of the viewing lens are clearly not conjugate in this arrangement, but since

 

39

 

Reference beam

 

 

 

e Beam splitter TV ‘camera
Object

 

Fig. 2.12
A smooth, in-line reference beam interferometer which uses

a beam splitter to combine the object and reference beams

 

 

 

 

4O

 

 

 

 

 

 

Scattered
l Object beam
Imaging lens
Reference beam
’1‘

—>U
Concave 14 TV
lens L1 Mirror with a hole camera

Fig. 2.13

A smooth, in-line reference beam interferometer

based on the hole-in-mirror principle

the tolerance along the optical axis direction is large, this layout can be made to function

within the limits specified by equation (3.32).

Chapter 3

ESPI System

In this chapter we will discuss the electronic part of an ESPI system. Considered are

the video processing, resolving power of the system, and phase measuring techniques.
3.1 Introduction

As stated in the introduction, for speckle pattern correlation interferometry the
resolution of the recording medium used need be only relatively low compared with that
required for holography, since it is only necessary that the speckle pattern be resolved,
and not the very fine fringes formed by the interference of object beam and reference
beam. The speckle size can be adjusted to suit the resolution of the TV camera ( a CCD is
usually used in ESPI). Thus, video processing may be used to generate correlation fringes
equivalent to those obtained phorographically. The major feature of ESPI is that it
enables real-time conelation fringes to be displayed directly upon a television monitor
without recourse to any form of photographic processing, plate relocation, etc. This
comparative ease of operation allows the technique of speckle pattern correlation
interferometry to be extended to considerably more complex problems of the real world.
Some of the advantages have been mentioned in the introduction. A block diagram of a
typical ESPI system is illustrated in Figure 3.1.

3.2 Video System and Other Electronics in ESPI

The video system comprises the television camera, signal processing and picture

storeage unit, and display monitor. The aim of the system design is to obtain maximum

41

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visibility fringes. Electronic noise and, in particular, high frequency noise should be
minimized. Since the cost of a laser increases approximately in proportion to the output

power, it is important to optimize the sensitivity of the video system.

The most noise-sensitive part of the signal processing is at the first stage of video signal
amplification, which is canied out at the camera head amplifier, so that this section of the
system must be carefully designed. Usually, DC-coupling is used to link the output signal
to a high-impedance and low-noise device such as an FET, which is connected directly to

the detector plate (CCD array).

The CCD camera is used in modern ESPI systems because it has (1) wide range of
linearity; (2) low noise at low light intensity; (3) high signal-to-noise ratio; (4) and peak

spectral response about 0.6 um.

The vertical resolution is determined by the number of scan lines, which is fixed when
a standard video system is used. The frequency response of the system should be such

that the horizontal spatial resolution is as good as the vertical resolution.

A video system converts an image which is formed on the detector plate of a television
camera into an equivalent image on a television monitor screen. With light incident on
the CCD array, a charge pattern will build up corresponding to the intensity distribution of
the incident light. Charge is then tranSferred from collection site to collection site by
changing potentials within what is essentially an insulator. The output will give rise to
voltage signal. A standard television system has 525 vertical lines in mm], and a
complete scan is performed at a rate of 30 frames per second (U .8. standard). For a
standard video camera the active area of the camera is about 13 x 10 mm, so that the image
must be reduced to this size. After amplification and the addition of timing pules, the
camera signalis used to modulate an electron beam which scans the screen of a television

monitor so that the brightness of the screen is made to vary in the same way as the

44

intensity of the original image varies. Ideally, the brightness of the monitor should vary
linearly with the intensity of the original image. The exact relationship between the
monitor and original image intensities is a complicated function of the electronic
processing as well as the brightness and contrast controls of the television monitor. In the
analysis of the video display of speckle correlation fringes, it will be assumed that (a) the
camera output voltage is linearly proportional to the image intensity and (b) that the

monitor brightness is proportional to the camera output voltage.

Intensity correlation fiinges in ESPI are observed by a process of video signal
subtraction or addition. In the subtraction process, the television camera video signal
corresponding to the interferometer image plane speckle pattern of the undisplaced object
is stored electronically. The object is then displaced and the live video signal, as detected
by the television camera, is subtracted from the stored picture. The output is then
high-pass filtered, rectified and displayed on a television monitor where the correlation
fringes may be observed live. In this process, sophisticated software may be used to
process the fi'inge data, calculate the desired information, and display it graphically on the
screen. For the addition method, the light fields corresponding to the two states are added
at the image plane of the camera. The television camera detects the added light intensity,
and the signal is full-wave rectified and high-pass filtered as in the subtraction process.

Again the correlation fringes are observed on the television monitor.
3.3 Speckle Correlation Fringe Formation by Video Signal Subtraction

The detector plate of the camera is located in the image plane of the speckle
interferometer. Under these conditions the output signal from the television camera, as
obtained with the object in its initial state, is recorded in the computer’s RAM memory.
The object is then displaced and the live camera signal is subtracted electronically from
the'stored signal. Those areas of the two images where the speckle pattern remains

correlated will give a resultant signal of zero, while uncorrelated areas will give non-zero

45

signals. We can see this by considering the intensities [before and 10f, 8, given by equations

before and after displacement [23]

[before = lr+lo+2./Irl0cos¢ (3.1)
lafm = lr+lo+2./I,Iocos (¢+A¢) (3.2)

where d) is the phase difference between the reference beam and the object beam before
the displacement. Ad) is the phase change caused by the displacement. If the output
camera signals Vbeflmand Vafm are proportional to the input image intensities, then the

subtracted signal is given by

Vs = (Vbefore - Vafter) “ (1 before - I after)
= 2,/l,lo [cosqa - cos (4) + A¢)]

= 43/11.... (¢+§A¢) sin (gm/>1 (3.3)

This signal has negative and positive values. The television monitor will, however,
display negative-going signals as areas of blackness. To avoid this loss of signal, V3 is
rectified before being displayed on the monitor. The brightness on the monitor is then
proportional to |V3.| , so that the brightness B at a given point in the monitor image is

given by

B = 4Kljl_3,sin (¢+ $1M” sin ($44)) ' (3.4)

where K is a constant.

46

If the brightness B is averaged along a line of constant A d), it varies between maximum

and minimum values 3». and Bm-n given by

ax

B a = 2K 1,10, A4) = (2n+1)1t, n = O,1,2,3 (3.53)

B ~ = O, Atb = 2n1t, n = 1,2, 3 (3.5b)

mtn

To enhance the fringe clarity, the signals should be high-pass filtered to improve fringe
visibility by removing low frequency noise together with variations in mean speckle

intensity.
3.4 Speckle Correlation Fringe Formation by Video Signal Addition

In this case, the two speckle patterns derived from the object in its two states are added
together on the camera detector plate. The two images do not need to be superimposed
simultaneously since a given camera tube has a characteristic persistence time (about 0.1
second for a standard tube), so that the camera output voltage will be proportional to the
added intensities if the time between the two illuminations is less than the appropriate
persistence time. This technique is employed for the observation of time-averaged fringes

when studying vibrations, and it is also used with a dual-pulsed laser.

When the two speckle patterns are added together, areas of maximum correlation have
maximum speckle contrast and, as the correlation decreases, the speckle contrast falls. It
reduces to a minimum, but non-zero, value where the two patterns are uncorrelated. This

is seen as follows:

The voltage Va is proportional to I before + I “f,” and is given by

47

l 1
Va cc (Ibefon, +143”) = 21r“' 210 + 4,/I,Iocos (d) + 2A¢) cos-z-Atp (3.6)

The contrast of the speckle pattern can be defined as the standard deviation of the

intensity. For a line of constant Ad) , this may be shown to be [24]

1
1 i
o 3 = 2[o§+ 03+ 8(1,)(10)cos2§A¢] (3.7)

r

where (1,) and (10) are the intensities of the speckle pattern averaged over many points in

the reference and object speckle pattern fields respectively, and

or = /(lf)— (13)2 = (1,) 00 = [(13)_(10>2 = (10) (3.8)

or and 00 are the standard deviations of I, and 10. It is seen that 0333 varies between

maximum and minimum values given by

1
_ 2 2 i _ _
[om] — 2[of+oo+21,lo] , Ad) — 2nrt, n — 0,1,2 (3.9a)

max

1
o ] , .= 2[of+o323]2, A4) = (2n+1)rt, n : 0,1,2 (3.9b)

[ '0 mm

While the contrast of the added intensities varies, the mean value along a line of constant

A¢ is the same for all Ad), and is given by

\

(1,3,3,3+13fl3,) = 2(r,)+ 203) (3.10)

Thus, when the sum of the two speckle patterns is directly displayed on the television
monitor, the average intensity is constant, and the variation in correlation is shown as a

variation in the contrast of the speckle pattern but not in its intensity. The DC component

48

of the signal is removed by filtering, and this signal is then rectified. The resulting

monitor brightness can then be considered to be proportional to cm, so that

NI“

B = K[o'3+o%+2(I,)(Io)cosz-%A¢] (3.11)

Hence the intensity of the monitor image varies between maximum and minimum values
given by equations (3.9a) and (3.9b). Comparison of equations (3.5a) and (3.5b) shows
that the fringe minima obtained with subtraction correspond to fringe maxima obtained
using addition. It can also be seen that subtraction fringes have intrinsically better visibil-
ity than addition fringes, since the subtraction fringes have zero intensity, while addition
fringes do not. However, when addition is used to observe the fringes, a video storeage is
not required. Vibration fringes can also be produced by the time-average subtraction

technique, which gives more clear fringes [25].
3.5 The Measurement of Real Time Vibration Pattern

For vibration pattern measurement, the ESPI is operated in time—average mode. In
time-averaged mode the images are being taken while the object is vibrating. At a given

time, t, the intensity in the image plane is given by I(t) where

I(t) = I +Io+2 [flocos[0+4—fna(t)] (3.12)

where a (t) represents the position of a given point on the object at time t. The intensity

is averaged over time 1’ to give

49

T
1 41:
I,t = lr+lo+22“’1J0£COS[G+Ta(t)]dt (3.13)

When this is evaluated for a sinusoidal vibration,

a (t) = aosincot (where 21t/0) << 1:)
we get
2 47‘ .
I1 = I,+_10+2,/I,IOJO(TaO) 0058 (3.14)

The value of I.[ averaged along many speckle patterns is constant over the whole image,
but it can be seen that the contrast of the speckle will vary as the value of the 1% function
varies. When 1(2) has a value of zero, the intensity varies only as Io varies; whereas when

13 has a maximum value, the intensity varies with variation in 10 and

ZHCOSO. (3.15)

Figure 3.2 shows the 13 distribution.

Correlation fringes are thus observed which map out the variation in do, the amplitude
of the vibration across the object surface. The fringe minima correspond to the minima of
the Bessel function. Table 1 shows the relation between the fringe order N and the

vibration amplitude a.

In the time-averaged mode, the phase information of the vibration components is lost
due to the averaging of the displacements over a vibration cycle. This limitation is
eliminated if stroboscopic technique is used [26]. Another way to record the phase
information is to use a dual-pulsed laser [27], or to move the PZT mirror in the reference

beam path at the same vibration frequency [28].

50

 

1
J02(41ta/l)

 

0.8

T

0.8-

0.4 b

0.2L-

 

N=5
A

 

 

0

0.6

Fig. 3. 2
The first few cycles of the 102 distribution which defines the
intensity distribution of time-averaged speckle fringes for a

 

 

 

 

 

 

sinusoidally vibrating surface
N (fringe order) a (amplitude, pm)
0 0
1 0.19
2 0.35
3 0.51
4 0.67
5 0.83
Table l

Fringe order N vs vibration amplitude in
time-average ESPI mode.

0.8

1

run

51
3.6 The Measurement of Dynamic Displacements

When taking a speckle picture in ESPI it is necessary that all the components are stable
to considerably better than a wavelength during the exposure time (1/30 second). So,
only static or quasi-static displacements can be measured using continuous lasers. \Vth
the use of a dual-pulsed laser, ESPI can be extended to the measurement of dynamic
displacements. The dual pulsed technique can also be used to measure large amplitude
periodic displacements. If, for example, the period of oscillation is 10'3 second, a pulse
separation of 10 its will enable 0.01 of the overall amplitude to be measured in a single
recording. This procedure extends the range of vibration measurement to amplitudes

approaching 103 is.

3.7 The Optimization of Light Intensity in ESPI

For a given type of TV camera, a certain minimum intensity is required to create a
camera voltage output which can be detected above the background electronic noise. An
increase in the incident intensity gives an increased output camera voltage until the
intensity reaches the camera saturation level, beyond which the output voltage remains

constant for any further increase in incident intensity.

The intensity of the speckle pattern varies randomly across the image, and, to avoid
losing information from the speckle pattern, the overall intensity should be below the
saturation level of the camera for all of the useful picture area. If the mean value and the

standard deviation of the speckle pattern are given by (1,) and 0‘, then, when

(I,)+2<r,<lm (3.16)

the intensity will be less than the saturation level of the camera for 95% of the image.

Here I is the camera’s saturation intensity.

301

52
3.7.1 Two Speckle Beam Case

When two speckled beams are used in a subtraction correlation system, the mean
intensities of the two beams at the image plane should be equal, and the combined peak

intensities should be approximately equal to the camera saturation intensity.
3.7.2 Smooth Reference Beam Case

Based on our experience, the best results are obtained when the reference beam

intensity is set as,

(3.17)

30!

1 1
2.1“, s (1,) s 51

This depends on the signal-to-noise ratio and and the threshold set in the software. The

sum of the intensities should be such that the peak intensities are near the saturation level

of the camera.
3.8 Spatial Resolution of the Video System and Its Effect on ESPI

The spatial resolution and dynamic range of video systems are considerably less than
those of photographic and holographic emulsions. These factors affect the design of

speckle pattern interferometers which use video systems to display the correlation fringes.

The ability of the video system to resolve fine detail in the image is limited. Thus, if a
coarse black and white grid is imaged on the face plate of the TV camera, an equivalent
grid will be observed on the monitor. As the spacing of the grid is reduced, the contrast of
the grid observed on the monitor is reduced; and when the grid spacing is sufficiently

small, no grid structure is observed on the monitor.

The limit to the spatial resolution in the vertical direction is governed by the number of
scan lines. A standard system having 525 lines and an active face plate area of about 13

x10 mm should have a minimum vertical resolution of ~20 run on the face plate.

53

The resolution in the horizontal direction is governed by the temporal frequency
response of the video system, which is determined by the electronic design of the system.
Typically, this hequency response is fairly uniform up to 4 MHz and falls to a very low
value at 10 MHz. The temporal frequency response is clearly related to the spatial
frequency in the image. A sinusoidal intensity distribution in the image plane of spatial

frequency 106/ WNM mrrl‘l will give a sinusoidal output voltage of 1 MHz, where
W = width of the active face plate area in m
N = number of scan lines
M = number of frames per second

For a standard TV system, 1 MHz corresponds to a spatial frequency of ~5 mm'1
(spacing ~200 ttm).

A grid having a 20 run spacing in the horizontal direction will give an output voltage
of frequency 9.45 MHz. Since the frequency response is very low at 10 MHz, 20 pm can

also be taken as the upper limit of the spatial resolution in the horizontal direction.

It was assumed in deriving equations (3.4) and (3.11), which describe the variation in
monitor brightness to give subtraction and addition conelation hinges, that the random
variations in I r, I 0 are fully resolved by the television camera, so that the camera signal
hom a given point in the image is proportional to the intensity at that point. When the
points are not fully resolved, the output voltage is a function of the intensity of the image
averaged over the resolution area of the camera, and the effect of this averaging is to
reduce the standard deviation or contrast of the output voltage [29]. Consider, for
example, the case of two speckle patterns whose intensities have the same mean value and
standard deviations, one of which is fully resolved by the TV camera and the other of

which is only partially resolved. The output camera signals will have the same mean

54

values across the image, but the standard deviation of the signal will be less for the
partially resolved pattern. If the speckles are sufficiently small, the output signal will be
uniform. It will be shown below that the effect of this reduction in the standard deviation

of the output signal is to reduce the visibility of the correlation hinges.

From equations (3.4) and (3.5) the correlation fringes are seen to arise from the
variation with A6 of the standard deviation of the subtracted or added signals; if the
contrast of the individual signals is reduced, the standard deviation of the subtracted or
added signals is also reduced, and the visibility of the correlation hinges is decreased. If

we write the output camera signal as

V” = Vo+ (v (3.18)

C0") ',0

where V0 arises from the (1, +10) term and (V 0 arises from the 2,/1112cos¢ and

a...) ,,
2 m cos (4) + Art) terms, then, since V0 remains unchanged when the object is
displaced, it is a noise term. Consequently, the correlation hinge visibility is maximized
when the standard deviation of (V ) 0 is maximized. We can write the value of

CO" r,

(V

cm) r. a at a given point in the image as

(Vcorr),’o = k<Jl—,’—.,COS(¢+A¢)>AA (3.19)

where k is a constant, and A6 is the phase difference between the reference beam and the

object beam AA is the resolution area of the camera.

If the variation of ([1 over the resolution area is very much less than 21:, then the value
of (an) r o for constant Ao varies between i [k(,/l ,1 ocosA¢)] max. When the value

of (it varies by 21: or more over the resolution area, then the value of (Vc over the

arr) r.0

whole image is approximately zero, and in this case correlation hinges are not observed.

55

Thus, the spatial frequency distribution of cos¢ must be such that the components of that

distribution are at least partially resolved by the video system.
3.8.1 Spatial Resolution (Two-speckled-beam case)

When the two wavefronts I, and 10 are speckled, the spatial frequency distribution of
the combination of the two beams will be similar to that of I, or I 0. The maximum
spatial frequency fm of the distribution is determined by the diameter of the viewing

lens aperture 0, and is given by the equation

1.. ~1.22(1+M)Z;3. (3.20)

fmax
where v is the lens-to—image distance. M is the magnification of the lens. If the
object-to-viewing-lens distance is considerably greater than the lens-to-image distance,

the lens equation gives that v 1» f. The minimum speckle size 3min is then given by

s . =f—1—=1.22(1+M)1.(NA) (3.21)

"I”!
max

where NA = 13’ is the numerical aperture of the viewing lens.

If the smallest spot resolved by the video system is 20 um, corresponding to a spatial

frequency of 50 mm'l, then, to resolve fully the spatial frequencies arising from the

speckle distribution, we must-have
(NA) > 25

Thus, quite a small aperture must be used if the scale of the speckle pattern is to be

large enough to be fully resolved by the video camera.

56

If the numerical aperture of the lens is reduced below this value, the spatial frequency
of the speckle pattern will increase and it will no longer be fully resolved. However, the
amount of light transmitted through the lens will increase, so that the value of ch does
not necessarily decrease. An exact analysis of the relationship between Vcorr and the
viewing lens aperture diameter is quite difficult. However, the optimum value can be
readily found in practice simply by adjusting the aperture size until maximum speckle

contrast is obtained.
3.8.2 Spatial Resolution (smooth reference beam case)

In this system, la is a random speckle intensity, while I, is nominally uniform across

the image plane. The phase difierenee 4) between 10 and I r is given by

21:10p 21:10.p
4’ = ¢s+T‘[¢r+—x—]
2
= ¢S - ¢r + g (lop — lo‘p) (3.22)

where O is the center of the aperture of the viewing lens, 0’ is the point from which the
reference beam appears to diverge, and P is a point in the image plane (see Figure 3.3).
4% is the phase of reference beam at 0’ and is constant across that beam, while 0, is the

random phase at 0. lap and lo.p are the distances from O and 0’ to P.

57

Illuminating beam

 

 

 

Image
Object Plane

Aperture

Fig. 3.3

The general geometry of a smooth reference beam interferometer

It was pointed out that if 41 varies by 21: or more within the resolution diameter of the
resolution area of the camera, the correlation signal Vcorr will be very small. The
variation in 4), is governed by the viewing lens aperture diameter, as in the case of the
two-speckled beams system, and a suitable aperture ensures that it does not vary too
rapidly. Clearly, the variation in the last term (2 = 27:5 (lap - 10.?) with P must be such
that Q varies by considerably less than 21: over the diameter of the resolution area. If 0
and 0’ are coincident, Q is zero so that, if possible, this condition should be satisfied (0

and 0’ are then referred to as being conjugate).

To determine the departure from conjugacy that can be tolerated, we assume that the
coordinates of O and 0’ are (0, 0, lo) and (Ax, 0, 1,); the resolution diameter is 1:” When
Ax, A1 = 10- IT << 10, we have;

 

58

-—Ax 2
lap - 10.}, ~ (10+ 5%) — [1, + 9731—] (4.23)

Neglecting second order terms of Ax and AI, we have;

xAx szl

 

 

— . z .24
lap 10 p Al + 10 213 (3 )
It is seen that a lateral displacement, Ax, of 0’ with respect to 0 produces a linear

variation in 4) across the image plane. 4) varies by 21: across an interval 8x given by;

5 _ 10).
x _ Z? (3.25)

If this is to be resolved by the video system, 8x should be considerably greater than x, ,

i.e.;
[OX 3 26
If « E ( . )
or
101.
Ax « — (3.27)
xr

Thus, the lateral departure from conjugacy must be less than that specifiedby the

equation (3.27). For a lens-to—image distance of 100 mm and x, = 20 um, we have
Ax << 3.2 mm.

A longitudinal departure hem conjugacy of Al gives rise to a variation in (1) which
varies as 1:2. The maximum gradient of 4) occurs at the edge of the image. Here it can be

seen that the distance fix in which 4) varies by 21: is given (taking absolute value) by;

59

6 X1: 3 28
X - E—Al ( . )
If this is to be resolved, we must have;
“‘2’ (3 29
.711 ” "r ° )
or
2.13
Al « — (3.30)
xx,

Let x take its maximum value, which is equal to the half width of the active area of the
camera tube, typically about 5 mm. For a lens-to-image distance of 100 mm and x, = 20

um, we have;
Al « 63 mm

To optimize the visibility of the correlation fringes, Ax and Al should be made as small
as possible. It is seen that displacements in the lateral direction give rise to much more
rapid variation of 6 than equivalent variations in the longitudinal direction, so that the
lateral shift in particular should be minimized. It is not difficult in practice to do this. In
addition, the size of the viewing lens aperture should be adjusted to give optimum speckle

contrast.

If x, =20 um, because the speckle size is doubled resulting from the interference with
the reference beam, the aperture needed to make the speckle size equal to the detector

element size can be reduced to,

(NA) =13

3.8.3 General Conclusion

Because of resolution limitations, the use of a television camera to observe speckle
correlation fringes requires the use of a small aperture in the viewing lens and results in

relatively large speckles. This affects the performance of the interferometer in two ways.

First, the spacing of the correlation hinges must be greater than approximately 1/ 120 of
a screen width. This follows because when the fringe spacing becomes comparable to the
minimum speckle size, the hinge visibility decreases and drops to zero when they are
equal. A minimum ratio of fringe spacing to speckle size of about five is necessary to
give reasonably visible hinges. Since the minimum speckle size is about 20 um, then the
minimum fringe spacing is of the order of 100 pm. This corresponds to a fringe spacing
of 1/120 of a target plate of 12 mm width. Hence a maximum of 120 fringes of uniform
spacing should, in theory, be observable. With a hinge pattern of variable spacing, the
maximum number under optimum viewing conditions is found in practice to be about 50.
If the number of hinges in one full screen is greater than 50, it will likely give rise to

fringe counting error.

Second, the use of a small aperture means that the system is not very efficient in light

usage compared with the equivalent photographic speckle correlation system.

However the speed and convenience of video processing compared with photographic
processing generally outweighs these disadvantages. One also can use a laser with greater
power. Most systems use a 10-15 mw laser. A high power laser such as an Argon laser

can also be used for testing large objects.
3.9 Error Sources

Several possible sources of error and their contributions to measurement inaccuracy are

listed below:

61
1. Frequency instability of the light source;

This instability may cause 2» to change slightly, but this effect is very small and

negligeable.
2. Reference phase error;

This is the deviation for the ith shift or step between the actual and desired values of
ai, by carefully calibrating the PZT used, this error can be eliminated.

3. Detector nonlinearity;

In technical manuals for detectors, the nonlinearity of the detector is often described
as: I,- = If (0 < r < 1). For CCD detectors the nonlinearity is negligible (r a 1), but
for vidicon tubes the nonlinearity can be considerable (r a... 0.7 ). A CCD camera is com-

monly used in ESPI system.
4. Instability of the light source;

The light source intensity during recording of the frames may vary from one frame to

another. When the laser is already warmed up this error is negligeable.
5. Environment disturbances, vibration and air turbulence;

By looking at live correlation hinges, we can see the disturbances; if they do not affect

the hinge pattern, then it does nor matter.
6. Noise of the detector output and quantization noise of the measured intensity;

For a CCD camera this is very small and negligeable.

62
3.10 Displacement Measurement Using Phase Information:
3.10.1 Principal Phase Determination

As shown in Figure 3.4. The light from a He-Ne laser is split into object and reference
beams by a beam splitter. The object beam is further expanded by an objective lens and
filtered by a pin-hole to illuminate the object. Diffusely scattered light from the object is
collected by an imaging lens and imaged on the detector plate of a TV camera. The
reference beam is also expanded and filtered through a spatial filter to interfere with the

speckle image of the object on the detector plate of a TV camera.

If the detector elements are several times larger than the smallest speckles in the
pattern, the modulation that is generated by changing the phase of the reference beam is
reduced. This reduction is offset by the increased light level on the detectors, so there is a
trade-off between light level and modulation [30]. The best result can be determined by

experiment.

In order to calculate the phase information, a mirror mounted on a PZT device is placed
in the reference beam path to artificially change the optical path difference between
reference and object beam The light intensity of the interference speckle image pattern is
sampled to yield a digital picture made up of 512 x 512 sample points. Each sample point
is quantized to 256 discrete gray levels. The digital picture is stored in a digital frame
memory at a speed of 1/30 sec. Further processing depends on the application and

calculation algorithm.
3.10.2 Phase Measm'ement

In order to detect the deformation, phase-measurement interferometry (PMI) is used.
Although the basic techniques for phase-measurement interferometry have been known

for many years [31-39], it is only recently that PMI has become of practical use. Two

63

Test Specimen

Beam splitter

    

PZT Mirror

 

 

 

 

 

 

Digitizer &
Frame grabber

PZT Controller

 

 

 

Fig. 3.4

Schematic for measuring phase using a PZT mirror as the phase
shifter and sending data to a computer for the phase calculation.

64

major developments make this possible, namely, solid-state detector arrays and fast
microprocessors. When a detector array is used to detect hinges, and a known phase
change (can be unknown for Carre technique) is induced between the object and reference
beams, the phase of a wavefront may be directly calculated from recorded intensity data.
Generally, a number of data hames are recorded as the reference beam phase is changed in
a known manner. The data are fed into a computer where the phase at each detector point
is calculated. Information about the test surface is geometrically related to the calculated

wavefront phase.

The direct measurement of phase information has many advantages over simply
recording interferograms and then digitizing them. First, the precision of phase
measurement techniques is ten to a hundred times greater than that of digitizing fringes.
Second, it is simple. A detector array is placed at the image plane, and a phase-shifting
device is placed in the reference beam. Using solid-state detector arrays, data can be
taken very rapidly, thereby reducing errors due to air turbulence or vibration. Third,
automatic hinge enhancement, counting and ordering can be carried out using
microcomputers. Full field displacement information can be calculated using pipe-line

processing in a very fast fashion.
3.10.3 Means of Phase Shifting

There are many ways to determine the phase of a wavehont. For all techniques a
temporal phase modulation (or time-dependant relative phase shift between the object and
reference beams in an interferometer) is introduced to perform the measurement. By
measuring the speckle pattern intensity as the phase is shifted, the phase of the wavehont

can be determined with the aid of a computer-controlled electronic processing system.

Phase modulation in an interferometer can be induced by moving a mirror, tilting a

glass plate, moving a grating, rotating a half-wave plate or analyzer, or by using an

65

acousto-optic or electro-optic modulator [34, 40, 41]. Phase shifters such as moving
mirrors, gratings, tilted glass plates, or polarization components can produce continuous

as well as discrete phase shifts between the object and reference beams.

The most common and straightforward phase-shifting technique is the placement of a
mirror pushed by a piezo-electric transducer (PZT) in the reference beam [38]. Many
brands of PZTs are available to move a mirror linearly over a range of several microns. A
high-voltage amplifier is used to produce a linear ramping signal from 0 to several
hundred volts. If there are nonlinearities in the PZT motion, they can be accounted for by
using a programmable waveform generator. If a phase-stepping technique is preferred to
a continuous modulation, any calibrated PZT can be used because only discrete voltage

steps are needed.
3.10.4 Phase-measurement Algorithms

Phase-measurement techniques using analytical means to determine phase all have
some common denominators. These techniques shift the phase of one beam in the
interferometer with respect to the other beam and measure the intensity of an interference
pattern at many different relative phase shifts. To make these techniques work, the
interference pattern must be sampled correctly to obtain sufficient information to
reconstruct the wavehont. The detected intensity modulation as the phase is shifted can
be calculated for each detected point to determine if the data point is good (sufficient
modulation)

Fringe modulation is a fundamental problem in all phase-measurement techniques [42].
When a hinge pattern is recorded by a detector array, there is an output of discrete
voltages representing the average intensity incident upon the detector element over the
integration time. As the relative phase between the object and reference beams is shifted,
the intensifies read by the detector element should change. Because any array samples the

image over a finite number of discrete points, the maximum image spatial frequency that

66

can be unambiguously transformed is the Nyquist frequency, at which each sensing
element corresponds to either a maximum or a minimum in the image. Therefore, if we
have at least one detector element for each speckle, the Nyquist frequency condition will
be satisfied. However, if there is one fringe over the area of the detector element, there
will be no modulation. Figure 3.5 illustrates three different cases; (2) indicates a highly
sampled condition where speckle size is much larger than the detector element; this gives
highly detailed modulation output. (3) represents the sufficiently sampled case, where the
speckle and the detector element have almost the same size and the output has high
modulation. (4) shows the undersampled case where the speckles are much smaller then
the detector element and the output has low modulation. Thus the detector size influences
the recorded hinge modulation, whereas the detector spacing determines if the wave front

can be reconstructed without phase ambiguities.

Many different algorithms have been published for the determination of wavefront
phase [ 30 -35, 38-39, 43- 46]. Some techniques step the phase a known amount between
intensity measurements, whereas others integrate the intensity while the phase is being
shifted. Both types are phase—shifting techniques. The first is the so-called phase-
stepping technique, and the second is usually referred to as an integrating-bucket
technique. A minimum of three measurements is necessary to determine the phase, since

there are three unknowns in the interference equation;

I = l,+lo+2,/I,locos¢ (3.31)

These unknowns are the reference beam intensity 1,, the object beam intensity [0 and the
phase difference 4) between the reference beam and object beam. The phase shift
between adjacent intensity measurements can be anything between 0 and 1t as long as it is

constant (for phase-stepping method) or linear (for integration method).

67

(1) CCD Array

(2) Highly Sampled

 

High Detailed Modulation ‘
Sufficient] Sam led

(4) Undersampled

   

 

 

76’ '3
5» E)
.a {A
High Modulation t Low Modulation
. = Speckle
I = Detect element

Fig 3.5

(1) CCD array with finite -sized detectors. (2) Detector element much smaller than

speckle size. (3) The size of detector element and speckle are almost equal. (4) Speckle
size is much smaller than detector element.

68

In general, N measurements of the intensity are recorded as the phase is shifted. For
the general technique the phase shift is assumed to change during the detectors’
integration time, and this change is the same from data frame to data frame. The amount
of phase change from hame to frame may vary, but it must be known by calibrating the
phase shifter or measuring the actual phase change. Unless discrete phase steps are used,
the detector array will integrate the hinge intensity data over a change in relative phase of

A. One set of recorded intensities may be written as [45];

1,. (x. y) = g ] [2:310 (x. y) {1 +1,cost¢(x.y) +a<t> l}da(t) (3.32)

where 10 (x, y) is the average intensity at each detector point (DC component), 70 is the
modulation of the hinge pattern, 01‘. is the average value of the relative phase shift for the
ith exposure, and 4’ (x, y) is the phase of the wavefront being measured at the point (x,y).
The integration over the relative phase shift A makes this expression applicable for any
phase—shifting technique. After integrating this expression the recorded intensity is found
to be;

' 1 A
1,- (X. y) = 10(x.y) {1+yo(81?([1(/2/)2:] ] )cos{¢(x.y) +a,-l} (3.33)

 

It is important to note that the only difference between integrating the phase and stepping
the phase is a reduction in the modulation of the interference hinges after detection. If the

phase shift were stepped (A a. 0) and not integrated, we have;

(sinéA)/(-;-A) = 1 (3.34)

69

Therefore, phase stepping is a simplification of the integrating method. At the other
extreme, if A = 21:, there would be no modulation of the intensity. Since this technique
relies on a modulation of the intensities as the phase is shifted, the phase shift per exposure

needs to be between 0 and 1:.

For a total of N recorded intensity measurements, the phase can be calculated using a
least-squares technique. This type of approach can be found in references [44, 45, 47].

First, equation (3.33) is rewritten in the form
I‘- (x, y) = 00 (x, y) + a1 (x, y) cosori + a2 (x, y) sina‘. (3.35)
where

do (10’) = 10 (X, y) (336)

 

 

sin [ (1/2)A1
r = I ’ ,
a1(x Y) 0(1 YWO [(1/2)A] COW (x y) (337)
_ sin [ (1/2)A1 .
a2 (LY) - ’0 (192970 [(1/2)A] 81nd) (x,y) (3.33)

The unknowns of this set of equations are 10(x, y) , 70 and 9 (x, y) . The least-squares

solution to these equations is

as (Jay)
01 (x, y) = A-l (0'98 (1, yr mi) 9 (3.39)

02 (x: y)

7O

 

 

where
N Ecosor‘. Zsinai
A(ai) = Ecosori 2(cosai)2 Ecosaisina‘. ,
Esinai Zeosotisinai 2‘.(sinoci)2
and ’

 
  

21" (x, y)
B (011.) = 21,- (x,y) cosot‘.
21,- (x, y) Sinai

The matrix A needs to be calculatedand inverted just once because it is dependent only
on the phase shift. The phase at each point in the speckle pattern is determined by
evaluating the value of B at each point and then solving for the coefficients al and a2.

Finally, we obtain

8in[(1/2)A] .
a2(x.y) _ ’070 [(1/2)A] “”0“”

a,(x.y) ’ sin[(1/2)A]
1070 [(1/2)A] COS¢(X,}’)

 

 

 

tan¢ (x. y) = (3.40)

 

This phase calculation assumes that the phase shifts between measurements are known

and that the integration period A is constant for every measurement.

Besides a reduction in intensity modulation due to the integration over a change in
phase shift, the finite size of the detector element will also contribute to a reduction in
intensity modulation. To make reliable phase measurements, the incident intensity must
modulate sufficiently at each detector point to yield an accurate phase. The recorded

intensity modulation can be calculated from the intensity data using the equation,

71

 

sin[(1/2)A] _ ,/a,(x.y)2+a2(x.y)2

7‘“) =70 [(1/2)A] ' astray) (3'4”

 

 

This expression can be used to determine if a data point will yield an accurate phase

measurement or if it should be ignored.
3.10.4.1 Three-step technique

Since there are three unknowns in the equation (3.31), a minimum of three sets
(exposures) of recorded hinge data are needed to reconstruct a wavefront; the phase can
then be calculated from a known phase shift of ai per exposure. There are two common
choices for the phase shift value, namely, A = 1E: and A = 1;.

4 4
measurements may be expressed as [24].

(a) When 01.. = 11:, 21:,and 21:,thatisN=3,A= 5"" The three intensity

11(x.y) = 10(x.y) (1+1cos:¢(x.y) +7115) (3.42)
11(x.y) = 100:3) (1 +1008 F¢(x.y) +41) (3.43)
11 (m) = 10(x.y) (1+1cos 71> (x. y) +215) (3.44)

 

 

When discrete steps are used, 7 = 70, and when the phase is integrated over a %1: phase

shift per frame, 7 = 0.9yo_. The phase at each point is then simply;

 

¢(x.y) = arctan( (3.45)

13 (x, Y) ‘12 (It?)
11(x9y) -12(xry) J

72

and the intensity modulation is;

 

[111 (x. y) —12<x.y)12+ 1120:.» -13 (x. y)]2

 

 

 

 

Y(x.y) = 210 (3.46)
. o 2 . 2 2 2
(b) Ifaphase shrft of 120 (§1:) rs used, ori = -§1:, 0, §“’ and A = 31:. We have
75 (I3 (x. y) — 120w) )
. = tan 3.47
4’ (x Y) a” [21, (x. 3) -I2 (m) -I, (x. y) ) ( ’
for the integration method, 7 = 0.83 70, and the detected intensity modulation is
3 [1 (Ly) -1 (x,y)12+ [21 (x.y) -1 (x.y) -1 (1:3)]2
10:, y) = ”l 3 2 2,10 2 3 (3.48)

3.10.4.2 Four-step Technique

This is a common algorithm for phase calculations [17]. In this case or; = 0, gr,

1:,and 34:. 'y = 70 for the four-step technique and y = 0.9 70 for the integration
technique (A = £1: ). Note that integrating the phase produces a very small effect for a

$4: phase shift per exposure. Thus, linearly ramping the phase shifter while taking

measurements makes more sense than stepping and waiting for the reference beam to

73

settle down. Using calculations similar to that for three-step technique, the phase at each

point for the four-step method is

 

 

 

1., (x. y) -12 (x. y)
W”) " ”“3“(11 (x, y) -I3 (x. n) (3'49)
and the recorded modulation can be calculated from,
[I(x.y)-1(x.y)12+[l (Jaw-101.3012
7(X.y) = J 4 2 1 3 (3.50)

210
One nice thing about this technique is that by using pipe-line image processing (using
look-up tables) the noise due to the speckles can be removed, which gives noticeable

fringe visibility improvement [49].
3.10.4.3 Carre Technique

In the previous equations the phase shift is known either by calibrating the phase shifter
or by measuring the amount of phase shift each time it is moved. Carre [31] presented a
technique of phase measurement that is independent of the amount of phase shift. It

assumes that the phase is shifted by at between consecutive intensity measurements to

 

 

yield four equations
[1(XJ) = I0 (x. y) {1 +1cos ”v (x. y) —§a‘} (3.51)
120:.» = 10o.» {1+1cos 31> (x. y) - get} (3.52)
I3 (x. y) = 10 (x. y) {1+1cos "v (x. y) + 50:} (3.53)
I,(x.y) = I0 (x. y) {1+1cos at...) + 33:05} (3.54)

 

 

74

where the phase shift is assumed to be linear.with time. From these equations the phase at

each point can be calculated by,

 

fl3(12-l3)-(11-14)] [(12-13)+(11-14)]

 

 

 

x, = arc tan 3.55
M y) (12+13)—(11+14) ( )
For this technique the intensity modulation is,
1 [(12—13)+(11—14)]2+ [(12+13)-(11+14)]
y = ._ (3.56)
210 2

where this equation assumes that at is near én. An obvious advantage of the Carre
technique is that the phase shifter does not need to be calibrated. It also has the advantage
> of working when a linear phase shift is introduced in a converging or diverging beam

where the amount of phase shift varies across the beam.
3.10.5 Comparison of Phase Measurement Techniques

In general, the integration methods give the same results as the phase-stepping methods
except in the case of nonlinear phase-shift errors, where the integration method is superior.
The Cane algorithm is the best to use where phase-shifting errors are present, and the
four-step technique is the best for eliminating effects due to second and ihird order

detection nonlinearities.

75
3.10.6 Phase Unwrapping

Because of the nature of arctangent calculations, the equations presented for phase
calculation are sufficient for only a modulo 1: calculation. To determine the phase modulo
21:, the signs of quantities proportional to sin (b and cos (I) must be examined. For all
techniques but Carre’s [42], the numerator and denominator give the desired quantities.
Table 2 shows how the phase is determined by examining the signs of these quantities
after the phase is calculated modulo $1: using absolute values in the numerator and
denominator to yield a modulo 21: calculation. Once the phase has been determined to be
modulo 21:. The phase ambiguities due to the modulo 21: calculation can be removed by
comparing the phase difference between adjacent pixels. For reliable removal of
discontinuities the phase must not change by more than 1: between adjacent pixels. As

long as the data are sampled as described in the sampling requirements, the wavefront can

be reconstructed.

For the Carre technique, simply looking at numerators and denominators is not
sufficient to determine phase modulo 21: [42]. It is somewhat complicated and will not be

discussed here.

Any phase unwrapping needs some reference point, that is a point to start. If the
reference point is a fixed point, say a point in the fixture which holds the object being
tested, the calculated phase change will be an absolute value. Otherwise, the calculated

phase change would be relative value.

To calculate the displacement, the phases before and after displacement are suthaCted

from each other. These phase values have been unwrapped before the subtraction.

M (x,y) = 45 (x. y) - it, (x. y) (357)

76

 

TABLE 2

Determination of the phase modulo 21:.

 

 

Numerator

[sin¢l

positive

positive

negative

negative

positive

negative

 

Denominator Adjusted phase Range of phase values
1 cos it 1
. . 1
posrtrve (p 0 - 2 1:
. 1
negatrve 1: - q) 2 1: — 1:
. 3
negatrve 1: + o 1: - 2 1:
. . 3
posrtrve 21: — ¢ 51: - 21:
anything 1: 1:
l
0 '2'- 1t 2 7t
3 3
O '2- 1: 5 7C

 

 

 

 

77

Of course, if we are interested only in the surface shape, we do not need to measure the
deformed stage of the object and do the phase subtraction. What we need to do is to

measure the phase of the stable object and do the phase unwrapping.
3.10.7 From phase change to displacement

Once the phase change is known, the corresponding displacement can be determined

horn the phase information. The surface displacement H at the location (x, y) is

44> (x, y) l

21: (cosei + cosOv) (3.58)

H(x,y) =

 

where 7: is the wavelength of illumination, and 0‘. and By are the angles of illumination
and viewing with respect to the surface normal. We can see here that the illumination
and viewing directions will afiect the measured value. The detailed relationships between

actual and measured displacement have been discussed in chapter 2.

Chapter 4

Nondestructive Test of Composite Using ESPI

In this chapter we will first discuss some commonly used stressing techniques for
nondestructive testing (NDT) using optical interferometry, then some NDT experimental

results on composite material using ESPI will be presented.

The most successful methods of nondestructive testing at present would be pitch-catch,
pulse-echo ultrasonics, and dye-penchant enhanced x-ray radiography. Use of any of
these non-destructive evaluation techniques requires that some forethought be given to the
type of failure mode likely to be encountered. With both ultrasonic methods, liquids
are generally used to carry acoustic waves into the panel. _ Similarly, the radiopaque pen-
etrant used in radiography is also a liquid. The penetration of these liquids into the frac-
ture surface can constitute a form of chemical contamination. A new NDT method
urgently needed. The ESPI technique has a great potential to become a new generation
of NDT tool.

4.1 Stressing Techniques

The object under test can be mildly stressed in several ways, which include mechanical
stressing, thermal excitation, pressmization, and acoustic or mechanical vibration. The
[method employed would depend upon the object itself, the type of defect to be detected,

and the accessibility of the object
4.1.1 Mechanical Stressing

Mechanical stressing refers to loading the test objects in simple tension, compression,

torsion, bending, or by applying point loads. ‘ Mechanical shakers also have been used for

78

79

object vibration analysis. The approach chosen for a particuler test will depend upon
object geometry and the particular type of defect being sought. Many of the techniques
mentioned above have been utilized in conventional holographic interferometry, and they
can also be used in ESPI. Tension and bending loading have been used to locate fabric
cuts, delaminations, and overlaps in flat sheets of fiberglass reinforced plastics.
Grunewald et al. [50] have demonstrated that the sensitivity of flaw detection in this type
of application depends on the relative orientation of the flaw and the applied stress, and
also the depth of the flaw below the fibers. One method which has fairly wide acceptance

is the use of mechanical shakers for vibration analysis.

For NDT of composites, the most simple mechanical loading setup maybe is to use
gravity force. In this setup, the specimen is placed with minimum supporting force or just
allowed to stand freely by itself. This method will be discussed later in this chapter.

When designing a mechanical loading device, care should be taken to ensure the
mechanical stability of the fixture. Before and after stressing the specimen, the fixture
should not deform in comparison with the wavelength. Otherwise, the fixture will

introduce hinges to the speckle pattern of interest.
4.1.2 Thermal Stressing

Thermal stressing has been used for various applications of holographic nondestructive
testing. This technique is used to observe mechanical deformation which occurs in
response to changes in temperature. The test object can be heated by a heating device
such as a hot air gun, quartz heater, inhared lamp or even a resister. It also can be cooled
by evaporation after a volatile substance like alcohol has been sprayed on it. Air spaces
created by debonds conduct less heat than do regions where a good bond exists, so the
temperature field itself is distorted. Similar thermal distortion can be caused by crushed
honeycomb cores, voids, delaminations, or by other nonhomogeneities in composite

materials.

80

Some other applications with thermal stressing are the inspection of electronic

components and circuit boards [51-53].

In our experimental study, we found that using steamed air (vapor) to introduce
temperature into material, especially composite material, is very effective. The steamed

air can be directed to a localized area, or spread to a large area easily.

Creating a small temperature difference (AT about 10 °C) between the specimen and
the ambient, then allowing the specimen to expand freely or under some constraint was

also found to be very effective and easy to do. A small reh'igerator was used in our study.
4.1.3 Pressure Stressing ,

Burchett [54] has studied the applicability of holographic interferometry to

nondestructive testing of carbon composite cylinders by using pressurization.

The pressurization method is ideal for pressure vessels and other structures that can be
pressurized. With the double-exposure technique, the structure under test is pressurized
between the exposures. The sequence of the exposures is immaterial. The structure may
also be initially pressurized and then additionally pressurized. Pressurization usually
does not introduce intolerable rigid-body motion. Internal pressurization may also be
employed to inspect honeycomb structures. Honeycombs are generally sealed and
therefore can be pressurized easily. By drilling a small hole through the skin, the
structure can be internally pressurized through the hole. The hole is then mended after
testing. The technique may be developed into a method for inspecting honeycombs in an
aircraft in the field. A permanent access of pressurization may be built in the structures for

regular inspection in service.

Some commercial I-II systems for nondestructive testing of automotive and aircraft tires
utilize pressure and vacuum stressing. The objective of this testing is to locate a variety of

flaws such as separations, broken belts, debonds, and voids that can occur in tires. A

81

differential vacuum between holographic exposures induces a slight change in the overall
tire shape and also causes a bulging at debond regions, which contain entrapped air.
This appears to be the most satisfactory method for holographic inspection of tires [55].

ESPI can also be used in these areas with similar procedures.
4.1.4 Acoustic Stressing

Ultrasonic waves can be used to introduce a mechanical and internal stressing
condition. This technique can be used for NDT on a composite material. Now that some

kind of medium is needed for coupling ultrasound into the specimen.
4.1.5 Vibrational Excitation

Vibrational excitation is useful for detecting debonds in composite materials and for
disclosing inhomogeneites in materials or structures. The technique can be used in two
ways; First, the entire structure being analyzed can be vibrated in a resonant mode. This
creates bending stresses or torsional stresses which may cause anomalous deformation
near flaws such as voids, delamination or matrix crushing. This method has been used to
test turbine blades [56] and to detect flaws in fiberglass-reinforced plastics [45]. Second,
debonds near the surface, for example, between the skin and the core of a honeycomb

. panel, create a locally flexible structure which can be caused to resonate.
4.1.6 Microwave Excitation

Microwave stressing is used to detect the presence of moisture in materials. Between
the exposures, the object is excited by microwaves having the frequency which excites
water molecules. The microwave excitation causes the moisture in the materials to heat
up and this induces highly localized deformation detectable by ESPI. This method of

stressing is only applicable to nonmetallic materials.

82

4.2 NDT Results of Composite Using ESPI

In this study, we mainly used three stressing techniques--thermal stressing, gravity
force and vibration excitation. Composites studied were glass/epoxy plate and carbon fi-

ber (A s—4/828 mPDA) plates.

The objective was to gain more understanding about how the defect (damage) is affect-
ing the mechanical, thermal and dynamic properties. The ESPI system used is illustrated
in Figure 4.1.

4.2.1 Using Thermal Stressing

Refer to Figure 4.2 for the specimens used in this analysis. Thermal stressing
technique is especially suitable for the NDT of composites. This is based on the

following factors:
4.2.1.1 Fundamentals

(l) Fibers have significantly smaller coefficients of thermal expansion (CTE), the CTE
of glass fiber is 5.0 x 10*5 / K, while a typical epoxy value is 54 x 10*5 / K. Carbon and
graphite fibers are anisotropic in thermal expansion. The CTE are usually extremely
small, either positive or negative, of the order of 0.9 x 10'6 / K. It follows that a
unidirectional fiber composite has very small CTE in the fiber direction because the fibers
will restrain matrix expansion. On the other hand, transverse CTE will be much larger
because the fibers move with the expanding matrix and thus provide less restraint to

matrix expansion.

83

    

  

 

 

 

BAG :3an

332% 88m

   

552

8:52 .33me

sci... Emm 2: 3 .ma

8.83 @6888 owns:

 

 

    

0% 823m 359800
wawNow n5

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use scam

 

 

 

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SSH—cusses oEmtm>

84

#8 “53/03/1531

 

 

 

 

[453/03/453]

 

 

 

Fig 42

Impact damaged composite (glass/cpoxy)specimens used in NDT using ESPI
gravity and thermal stressing techniques

85

These phenomena are of considerable practical importance, particularly for laminates
made of unidirectionally reinforced layers. When such a laminate is heated, the
expansion of any layer is prevented by the adjacent laminae because the fiber directions in
all layers are difierent. This causes internal stresses that could be considerable, even

when the laminate is allowed to expand freely.

(2) All polymetic matrix viscoelastic properties, such as creep and relaxation, are
significantly temperature dependent. This will also introduce deformations when there is

a temperature change.

No mater how complicated the stress field is, looking at the large scale, the stress -
introduced displacement field should be uniform if the composite plate is uniform. So, for
NDT we are looking for any irregularities.

4.2.1.2 Heating Devices
Three devices were used for thermal study.

(1) A resistor (25 ohms and 12 W) with adjustable current was used. The temperature
was controlled at about 60 °C (see Figure 4.3 for the setup). During the heating process,

the resistor was at a distance of 2 to 3 mm from the specimen.

(2) Steamed air (vapor) was generated from a cofi’ee pot and conducted through a
flexible plastic pipe towards the specimen (see Figure 4.4 for the setup). Vapor can be
brought to a localized small area or spread to the entire Specimen.

(3) A small refrigerator was used to create a uniform temperature gradient between the

specimen and the ambient. The temperature difference used was about 8 to 12 °C.
4.2.1.3 Results

Results are presented in Figures 4.5 - 4.11. Please refer to Figure 4.2 for the

configurations of the specimens. The ‘free expansion’ results were actually the

86

 
 

Specimen

    

 

  
 

Vacuum
Chamber

 
 
 

Air Table (top view)

 
 
 

Adjustable
Voltage

VCR

 

    
  
 
 

PZT Driver

High Resolution

  
  

Display

 

 

 

Fig. 4.3
Setup for NDT of Composite using
ESPI thermal (resistor) method

87

      
    
  
    

Composite
Plate

 

Air Table (top view)

lazy. 3'

PZT Driver Steamer

High Resolution

  
  

Display

 

 

Fig. 4.4
Setup for NDT of composite using ESPI thermal (steamer) method

88

    

         

           

    

    

.. . twumnhfl wLIIWwi,
. . 4 . ,5 .... . Li a 1.6.» l
.t.v.ruv.\mr1lt.,m.,.rwr “7 a? ehwtmxnuwmw Q». .“n
. .. filtqulll7hu2hwsmxfib twflwnzflnmvfia .ufl _ _ _
. . mtxtsAhYdelifiu )vafivr4mflwuuuwww 5%.. .(ntruit

. 9. mirflhfiunwumhvfitfiwfigwflmww :fi:m.wt

. \ 1x
.\

                      

l (vfllounfi uflufiKVlfim
unfit")! .1; hr...“ N6”. t 2n\\-. .1...
”Wang Wat...» a timhwuwn ...\....\H _I_
. v "I; l...v . t.\ .. ..
fflaJanhHWflafll Nani)... MIIuHMmmV \. Nsvu\tu\\\n.‘\ \x\ . ..

13./mil»? . titular. are, ......\ .
.v/mwrhrm.nmoui.u..m\\w.§\xxw .
- . .

.\||\

 

l nu“.

      

     

    

away... __ _

II. \.
I‘ll l\l|. I l I . r
lrllmtl» .li .\ l. I .. . .
. Ir It'll ..l 1 . . .
. {hl.lu”r\1)trlulllrxx\wn..n~\.\ » . r. .r/ / 1.11}... = _
lll.truJIll..-.l$a Inuit. ..u . I; (it?)

      

..nl filth It...
. f. -E

Fig. 4.5

Fringe pattern obtained when composite plate #7 is ‘point heated’ at the

tor heating device and then with the heater removed.

center using a rests

89

        

       

3...-
E54:

       
                              

. . : _
.s. z.»
.v. . . .\<...tr.¢;. .
,..\ . .Ikflfir..x.rfiflwmfi%nnnwfl '

....Vu¢..y.>zil..fifl~ .fimumum%u .
. x.‘.tn.§ “J hwwmflulvkw n ,.
. ,...:{n/\. «RV fut”. .lql “Ewan“
.. . . in», Lawsuit. .. .

    

  
   

J.

T5
fl:-
5:=——

'-==

"h—

-—-— __—.__
_ -__=
———

f_'———r——

 

. uslr weur.flfi)$( u...

I.

_—

--__
_

—§E

, . . (2%....
. . av 5,55%. 4... =

_-_._-—I_-

Fig. 4.6
Fringe pattern obtained when composite plate #7 is heated at the upper

rs removed.

stor heating device and then the heater '

mg a resi

ht comer us

ng

9O

 

l:-_
Z—Z

-l—_
.—
.-

ufl§wdflkxn§uh .

!-—_—_—__-:
4-4—3r:

.\. ..
as.) . — :—

Fig. 4.7

Fringe pattern obtained when compos

late #7 is in free

rte p
AT about 8 °C (23-15) with At about 5 seconds.

expansron at

91

           
                         

Fig. 4.8
Fringe pattern of plate #9 when heated at the upper right

corner and then with the heater removed.

92

Peak to valley I 8% l‘licmns

       
    

I

I

-— '/ .Jd
J’

  

 

 

 

 

 

32:: FEE—5L—

3—D ’ ISMETRIC’ PLOT 0F UJT OF FIRE DISPLHCWT

Fig. 4.9
This is the 3D plot of Figure 4.8.

93

Part ID : Image

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Serial 3 2 file Rou 281
D g l
i a .429 "' 4
s 3
P 5
1 i
a 8 .28
c »-\—._ - J...
m "---., ‘--._ NW7 yum. ‘_._.
B 8 . 88 ' --__.‘..M /./
n I
t /
1 -8 28 \ f
n
. \ ’l

u 7. J , i.
m -8 .48

Left Centre Right

Fig. 4.10

2D plot of Figure 4.8 of the section
where the damage spot is located.

 

94

Part ID i Image

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Serial it I file ' ‘ Run 114
D I.
i a .48 F
S I
P Q
1 ' 4L .
a 8 .28 ‘-""-’--.._,_% _...-”"' ”--
C i i -fihflx— “" ‘ I. - h“ "
E} E d~.__',.,..,.,_,~" '-
n I
F; B .88 ' l
n i
t I
1 -8 .28
n
u
.1 -8 .48 L -
Lei 1 Centre R iglrl
Fig. 4.11

2D plot of Figure 4.8 of a arbitrary
section away from the damaged spot.

95

combination of thermal and creep effects.
4.2.1.4 Discussion and Summary

For an undamaged plate, when the heat source is removed, the created fringe pattern
will tend to trace back into the original (or primary) heat point or the area which generates
those fringes, and the speed of the ‘trace back’ is very fast (several seconds). If there is
damage, the damaged zone will block this ‘trace back’ and act as another heat source
creating some ‘secondary’ fringes, and these ‘secondary’ fringes will rest there for quite
some time. These phenomena were checked on different specimens using different
heating location. This happens because in the damaged zone the matrix is loosened,
some fiber may be broken and likely there will be some air trapped in the matrix and
between laminates. Overall, these will decease the thermal conductivity in the damaged
zone area. When we monitor the live change of this phenomena it is quite obvious. To
characterize the size of the damage and the depth of the damage more work need to be

done.

The steamer we used is very simple. A more sophisticated device can be built to have

adjustable heat flow.
4.2.2 Using Gravity (creeping)

This is unique and simple to do, and it seems especially suitable for composite

materials. Figure 4.12 is the setup.

All polymers exhibit time dependence of material response. This manifests itself by
the increase with time of deformations under constant load, which is called creep, and
conversely, by the decrease with time of stresses under deformation constraints, which is

called relaxation. These phenomena may be used to do NDT for a composite material.

96

Specimen

 

 

Air Table (top view)
A
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t

 

 
 

High Resolution

  
 

Display

 
 

 

Fig. 4.12

Setup for gravity creeping test of composite using ESPI

97

The effects described are of considerable engineering importance for fiber-reinforced
composite structures, because stresses and deformations determined on the basis of elastic
analysis may change considerably with time because of polymeric matrix time
dependence. ESPI can be used to monitor those time-induced deformations in real time,

and, therefore, provide more understanding about composite materials.

All polymeric matrix viscoelastic properties, such as creep and relaxation, are
significantly temperature dependent, so, creep and thermal techniques can be combined to

create a new NDT method for composite.

We found that even at room temperature the damaged and undamaged composite plate
will give significant difference in terms of the number of fringes and shape of the fringes
accumulated in certain time period. Those fringes are induced only by gravity force.
Certainly, this has something to do with the nature of the damage and the size of the
damage zone. Some results are presented in Figures 4.13 - 4.15.

4.2.3. Using Vibration Method

The experiments we did were on impact damaged glass/epoxy plates with various
layouts. Two samples are presented here (Figure 4.16). A speaker was used as the
excitation for this study (Figure 4.17). Results shown in Figures 4.18 - 4.26.
Unidirectional carbon fiber plates (A s-4/828 mPDP) with cuts. were also studied (Figure

4.27), and results are presented in Figures 4.28 - 4.29.
We found that:

(1) At low frequency, damaged and undamaged plates have similar vibration modal
shapes. At higher frequency, the vibration modal shape becomes very different.

(2) Many resonant frequencies are under 1000 Hz., and the excitation of those

frequencies is easy.

98

           

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Fig. 4.16
Impact damaged composite (glass/epoxy)specimens used in NDT
using ESP time-average mode, speaker was used for excitation.

Dimension is 6” x 6”.

102

 

 

 

 

Air Table (top view)
' Speaker Driver
A
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Fig. 4.17

Setup for vibration test using a speaker

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Fig. 4.27
Experimental setup for nondestructive inspection using
ESPI’s time average vibration mode. The composite being
tested is A s-4/828 mPDA, 18 plies, the depth of cut is 9 plies.

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115

CONCLUSIONS AND RECOMENDATIONS

The improvement in image processing techniques, development of high resolution
cameras, and creation of faster and efficient algorithms have enabled ESPI to reach a stage
where it can be employed as a usable and reliable measuring tool. However, use of ESPI
in the industrial environment would be enhanced by maximizing cost effectiveness and
compactness while minimizing the need for a stable environment. The advantages
dictating the choice of ESPI over conventional methods are its non-contacting nature
and fast displacement and vibration modal shape presentation combined with high

accuracy and repeatability.

Compared with decorrelation of speckles, the ‘memory loss’ is more important. At the
present time, a standard TV system is used in ESPI, and it imposes some limits on the
capability of ESPI. The vertical resolution and horizontal resolution of a standard TV

system are about 20 pm with respect to the CCD’s image target.

To reduce environmental efl'ects, basically there are two ways to go. (1) Shortening
picture taking time, designing a special TV system, and improving the image taking
camera. (2) Making a ‘self-compensation’ setup, as used , for example, in the principle of

operation of shearography.

On the other hand, more study in the area of NDT of composite materials and other
materials should be carried out using the current ESPI system. Effort should be exerted to
get more insight and understanding of the different stressing techniques and their

effectiveness in testing various materials.

 

LIST OF REFERENCES

 

116

LIST OF REFERENCES

1. R. L. Powell and K. A. Stetson , “Interferometry vibration analysis by wavefiont
reconstruction,” Journal of the Optical Society of America, 55 (12) 1593-1598 (Dec.
1965).

2. C. M. Vest, E. L. Mckague, and A. A. Friesem, “Holographic detection of
microcracks,” Trans. ASME, Ser. D-J, Basic Engineering, 93, 237-246 (1971).

3. A. D. Luxmoore, “ Holographic detection of cracks in concrete,” Nondestr. Test 6, 258-

263 (1973).

4. M. J. Salkind, “Early detection of fatigue damage in composite materials,” J. Aircr.,
13, 764-769 (1976).

5. C. S. Bartolotta and B. J. Pemick, “Holographic nondestructive evaluation of

interference fit fasteners,” Appl. Opt., 12, 885-886 (1973).

6. C. M. Vest and D. W. Sweeney, “Applications of holographic interferometry to

nondestructive testing,” Int Adv. Nondestr. Test, 5, 17-21 (1977).

7. R. J. Parker and D.G.Jones, “Holography in an industrial environment,” Optical

Engineering, p055-063, vol. 27 No. 1 (January 1988).
8. A. Macovske, Appl. Opt. 16, 2722 (1971)

9. O. Schwomma, Austrian patent 298,830 (1972)

 

117

10. J. N. Butters and J. A. Leendertz, Opt. Laser. Technol. 3, 26 (February 1971)

11. J. W. Goodman, “Laser Speckle and Related Phenomena,” Chapter 2, ed. J. C.

Dainty, Springer-Verlag: Berlin (1975).

12. J. D. Rigden and E. 1. Gordon, Proc. 1. R. E. 50, 2367 (1962)

13. B.M. Oliver, Proc. IEEE 51, 220 (1963)

14. J .W. Goodman, Proc. IEEE 53, 1688 (1965).

15. E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).

16. S. Lowenthal and HR. Arsenault, J. Opt. Soc. Am. 60, 1478 (1970).
17. F. Eernike, Physica 5, 785 (1938)

18. J. C. Dainty, “Topics in Applied Physics”, Vol 9. p209.

19. J .M. Burch, Optical Instruments and Techniques, 1970 p213-229
20. J. C. Dainty, “Topics in Applied Physics”, Vol 9. p211.

21. Chaules M. Vest, “holographic Inerferometry,” John \Vrley and sons, Inc.(l979).
22.. D. Herbert, private communication.

23. Robert Jones and Catherine Wykes, “Holographic and Speckle Interferometry,”
Cambridge University Press, p167, 1983.

24. Robert Jones and Catherine Wykes, “Holographic and Speckle Interferometry,”
Cambridge University Press, p170 (1983)

118

25. Boxiang Lu, Xiangyang Yang, Harald Abendroth and Heiner Eggers, “Time-average
subtraction method in electronic speckle pattern interferometry,” Opt. Comm. Vol 70, 3,

177—180 (March 1989).
26. K. Hogmoen and O. J. Lokber, Appl. Opt., 16, 1869-1875 (1977).

27. T. J. Cookson, J. N. Butters and H. C. Pollard, Optics and Laser Technology, 10, 119-
128 (1978).

28. O. J. Lokberf and K. Hogmoen, Appl. Opt, 15, 2701-2704 (1976).
29. G. A. Slettemoen, Opt. Commun., 23, 213-16 (1977).

30. J. C. Wyant, C. L. Koliopoulos, B. Bhushan and O. E. George, ASLE Trans. 27, 101
(1984).

31. P. Carre, Metrologia 2, 13 (1966).

32. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfild, A. D. white and D. J.
Brangaccio, Appl. Opt. 13, 2693.(1974).

33. C. E. Sommargren, J. Opt. Soc. Am. 65, 960 (1975).
34. J. C. Wyant, Appl. Opt. 14, 2622 (1975).

35. J. H. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, ed. D.
Malacara (Wiley, New York)(1978).

36. N. A. Massie, Appl. Opt. 19, 154 (1980).
37. R. C. Moore and F. H. Slaymaker, Appl. Opt. 19, 2196 (1980).

38. J. C. Wyant, LaserFocus, p. 65 (May,1982).

39.

40.

119

J. C. Wyant, and K. Creath, , Laser Focus, p. 188 (November, 1985).

R. N. Shagam, and J. C. Wyant, Appl. Opt. 17, 3034 (1978).

41. H. 2. Hu, Appl. Opt. 22, 2052 (1983).

42. K. Creath, Appl. Opt. 24, 3053 (1985).

43. G. E. Sommargren, Appl. Opt. 20, 610 (1981)

44. C. J. Morgan, Opt. Lett. 7, 368 (1982).

45. C. J. Greivenkamp, Opt. Eng. 23, 350 ( 1984).

46. G. T. Reid, Opt. Lasers Eng. 7, 37 (1986).

47. Guanming lai and Toyohiko Yatagai, J. Opt. Soc. Am. W01. 8, 822 (May, 1991)
48. D. Kerr, F. Mendoza Santoyo, and J. R. Tyrer, J. Opt. Soc. Am. A/Vol. 7, 820,
(May, 1990).

49. K. Creath, “Hologram interfeometry and speckle metrology,” 473-497, SEM (1990 )

50.

K. Grunewald, W. Fritzsch, A. V. Hamier, and E. Roth, “Nondestructive testing of

plastics by means of holographic interferometry,” Polym. Sci. Eng., 15, 16-28 (1975).

51.

W. J. Harris and D. C. Woods, “Thermal stress studies using optical holographic

interferometry,” Mater, Eval., 32, 50-56 (1974).

52.

J. R. Crawford and R. Benson, “Holographic interferometry of circuit board

component failure,” Appl, Opt., 15, 24-25 (1976).

120

53. I. S. Klimenko, E. G. Matinyan, and L. G. Dubitskii, “Use of focused image
holography for the nondestructive testing of electronic parts,” Sov. J. Nondestr. Test, 10,

696-699 (1975).

54. O. J. Burchett, “Analysis techniques for the inspection of structures by holographic

interferometry,” Mater. Eval., 30, 25—31 (1972).

55. G. M. Brown, “Pneumatic tire inspection,” in Holographic Nondestructive Testing,

R. K. Erf (Ed.), Academic Press, New York, pp. 355-364 (1974).

56. L. A. Kersch, “Advanced concepts of holographic nondestructive testing,” Mater.

Eval., 29, 125-140 (1971).

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