vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
INTRODUCTION
1
1.1
Introduction
1
1.2
Objectives of Study
2
1.3
Scope of Study
3
1.4
Thesis layout
5
LITERATURE REVIEW
7
2.1
Introduction
7
2.2
The Principle of Interferometry and Interferometric
8
Testing
2.3
Generation of Acoustic Waves By Laser
9
2.4
Phase Association with Refractive Index and Pressure
10
2.5
Abel Inversion Technique
13
2.6
Techniques for Phase Measurement
17
2.6.1
Fringe Analysis
18
2.6.2
Phase Mapping Techniques
20
viii
2.6.2.1
Fourier Transform Method
21
2.6.2.2
Carrier Frequency Method
23
2.6.2.3
Phase Shifting Interferometry
24
2.6.2.4
Phase Shifting Algorithms
26
2.6.2.5
Phase Unwrapping
31
2.6.2.6
Error in Phase Unwrapping
34
2.6.2.7
General Error Sources and
36
Measuring Limitations in PSI
3
2.7
Phase Measuring Interferometry versus Fringe Analysis
37
2.8
Simultaneous Phase Measurement Interferometry
38
METHODOLOGY
40
3.1
Introduction
40
3.2
The Laser
42
3.2.1
The Nd:YAG Laser
43
3.2.1.1
44
The Focusing system for Nd:YAG
laser
3.2.2
The Nitro-dye Laser
47
3.2.2.1
47
The magnification and the
collimation of Dye laser beam
3.3
The Interferometer
49
3.4
Alignment of the Interferometry System
53
3.5
Localization of the Fringes
54
3.6
Magnification and Focusing of the image
55
3.7
Quadrature Imaging
57
ix
3.8
4
5
High-speed Photography System
58
3.8.1 The CCD camera
59
3.8.2 The Frame Grabber
59
3.9
Synchronizing and Triggering
60
3.10
Image Production
64
3.11
Photography Techniques
66
3.12
Phase Retrieval
68
IMAGE PRODUCTION AND IMAGE PROCESSING
71
4.1
Introduction
71
4.2
The Photographic Images
72
4.3
Image Synchronization
76
4.4
Fourier Filtering
77
4.5
The Intensity
80
4.6
The 90° Phase Difference
83
4.7
The Effects of the Number of Fringes and their Shapes
90
4.8
Postprocessing Fringe Patterns
90
4.9
Summary
91
SINGLE-INTERFEROGRAM PHASE
93
INTERFEROMETRY
5.1
Introduction
93
5.2
Fringe Analysis Technique
94
5.3
FFT Phase Mapping Technique
98
5.4
Problems of Single Interferometry Phase Mapping
104
x
5.5
6
Summary
SIMULTANEOUS PHASE MEASUREMENT
105
107
INTERFEROMETRY
6.1
Introduction
107
6.2
Simultaneous Phase Measurement Interferometry
108
6.3
Refractive Index, Density and Pressure Profile of
117
Image
6.4
Pressure of Acoustic Waves from Laser Interaction
120
6.5
Image Representation
123
6.6
Comparison with Fringe Analysis
128
6.7
The Advantages of the Simultaneous Phase
130
Measurement
7
6.7.1 Phase Ambiguity Reduction
130
6.7.2 Visual Observation
138
6.7.3 Intensity Independency
138
6.7.4 Fringe Shapes and Sizes
139
6.7.5 User-friendly System
142
6.8
The Disadvantages of the System
142
6.9
Discussion: Error Contributors
143
6.10
Summary
145
CONCLUSION AND RECOMMENDATIONS
147
7.1
147
General Conclusion
xi
7.2
Recommendations for Future Work
150
REFERENCES
152
Appendices A-P
160 – 190
xii
LIST OF TABLES
TABLE NO.
Table 4.1
TITLE
Some combinations for the 90° phase
PAGE
86
difference
Table 6.1
Distribution of maximum pressure change
122
xiii
LIST OF FIGURES
FIGURE NO.
2.1
TITLE
Cross section of the spherically symmetrical
PAGE
14
refractive index distribution.
2.2
The zone and chordal divisions.
15
2.3
Fringe deviation measurements.
19
3.1
The general layout of the system.
40
3.2
Nd:YAG laser in Gaussian mode and the
45
amplitude distribution in the transverse direction.
3.3
The beam waist w along propagation axis.
45
3.4
Focusing system for Nd:YAG laser.
46
3.5
Magnification of dye laser beam.
48
3.6
The modified Mach Zehnder interferometer with
50
three outputs.
3.7
Fringe Localization.
57
3.8
A U-shaped Aluminium plate as reference frame
58
for the interference pattern.
3.9
Master slave configuration.
60
3.10
Arrangement for controlling the width and delay
62
of the three frame grabbers.
3.11
The optical detector used for laser delay
63
measurement.
3.12
The time chart for image capture
64
3.13
Shadowgraphy arrangement
66
3.14
Schlieren arrangement
67
4.1
The development of acoustic wave propagation
73
using (a) the Schlieren and (b) shadowgraphy
techniques
xiv
4.2
Stages of development of waves by
74
interferometric method.
4.3
Plot of the radius of wave with time.
75
4.4
Synchronization of center of interaction.
77
4.5
Cut-off frequency in Fourier filtering.
79
4.6
The unfiltered and the filtered intensity signal.
79
4.7
Intensity distributions of the three undisturbed
81
images.
4.8
The filtered intensity of the undisturbed images.
81
4.9
The sequence of the 90°-90° phase difference.
85
4.10
The wrapped phase.
87
4.11
The unwrapped phase wavefronts.
87
4.12
The fluctuation of the 90°-90° phase difference.
88
5.1
(a)The image at 3.6 µs. (b) The corresponding
95
fringe shift.
5.2
Profile of pressure change of the event.
97
5.3
(a)The interferogram at t = 3.6 µs. (b) The phase
100
change profile by FFT method.
5.4
Profile of the corresponding pressure change.
101
5.5
(a) Interferogram at 3.2 µs. (b) The associated
103
phase change exhibiting ambiguity.
5.6
The extra fringe in the interferogram.
104
6.1
The images of laser interaction from the three
110
CCD cameras at 3.6 µs delay.
6.2
Intensity distribution of the three images at y = 15.
111
6.3
The unfiltered an the filtered signals for the three
112
images.
6.4
(a)The wrapped phase spectrum. (b) The
114
unwrapped phase wavefront and its deviation from
its reference
6.5
The phase change with the first algorithm
115
6.6
The phase change with the second algorithm
117
6.7
Change in the refractive index due to interaction
118
xv
6.8
Change in density due to laser interaction.
119
6.9
Profile of pressure change of the event.
119
6.10
Distribution of maximum pressure change.
122
6.11
(a)3-D image of phase change with first
125
algorithm. (b) 3-D image of phase change with
second algorithm.
6.12
(a) Cross-section of the image. (b) Another view
126
of the cross section.
6.13
A quarter section of the event.
127
6.14
Profile of phase change at different locations
127
across the image.
6.15
Maximum pressure change profiles using the two
128
methods.
6.16
Field of view at three different locations.
130
6.17
Images at t = 3.8 µs.
131
6.18
Phase change profiles individually analyzed.
132
6.19
Phase change profile with simultaneous analysis.
133
6.20
Images at t = 3.4 µs.
133
6.21
Phase change profiles of images when analyzed
134
individually.
6.22
Phase change profile simultaneously analyzed.
135
6.23
Phase change profiles of the three images
137
individually analyzed.
6.24
Phase change profile simultaneously analyzed
138
6.25
Simultaneous phase analysis from high-intensity
140
images
6.26
Phase change from low intensity images
141
xvi
LIST OF ABREVIATIONS
ξ
-
spatial frequency coordinate
η
-
high frequency noise
2D, 3D
-
two and three dimensional
α
-
phase step
atm
-
atmospheric pressure
B
-
Bulk modulus
c
-
Velocity of light
CCD
-
Charge Couple Device
CCIR
-
Comite Consultive International Radio
cR
-
Rayleigh wave velocity
∆F
-
fringe shift
∆f
-
fractional fringe shift
∆φ
-
phase change
∆L
-
optical path difference
∆n
-
change in refractive index
∆P
-
change in pressure
∆ρ
-
change in density
E
-
electric field amplitude
f
-
frequency
xvii
FFT
-
Fast Fourier Transform
γ
-
coherence modulation
HD
-
Horizontal drive synchronization
He-Ne
-
Helium Neon
I
-
intensity
ISA
-
Industry Standard Architecture
λ
-
wavelength
LASER
-
Light Amplification by Stimulated Emission of Radiation
MHz
-
MegaHertz
µm
-
micrometer
MOSFET
-
Metal Oxide Semiconductor Field Effect
Transistor
µs, ns
-
microsecond, nanosecond
MW
-
MegaWatt
n
-
refractive index
Nd:YAG
-
Neodymium: Yttrium Aluminium Garnet
PAL
-
Phase Alternation Line
PMMA
-
polymethyl methacrylate
PMI
-
Phase Measurement Interferometry
PSI
-
Phase Shifting Interferometry
ρ
-
density of medium
TTL
-
Transistor Transistor Logic
VD
-
Vertical drive synchronization
w
-
width distribution of laser beam
xviii
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Laser Energy Produced At Laser Head.
160
B
The Trigger and Synchronize Unit Incorporating the
161
Nd:YAG and Nitro-dye Laser.
C
Power supply for trigger unit.
164
D
Formula Derivation For Simultaneous Phase Measurement.
165
E
Acoustic Wave Propagation.
167
F
Fringe Analysis.
168
G
Simultaneous Phase Measurement.
173
H
3D Representation of the Phase Change
183
I
The Cross-section of the Phase Image
187
J
Distribution of the Maximum Pressure Change by Fringe
190
Analysis and Simultaneous Method.