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University of Bath
PHD
An evaluation of the technique of photothermal radiometry for the non-destructivetesting and characterisation of plasma-sprayed coatings
Patel, Pravinkumar M.
Award date:1988
Awarding institution:University of Bath
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TITLE
An E v a l u a t i o n o f t h e T e c h n i q u e o f P h o t o t h e r m a 1
Rad i o m e t r y f o r t h e N o n - d e s t r a c t i v e T e s t i nq and
C h a r a c t e r i s a t i o n o f P 1a s m a - s p r a y e d C o a t i n g s .
S u b m i t t e d b y
P r a v i n k u m a r M. P a t e l BSc , M S c .
f o r t h e d e g r e e o f D o c t o r o f P h i l o s o p h y
o f t h e U n i v e r s i t y o f B a t h
S e p t e m b e r 1 9 8 8
A t t e n t i o n i s d r a w n t o t h e f a c t t h a t t h e c o p y r i g h t o f
t h e s i s h a s b e e n s u p p l i e d o n t h e c o n d i t i o n t h a t a n y o n e
who c o n s u l t s i t i s u n d e r s t o o d t o r e c o g n i s e t h a t t h e
c o p y r i g h t r e s t s w i t h i t s a u t h o r an d t h a t no q u o t a t i o n
f r o m t h e t h e s i s a n d no i n f o r m a t i o n d e r i v e d f r o m i t may
b e p u b l i s h e d w i t h o u t t h e p r i o r c o n s e n t o f t h e a u t h o r .
T h i s t h e s i s may b e made a v a i l a b l e f o r c o n s u l t a t i o n
w i t h i n t h e U n i v e r s i t y L i b r a r y a n d may b e p h o t o c o p i e d o r
l e n t t o o t h e r l i b r a r i e s f o r t h e p u r p o s e o f
c o n s u l t a t i o n .
COPYRIGHT
t h i s t h e s i s r e s t s w i t h t h e a u t h o r . T h i s c o p y o f t h e
S i g n e d
P r a v i n M P a t e l
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UMI Number: U601407
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J a y n a , A n i 1 a n d M e t h o o n .
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7.5 2 4 APR 1989
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ABSTRACT
A r e v i e w o f f i v e p h o t o t h e r m a l r a d i o m e t r i c t e c h n i q u e s
b a s e d o n t h e a m p l i t u d e o r s p a t i a l m o d u l a t i o n o f an
i n c i d e n t e n e r g y s o u r c e f o r m a t e r i a l s t e s t i n g i s
p r e s e n t e d . M e a s u r e m e n t s a r e r e p o r t e d d e m o n s t r a t i n g t h e
p o t e n t i a l c a p a b i l i t y o f t h e p e r i o d i c h e a t i n g m e t h o d f o r
n o n c o n t a c t t h i c k n e s s g a u g i n g , s u b s u r f a c e d e f e c t
d e t e c t i o n a n d c h a r a c t e r i s a t i o n . E f f e c t s o f c o a t i n g
s t r u c t u r e s u c h a s s u r f a c e r o u g h n e s s a n d p o r o s i t y on t h e
r e c o r d e d p h o t o t h e r m a l s i g n a l a r e a l s o a s s e s s e d
e x p e r i m e n t a l l y an d t h e o r e t i c a l l y .
Two t e s t s y s t e m s w e r e e v a l u a t e d u s i n g l a s e r
i l l u m i n a t i o n f o r s a m p l e h e a t i n g . One u s i n g a 5 w a t t
a r g o n i o n l a s e r a n d t h e o t h e r , a 0 . 5 w a t t G a A l A s l a s e r
d i o d e w i t h i t s e m i s s i o n c o u p l e d t o a 2 5 0 Fm d i a m e t e r
o p t i c a l f i b r e . I n t h e l a t t e r s y s t e m a n e l l i p s o i d a l
m i r r o r c o l l e c t o r was u s e d t o e n h a n c e t h e i n f r a r e d
d e t e c t i o n e f f i c i e n c y . I n t h e e v a l u a t i o n o f t h e s e
s y s t e m s a s t u d y was u n d e r t a k e n t o d e t e r m i n e t h e
m a g n i t u d e o f p h a s e a n g l e e r r o r w i t h t h e d e t e c t i o n o f
c o h e r r e n t i n f r a r e d n o i s e s i g n a l s , i n c i d e n t l a s e r p o w e r
and s p o t s i z e , s a m p l e o r d e t e c t o r m i s a 1 i g n m e n t , and
i n t r i n s i c p h a s e n o i s e o f t h e m e a s u r e m e n t s y s t e m .
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ACKNOWLEDGEMENTS
I w i s h t o t h a n k t h e t e c h n i c a l s u p p o r t s t a f f o f t h e
S c h o o l o f t h e M a t e r i a l s s c i e n c e ; i n p a r t i c u l a r P e t e r
T a y l o r and I a n T u r n e r f o r t h e c o n s t r u c t i o n o f v a r i o u s
m o u n t s f o r h o l d i n g o p t i c a l c o m p o n e n t s i t e s t s p e c i m e n s
and l i g h t t i g h t e n c l o s u r e . To D r . S . G o rm an f o r
d e s i g n i n g and m a i n t a i n i n g v a r i o u s e l e c t r i c a l ' b l a c k
b o x e s ’ r e q u i r e d f o r t h i s r e s e a r c h p r o g r a m a nd B r a i n
G o s l i n g f o r h i s a s s i s t a n c e a n d a d v i c e i n o p t i c a l
m i c r o g r a p h y .
I a l s o w i s h e x p r e s s my d e e p e s t g r a t i t u d e t o D r s
D a r r y l P . A lm o n d a n d H a r r y R e i t e r f o r t h e i r e n c o u r a g i n g
d i s c u s s i o n s t h r o u g h o u t t h e r e s e a r c h p r o g r a m .
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CONTENTS
Page
T i t l e i
Abst rac t i i
Acknowledgements i i i
Contents iv
L i s t of Tab le v i i
L i s t o f symbols v i i i
Chapter 1 Photothermal I n f r a r e d Techniques
1.1 I n t r o d u c t i o n 1
Plasma Spray Coat ings and t h e i r Q u a l i t y C o n t ro l
1 .2 Review o f Photothermal NDE Techniques 3
1 . 2 . 1 Photothermal Radiometry and Thermography 5
1 .3 D e s c r ip t io n o f PTR Techniques 6
1 . 3 . 1 P e r i o d i c Photothermal Hea t ing 7
S igna l Process ing and I n t e r p r e t a t i o n 8
1 . 3 . 2 Pulsed Photothermal Heat ing 11
P o in t Hea t in g w it h P o in t I n f r a r e d D e t e c t io n 11
L in e Heat ing w i th L in e I n f r a r e d D e t e c t i o n 11
Area Heat ing and In f r a r e d Camera D e t e c t i o n 12
1 . 3 . 3 Step Photothermal Heat ing 13
1 . 3 . 4 C oord in ate Modulat ion Photothermal Heat ing 14
1 . 3 . 5 Scanning Photothermal Heat ing 14
1 .4 Summary o f PTR NDE Methods 15
1 .4 .1 S e l e c t io n o f PTR Technique 16
Tables and F ig u re s f o r chapter 1 17
Chapter 2 Photothermal Radiom etr ic D e t e c t i o n Theory
2 .1 I n t r o d u c t i o n 31
2 . 1 . 1 Thermal Emission C h a r a c t e r i s t i c s 32
2 . 1 . 2 Thermal Waves 34
2 . 2 One Dimensional Surface Temperature Express ions 36
2 . 3 Three Dimensional Sur face Temperature Expressions 38
iv
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2 . 4 A p p l i c a t i o n to Thermal Spray Coat ings 40
2 . 4 . 1 Coat ing on a S ubst ra te 40
2 . 4 . 2 Coat ing P o r o s i t y E f f e c t s 42
2 . 4 . 3 Sur face Roughness 43
2 . 4 . 4 C o a t in g / S u b st ra te I n t e r f a c e D e fec ts 45
2 . 4 . 5 D e fec t D e te c t io n S e n s i t i v i t y 46
2 . 4 . 6 Thermal Contact Res is tance 48
2 . 5 R e s o lu t io n and D e f i n i t i o n o f Subsurface S t r u c t u r e 51
2 . 6 Summary 53
Tables and F ig ures f o r Chapter 2
Chapter 3 Exper imen tal D e s c r i p t i o n
3 .1 Photothermal System 79
3 . 2 D e te c to r S e l e c t io n 80
3 . 3 Semi -conductor Laser 81
3 . 4 Laser S a f e t y 82
3 . 5 Sample and Measurement D e t a i l s 83
Tab les and F ig ures f o r Chapter 3
Chapter 4 Exper imen tal R es u l ts
4 .1 System E v a l u a t i o n 93
4 . 1 . 1 Removal o f Unwanted I n f r a r e d S ig n a l Sources 93
I n f r a r e d Emission from the Laser 93
R e f l e c t e d Laser L ig h t 94
4 . 1 . 2 Laser Power Level 95
E l l i p s o i d a l C o l l e c t o r 97
4 . 1 . 3 Sample and D etector R o ta t io n 99
4 . 1 . 4 D iscuss ion 99
4 . 2 Sur face Roughness 101
4 . 2 . 1 LC1B F in e and Rough co at in g s 102
4 . 2 . 2 G ra p h i te Samples 102
4 . 2 . 3 D iscu ss ion 104
4 . 3 Defects 105
4 . 3 . 1 Square D e fe c ts in LC1B Coat ings 106
Photothermal I n v e s t i g a t i o n 106
U l t r a s o n i c I n v e s t i g a t i o n 107
4 . 3 . 2 D i f f u s i o n Bonded D e f e c t Samples 107
V
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4 . 3 . 3 Thermal Contact Res is tance 109
4 . 3 . 4 Discussion 110
4 . 4 Semi-conductor Laser Diode System E v a l u a t i o n 111
4 . 4 . 1 Laser Power Leve l Study 111
4 . 4 . 2 S igna l Ampl i tude and Phase Angle V a r i a t i o n 111
wi th F i b r e Head P o s i t io n in g
4 . 4 . 3 LC1B Coat ing Thickness Measurements 113
4 . 4 . 4 Discussion 113
4 . 5 I n f r a r e d D e te c to r E v a lu a t io n 114
4 . 5 . 1 I n f r a r e d D e te c to r Frequency Response 114
4 . 5 . 2 Photothermal Frequency Response 115
4 . 5 . 3 Phase Angle Noise 115
4 . 5 . 4 Discussion 116
Tables and F ig u re s f o r Chapter 4
Chapter 5 D iscuss io n
5 .1 System Performance 169
Argon ion Laser verses Laser Diode PTR System 169
I n f r a r e d D e t e c t o r 170
5 . 2 A p p l i c a t i o n to NDT o f Surface Coat ings 171
5 . 3 F u r th e r Developments 173
Tables f o r Chapter 5
Appendices
1 Thermal Wave R e f l e c t i o n and Transmission 177
C o e f f i c i e n t s .
2 One Dimensional Complex Surface Temperature 179
D e r i v a t i o n .
3 E f f e c t i v e Thermal C o n d u c t iv i t y o f a Gas Trapped 186
Between N arrowly Spaced P a r a l l e l P l a t e s .
F igures f o r Appedix 1,2 and 3. 189
References . 192
v i
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Table 1.
Tab le 1.
Tab le 2.
Table 2 .
Tab le 2.
Tab le 3.
Table' 3 .
Tab le *f.
Tab le 5 .
Table 5 .
L i s t o f Tables
Advantages and d isadvantages o f thermographic
and photothermal r a d i o m e t r i c m a t e r i a l s t e s t i n g .
Advantages and d isadvantages o f PTR NDE
techniques .
Thermal p r o p e r t i e s and the thermal d i f f u s i o n
lengths o f some common e n g in e er in g m a t e r i a l and
plasma sprayed c o a t in g s .
One dimensional s u r f a c e tem pera ture express ions
f o r thermal wave NDT o f opaque s u r fa c e c o a t in g s .
S e r ie s summation r e p r e s e n t a t i o n o f the t h r e e
dimensional s u r fa c e tem perature d i s t r i b u t i o n
w ith Gaussian beam i l l u m i n a t i o n .
Argon ion l a s e r , IR d e t e c t o r and e l l i p s o i d a l
m i r r o r c o l l e c t o r d e t a i l s .
Exper imen tal i n v e s t i g a t i o n summary.
Summary o f the phase angle and u l t r a s o n i c
a t t e n u a t i o n change across the square d e f e c t s in
plasma sprayed LC1B c o a t i n g s .
A summary o f PTR measurements on plasma sprayed
c o a t in g s .
A comparison and performance o f the gas and
semiconductor l a s e r s f o r sample h e a t i n g .
y i i
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L i s t of L a t i n symbols
D e f i n i t i o n U n i ts
b i j thermal impedance r a t i o
c speed o f l i g h t in f r e e space m/s
d mean f r e e path m
e e xp o n e n t ia l constant
f l i g h t modulat ion frequency Hz
f r a c t i o n a l volume p o r o s i t y
hi rms roughness m
i i n t e g e r
j complex ro o t o f minus one
k thermal c o n d u c t i v i t y W/(m K)
km harmonic mean thermal c o n d u c t i v i t y W/(m K)
m in t e g e r
r r a d i a l d is ta n c e m
s u r f a c e o p t i c a l r e f l e c t i v i t y
r a d i u s o f contac t
r 0 gauss ian beam l / e a r a d iu s m
t t ime s
u d i s t a n c e between the mean p lane o f the * m
rough and f l a t su r face s
x d is t a n c e m
A0 apparent area o f c o n ta c t ma
At. t r u e area o f contac t me
C S p e c i f i c heat c a p a c i t y J / (K g K)
D* S p e c i f i c D e t e c t i v i t y m Hz” ty'a /w
F accommodation form f a c t o r
I 0 l a s e r beam i n t e n s i t y W / ma
Li l a y e r th ic kness m
Kc. bulk thermal c o n d u c t i v i t y o f a i r Ul/(m K)
vi i i
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K0 m o d i f ied thermal c o n d u c t i v i t y o f a i r
M m ole cu la r mass
N number o f contac t spots per u n i t a rea
P m a t e r i a l hardness
P0 la s e r power
R c o a t i n g - s u b s t r a t e thermal wave r e f l e c t i o n
c o e f f i c i e n t
ft thermal c o n ta c t r e s is t a n c e
Rm thermal contac t r e s i s t a n c e o f rough
s u r fa c e s in contact
S a p p l ie d s t r e s s
T m a t e r i a l temperature
c o a t i n g - s u b s t r a t e thermal wave t ra n sm is s io n
c o e f f i c i e n t
Tm(A) i n f r a r e d o p t i c s t ransmiss io n f a c t o r
Zi thermal impedance
L i s t o f Greek symbols
a thermal d i f f u s i v i t y
£ o p t i c a l ab so rp t io n c o e f f i c i e n t
§ e l e c t r o m a g n e t ic sk in depth
q e m i s s i v i t y
-q l i g h t to heat conversion f a c t o r
q i n f r a r e d c o l l e c t i o n angleo
^ wavelength o f l i g h t
thermal wavelength
^ thermal d i f f u s i o n length
H p e r m e a b i l i t y o f metal
p e r m e a b i l i t y o f f r e e space
m a t e r i a l d e n s i ty
Vo
pq e l e c t r i c a l c o n d u c t i v i t y
t her ma l wave ve c t or
W/(m K)
Kg
m-a
N/ma
Ul
ma K /W
ma K /W
N/ma
K
U/(ma K)
ma /s
m_1
degree
m
m
Kg m~3
( O m ) " 1
m ~1
I X
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q S t e f a n - B o 1tzmann constan t W/(m KB )e
^ t ime constan t s
(D angular f requency r a d ia n s~x
p Thermal wave r e f l e c t i o n c o e f f i c i e n t1 t
O S o l id ang le o f in f r a r e d r a d i a t i o n d e t e c t i o n s t e r a d ia nX Z I R
X
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C h a p t e r 1
P h o t o t h e r m a l I n f r a r e d T e c h n i q u e s
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CHAPTER i PHOTOTHERMAL INFRARED TECHNIQUES
1 . 1 IN TR OD U C TIO N
PLASMA SPRAY COATINGS AND T H E I R Q U A L IT Y CONTROL
S u r f a c e c o a t i n g s a p p l i e d b y p l a s m a s p r a y i n g a r e
b e i n g i n c r e a s i n g l y u t i l i s e d i n t h e p o w e r g e n e r a t i o n and
a e r o s p a c e i n d u s t r i e s t o p r o v i d e f u n c t i o n a l l y e f f e c t i v e
s u r f a c e s C l - 3 3 . T h e c o a t i n g p r o c e s s c o m b i n e s i n t o a
s i n g l e o p e r a t i o n t h e m e l t i n g , q u e n c h i n g and
c o n s o l i d a t i o n s t a g e s o f m a t e r i a l s p r o c e s s i n g . W i t h
p l a s m a s p r a y i n g t h e c o a t i n g p r o c e s s i n v o l v e s t h e
m e l t i n g o f p o w d e r e d c o a t i n g m a t e r i a l i n a p l a s m a f l a m e
a n d t h e a c c e l e r a t i o n o f t h e m o l t e n m a t e r i a l a t s o n i c
v e l o c i t i e s t o w a r d s t h e s u b s t r a t e . On i m p a c t w i t h t h e
s u b s t r a t e t h e s e p a r t i c l e s r a p i d l y d e f o r m , q u e n c h and
s o l i d i f y on t h e s u b s t r a t e ( o r p r e v i o u s l y s o l i d i f i e d
c o a t i n g m a t e r i a l ) . T h i s c a p a b i l i t y o f t h e t e c h n i q u e
a l l o w s m a t e r i a l s t o b e d e p o s i t e d w i t h c o m p o s i t i o n s
i n d e p e n d e n t o f t h e r m o d y n a m i c l i m i t a t i o n s , t h e c o n t r o l
o f c o a t i n g m i c r o s t r u c t u r e and i t s p h y s i c a l p r o p e r t i e s .
Common a p p l i c a t i o n s o f p l a s m a s p r a y e d c o a t i n g s
i n c l u d e t h e p r o t e c t i o n o f b a r e m e t a l l i c s u r f a c e s f r o m
w e a r , e r o s i o n , c o r r o s i o n , o x i d a t i o n ; f o r t h e r m a l o r
e l e c t r i c a l i n s u l a t i o n / c o n d u c t i o n and f o r r e c l a m a t i o n
o f w o r n c o m p o n e n t s . C o a t i n g t h i c k n e s s e s a p p l i e d r a n g e
b e t w e e n .1 and 1 mm, and m e t a l s , a l l o y s , c e r a m i c s ,
c e r m e t s and p l a s t i c s c a n b e d e p o s i t e d o n a l m o s t any
s u b s t r a t e . T h e g r o w i n g a p p l i c a t i o n s o f p l a s m a s p r a y e d
c o a t i n g s i n many h i g h - t e c h i n d u s t r i e s h a s l e d t o
i n c r e a s e s i n t h e d e m an d s f o r c o a t i n g q u a l i t y and
s u i t a b l e c o n t r o l m e t h o d s f o r a s s e s s i n g c o a t i n g
1
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i n t e g r i t y , d u r i n g b o t h d e p o s i t i o n and i t s s e r v i c e l i f e .
P r e s e n t q u a l i t y c o n t r o l m e t h o d s o f p l a s m a s p r a y e d
c o a t i n g s i n c l u d e
a) p r ocess c o n t r o l ,
b) d e s t r u c t i v e and
c) n o n - d e s t r u c t i v e t e s t i n g .
T h e p r o d u c t i o n o f h i g h q u a l i t y d e p o s i t s w i t h u n i f o r m
m i c r o s t r u c t u r e an d c o a t i n g t h i c k n e s s r e q u i r e s a c a r e f u l
c o n t r o l o f t h e c o a t i n g m a t e r i a l a nd s p r a y i n g
p a r a m e t e r s . C u r r e n t e f f o r t s i n g u a r a n t e e i n g
r e p r o d u c i b l e h i g h q u a l i t y d e p o s i t s i n c l u d e t h e
d e v e l o p m e n t o f s p r a y i n g s y s t e m s f e a t u r i n g c o m p u t e r i s e d
c o n t r o l o f s p r a y i n g p a r a m e t e r s a n d a u t o m a t i o n o f
c o m p o n e n t h a n d l i n g .
D e s t r u c t i v e t e s t m e t h o d s r e q u i r e s t h e u s e o f c o u p o n
s a m p l e s w i t h t h e r e s e r v a t i o n t h a t t h e t e s t s a m p l e may
n o t h a v e t h e same c r o s s - s e c t i o n n o r h a v e b e e n p r e p a r e d
i n e x a c t l y t h e same m a n n e r a s t h e c o m p o n e n t .
D e s t r u c t i v e e x a m i n a t i o n p r o c e d u r e s i n c l u d e a d h e s i o n
(ASTM C 6 3 3 - 7 9 ) and h a r d n e s s t e s t s , m e t a l l o g r a p h i c
exam i n a t i o n u s i n g o p t i c a l and s c a n n i n g e l e c t r o n
m i c r o s c o p y .
A p a r t f r o m d i m e n s i o n a l c h e c k s t h e u s e f u l n e s s o f
n o n - d e s t r u c t i v e t e s t i n g ( N D T ) m e t h o d s f o r m o n i t o r i n g
c o a t i n g q u a l i t y h a s y e t t o b e d e m o n s t r a t e d w i t h t h e
d e v e l o p m e n t and a p p l i c a t i o n o f a s u i t a b l e i n s p e c t i o n
t e c h n i q u e ( s ) .
F i g u r e s 1 . 1 a - c , s u m m a r i s e r e s p e c t i v e l y , t h e p l a s m a
s p r a y s u r f a c e c o a t i n g p r o c e s s , t h e common c o a t i n g
2
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m a t e r i a l s c u r r e n t l y u t i l i s e d a nd t h e p r i n c i p l e d e f e c t s
f o u n d i n t h e s e c o a t i n g s . T h e a b n o r m a l c o a t i n g
c o n d i t i o n s i n c l u d e , c o a t i n g / s u b s t r a t e , c o a t i n g /
c o a t i n g d e l a m i n a t i o n , s u r f a c e ' b r e a k i n g c r a c k s ,
p o r o s i t y , s u r f a c e / i n t e r f a c e and c o a t i n g t h i c k n e s s
v a r i a t i o n s . T h e m a i n r e q u i r e m e n t s o f t h e i n s p e c t i o n
t e c h n i q u e may b e s u m m a r i s e d a s f o l l o w s .
1) S i n g l e - s i d e d , n o n - c o n t a c t iv e and n o n - d e s t r u c t i v e .
2) P ro v id e d e fe c t d e t e c t i o n and th ic kness measurement.
3) Be a p p l i c a b l e to a wide range o f co a t in g m a t e r i a l s
and complex shaped components.
4) O f f e r remote c a p a b i l i t y and speed in o p e r a t i o n .
1 . E R E V I E U OF PHOTOTHERMAL NDE TECHNIQUES
D u r i n g t h e p a s t d e c a d e t h e r e h a s b e e n r e n e w e d
i n t e r e s t " i n t h e a p p l i c a t i o n o f t h e r m a l i n f r a r e d
t e c h n i q u e s f o r m a t e r i a l s t e s t i n g a n d c h a r a c t e r i s a t i o n .
T h i s h a s made b e e n p o s s i b l e d u e t h e c o m m e r c i a l
a v a i l a b i l i t y o f s t a b l e m e d iu m p o w e r l a s e r s o u r c e s ^
H i g h s e n s i t i v i t y 8 - 1 4 Hm i n f r a r e d < I R ) d e t e c t o r s
c a p a b l e o f d e t e c t i n g a m i l l i d e g r e e c h a n g e i n s u r f a c e
t e m p e r a t u r e ^ and a d v a n c e s i n e l e c t r o n i c s i g n a l
p r o c e s s i n g e q u i p m e n t .
T h e r e a r e i n t h e U n i t e d K i n g d o m s i x r e s e a r c h g r o u p s
c u r r e n t l y e x p l o i t i n g p h o t o t h e r m a l IR t e c h n o l o g y f o r
q u a n t i t a t i v e m a t e r i a l s c h a r a c t e r i s a t i o n and
n o n - d e s t r u c t i v e e v a l u a t i o n . Two - i n d e p e n d e n t r e s e a r c h
t e a m s a r e a t t h e U n i v e r s i t y o f S t r a t h c l y d e and o n e a t
e a c h o f t h e f o l l o w i n g e s t a b l i s h m e n t s . U n i v e r s i t y
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C o l l e g e L o n d o n , H a r w e l l NDT r e s e a r c h c e n t r e , CEGB
M a r c h w o o d L a s e r a p p l i c a t i o n s c e n t r e and t h e U n i v e r s i t y
o f B a t h .
I n t h e f o l l o w i n g p a r a g r a p h s s e v e r a l p h o t o t h e r m a l IR
t e c h n i q u e s a r e r e v i ewed d i s c u s s i n g i n g e n e r a 1 t h e i r
p r i n c i p l e o f o p e r a t i o n , t h e i r m e r i t s and s u i t a b i l i t y
f o r i n s p e c t i n g v a r i o u s t y p e s o f c o a t e d c o m p o n e n t s .
T h e r m a l i n s p e c t i o n m e t h o d s a r e b a s e d on t h e
d e t e c t i o n o f l o c a l v a r i a t i o n i n h e a t p r o p a g a t i o n i n a
s a m p l e . T h e p r e s e n c e o f a d e f e c t o r a t h e r m a l i m p e d a n c e
c h a n g e h a s a d i s t u r b i n g e f f e c t o n t h e h e a t f l o w p a s s i n g
t h r o u g h t h e s a m p l e . T h i s d i s t u r b a n c e i s t r a n s m i t t e d
t o t h e s u r f a c e , w h e r e i t a p p e a r s i n t h e f o r m o f a l o c a l
c h a n g e i n t h e s a m p l e s u r f a c e t e m p e r a t u r e . P h o t o t h e r m a l
r a d i o m e t r y ( P T R ) i s a m e a s u r e m e n t t e c h n i q u e w h i c h c a n
m o n i t o r t h e s e t h e r m a l v a r i a t i o n s t h r o u g h t h e
s y n c h r o n i s e d d e t e c t i o n o f e m i t t e d t h e r m a l r a d i a t i o n
f o l l o w i n g r a d i a t i v e h e a t i n g . To d a t e , a v a r i e t y o f
t e c h n i q u e s h a v e b e e n d e v e l o p e d o n t h i s m e a s u r e m e n t
p r i n c i p l e f o r t h e n o n - d e s t r u c t i v e n e a r s u r f a c e
e x a m i n a t i o n o f m a t e r i a l s [ 5 - 2 1 1 . T h e s e t h e r m a l m e t h o d s
o f f e r s e v e r a l a d v a n t a g e s o v e r c o n v e n t i o n a l NDT
t e c h n i q u e s s u c h a s u l t r a s o n i c s , X - r a y r a d i o g r a p h y and
e d d y c u r r e n t . T h e y a r e n o n - c o n t a c t i v e , s i n g l e - s i d e d
and o f f e r r e m o t e c a p a b i l i t y . T h e y a l l o w t h e i n s p e c t i o n
o f a w i d e r a n g e o f m a t e r i a l s a n d c o m p l e x s h a p e d
c o m p o n e n t s a n d s e v e r a l c o m p l e m e n t a r y t e c h n i q u e s b a s e d
on t h e same d e t e c t i o n p r i n c i p l e a r e a v a i l a b l e .
A p p l i c a t i o n s r e p o r t e d i n t h e o p e n l i t e r a t u r e
i n c l u d e :
4
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a) th ic kness measurements, d e f e c t d e t e c t i o n , imaging, thermal
p r o p e r ty d e t e rm in a t io n and monitor ing thermal cyc l ing
damage o f coat ings [ 6 , 8 , 9 , 2 2 - 2 5 3
b) d e t e c t i o n and imaging o f impact damage, f i b r e debonding and
e f f e c t i v e thermal p r o p e r t y e v a lu a t i o n o f composite
polymeric m a t e r i a ls [26 -283
c) semi-conduct ing m a t e r i a l s examinat ion f o r d e t e c t io n of
processing d e f e c t s , imaging o f doped reg io ns ,
d e t e r m in a t io n o f c a r r i e r e l e c t r o n i c p r o p e r t i e s and bonding
d e fe c ts in soldered j o i n t [29 -313
d) in s p e c t io n o f b i o l o g i c a l m a t e r i a l s [3 2 ,333
e) spec t roscop ic s tu d ie s o f opaque and t r a n s l u c e n t m a t e r i a l s
[ 3 ^ , 3 5 3 .
1« 2 • 1 PHOTOTHERMAL RADIOMETRY AND THERMOGRAPHY
PTR i s a d y n a m i c m e a s u r e m e n t m e t h o d r e l y i n g on t h e
a c t i v e h e a t i n g ( o r c o o l i n g ) o f t h e s a m p l e t o r e v e a l i t s
i n t e r n a l s t r u c t u r e . I n t h e a b s e n c e o f an a c t i v e
t h e r m a l s t i m u l u s , t h e t e c h n i q u e i s m o r e c o m m o n ly known
as t h e r m o g r a p h y o r t h e r m a l i m a g i n g [ 3 6 3 . T h e r m o g r a p h y
i s a p a s s i v e I R i n s p e c t i o n m e t h o d m o n i t o r i n g t h e
t h e r m a l e m i s s i o n d i f f e r e n c e d u r i n g h e a t e x c h a n g e
b e t w e e n t h e s a m p l e and i t s e n v i r o n m e n t t o r e v e a l
p a s s i b l e i n t e r n a l n o n - u n i f o r m i t i e s .
An im a g e o b t a i n e d b y m a p p i n g t h e p h o t o t h e r ma 1 s i g n a 1
a m p l i t u d e i s a s u p e r p o s i t i o n o f an o p t i c a 1 i m a g e ,
t h e r m o g r a p h i c i m a g e ( a r i s i n g f r o m s t r u c t u r e s o f a v e r a g e
t e m p e r a t u r e and IR e m i s s i v i t y ) , and an i m a g e o f t h e r m a 1
s t r u c t u r e s . T h i s l a t t e r p i e c e o f i n f o r m a t i on i s t h e
m ost r e l e v a n t f o r t h e r m a l ND T. I n add i t i o n , t h e t ime
5
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i n f o r m a t i o n c o n t a i n e d w i t h t h e p h o t o t h e r m a l s i g n a l c a n
b e p r o c e s s e d t o p r o v i d e a new s i g n a l t h a t i s o n l y
s e n s i t i v e t o t h e t h e r m a l and g e o m e t r i c p a r a m e t e r s o f
t h e s a m p l e . H e n c e , a c o m p l e t e d e s c r i p t i o n o f t h e
s a m p l e s ’ s u b s u r f a c e t h e r m a l s t r u c t u r e may b e p o s s i b l e .
F i n a l l y , t a b l e 1 . 1 s u m m a r i s e s t h e r e l a t i v e m e r i t s and
n o n - m e r i t s o f t h e r m o g r a p h i c and p h o t o t h e r m a l IR
m e t h o d s .
1 • 3 D E S C R I P T I O N OF PTR T EC H N IQ U E S
T h e p h o t o t h e r m a l e f f e c t i s t h e g e n e r a t i o n and
p r o p a g a t i o n o f h e a t i n a s a m p l e b y t h e a b s o r p t i o n o f
o p t i c a l r a d i a t i o n . H e a t i s g e n e r a t e d i n t h e s a m p l e
t h r o u g h a v a r i e t y o f n o n - r a d i a t i v e r e l a x a t i o n p r o c e s s e s
a l m o s t i n s t a n t a n e o u s l y , t y p i c a l l y l e s s t h a n 1 0 “ 10
s e c o n d s f o r c o n d u c t o r s and i n s u l a t o r s . T h e d e p t h o f
h e a t g e n e r a t i o n i n t h e s a m p l e i s d e t e r m i n e d b y t h e
o p t i c a l a b s o r p t i o n c o e f f i c i e n t o f t h e s a m p l e . W i t h
o p t i c a l i l l u m i n a t i o n on m e t a l l i c s a m p l e s l i g h t
a b s o r p t i o n i s c o n f i n e d t o t h e s u r f a c e t y p i c a l l y a f e w
t e n t h s o f a m i c r o m e t e r . T h e d e p t h o f l i g h t a b s o r p t i o n
c a n b e d e t e r m i n e d t o a f i r s t a p p r o x i m a t i o n b y t h e
e l e c t r o m a g n e t i c s k i n d e p t h f o r t h e s a m p l e C 3 7 1 :
w h e r e X i s t h e w a v e l e n g t h o f t h e l i g h t , c , t h e s p e e d
o f l i g h t , cr, i s t h e e l e c t r i c a l c o n d u c t i v i t y o f t h e
m e t a l , F and F,;;. a r e p e r m e a b i l i t y o f t h e m e t a l and f r e e
s p a c e r e s p e c t i v e l y . U s i n g t h e D r u d e f r e e e l e c t r o n
t h e o r y o f m e t a l s , i t c a n b e sh o w n t h a t t h e f r a c t i o n o f
i n c i d e n t p o w e r a b s o r b e d b y a m e t a l i s g i v e n
( l . i )J t O C H j l
6
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a p p r o x i m a t e l y by L371
( 1 .2 ) A = 4JtC [L
X aH e n c e s h o r t w a v e l e n g t h l i g h t s o u r c e s ( e . g . i n t h e
v i s i b l e and u l t r a - v i o l e t ) a r e m o r e e f f i c i e n t f o r
s a m p l e h e a t i n g as r e f l e c t i o n l o s s e s a r e t h e n a t a
p h o t o t h e r m a l t e c h n i q u e s a r i s e f r o m t h e f o r m o f s a m p l e
h e a t i n g a n d t h e IR d e t e c t i o n s c h e m e s u s e d . G e n e r a l l y
l a s e r s a n d i n c o h e r e n t o p t i c a l s o u r c e s a r e u s e d f o r
s a m p l e h e a t i n g . H e a t i n g c a n b e p e r i o d i c * p u l s e d , s t e p
i n t e n s i t y m o d u l a t e d , s p a t i a l l y m o d u l a t e d o r s c a n n e d on
t h e s a m p l e s u r f a c e . T h e h e a t i n g c a n a l s o b e l o c a l i s e d
t o a p o i n t , l i n e o r an a r e a o n t h e s a m p l e . T h e t h e r m a l
d e t e c t i o n c a n a l s o b e l o c a l i s e d a s t h e h e a t s o u r c e and
t h e s a m p l e d r e g i o n c a n b e c e n t r a l i s e d , p a r t i a l l y
d i s p l a c e d f r o m o r d i r e c t l y o p p o s i t e t h e h e a t e d r e g i o n .
T h e f o l l o w i n g s e c t i o n s d i s c u s s v a r i o u s p h o t o t h e r m a l
i n f r a r e d m e t h o d s . S p e c i a l a t t e n t i o n b e i n g g i v e n t o t h e
p e r i o d i c p h o t o t h e r m a l t e c h n i q u e d i s c u s s i n g i t s
i n s t r u m e n t a t i o n and m e t h o d s o f s i g n a l a n a l y s i s .
1 . 3 . 1 P E R I O D I C PHOTOTHERMAL H EA TIN G
I n f i g u r e 1 . 2 a s c h e m a t i c i l l u s t r a t i o n i s p r e s e n t e d
s h o w i n g t h e b a s i c c o m p o n e n t s o f a p e r i o d i c p h o t o t h e r m a l
NDT s y s t e m . I n t h i s t e c h n i q u e c h o p p e d s q u a r e w a v e o r
s i n u s o i d a l c o n t i n o u s - w a v e ( CW) o p t i c a l i l l u m i n a t i o n i s
u s e d f o r s a m p l e h e a t i n g f o l l o w e d b y l o c k - i n d e t e c t i o n
o f p e r i o d i c t h e r m a l e m i s s i o n t o o b s e r v e t h e r m a l
v a r i a t i o n s i n t h e s a m p l e .
A l m o s t a l l t h e c u r r e n t l a s e r s h a v e b e e n u s e d f o r
m i n i m u m . T h e d i f f e r e n c e b e t w e e n t h e v a r l o u s
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s a m p l e h e a t i n g . H o w e v e r , t h e Ar + i o n l a s e r a p p e a r s t o
b e t h e m o s t w i d e l y u s e d . T h i s l a s e r p r o v i d e s a
h i g h l y s t a b l e CUI e m i s s i o n s o u r c e w i t h w h i c h
c o n v e n t i o n a l o p t i c a l c o m p o n e n t s c a n b e u s e d w i t h o u t
s p e c i a l s e l e c t i o n .
Beam m o d u l a t i o n i s e i t h e r b y a m e c h a n i c a l c h o p p e r o r
an a c o u s t o - o p t i c d e v i c e . E a r l y e x p e r i m e n t s w i t h t h i s
t e c h n i q u e u s e d m e c h a n i c a l c h o p p e r s w h i c h c o v e r e d a
f r e q u e n c y r a n g e up t o a f e w k i l o h e r t z . M e c h a n i c a l
c h o p p e r s h a v e t h e a d v a n t a g e s o f s i m p l i c i t y and a 100*/.
d e p t h o f m o d u l a t i o n . T h e i r m a i n d i s a d v a n t a g e s a r e p h a s e
j i t t e r n o i s e a t l o w m o d u l a t i o n f r e q u e n c i e s . And a n
u p p e r l i m i t o n t h e m o d u l a t i o n f r e q u e n c y w h i c h
e f f e c t i v e l y s e t t h e t h e r m a l i m a g e r e s o l u t i o n ( s e e
s e c t i o n 2 . 5 ) .
A c o u s t o - o p t i c m o d u l a t o r s a r e now g e n e r a l l y u s e d .
T h e y p r o v i d e a d i g i t a l c o n t r o l o f t h e m o d u l a t i o n
f r e q u e n c y o v e r a w i d e r a n g e , 0 t o t e n s MHz and i m m u n i t y
f r o m t h e p h a s e j i t t e r a s s o c i a t e d w i t h lo w f r e q u e n c y
m o d u l a t i o n f r o m m e c h a n i c a l c h o p p e r s . T h e e x c i t i n g w a v e
f o r m c a n a l s o b e s e l e c t e d ( s i n e o r s q u a r e w a v e s ) and
t h e m o d u l a t i o n d e p t h c a n b e a s h i g h a s 90*/..
T h e r m a l e m i s s i o n f r o m t h e s a m p l e h a v e b e e n r e m o t e l y
s e n s e d b y a v a r i e t y o f IR d e t e c t o r s . G o l a y c e l l and
p y r o e l e c t r i c ( L i T a Q ' 3 , > T G S . . . ) - d e v i c e s i n t h e
f r e q u e n c y r a n g e l e s s t h a n , 2 0 0 H z . S e m i c o n d u c t o r ( C M T ,
I n S b , P b S n T e ) d e v i c e s a r e u s e d f o r h i g h f r e q u e n c y
o p e r a t i o n s up t o 100 KHz C 5 - 9 , 3 8 ] .
SIGNAL PRO CESSIN G AND IN T E R P R E T A T IO N
T h e p h o t o t h e r m a l s i g n a l g e n e r a t e d i n s o l i d s a m p l e s
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i s q u i t e w e a k . I t i s t h e r e f o r e n e c e s s a r y t o i n c r e a s e
t h e e l e c t r i c a l o u t p u t f r o m an I R s e n s o r b y a lo w n o i s e
p r e - a m p 1 i f i e r . T h i s e l e c t r o n i c c i r c u i t i s a l r e a d y
p r e s e n t i n m o s t c o m m e r c i a l l y a v a i l a b l e I R d e t e c t o r s .
The o u t p u t f r o m t h e d e t e c t o r c a n t h e n b e d i r e c t l y
a p p l i e d t o t h e l o c k - i n a m p l i f i e r . U s i n g t h e r e f e r e n c e
s i g n a l f r o m t h e o p t i c a l m o d u l a t i o n d r i v e r , t h e l o c k - i n
a m p l i f i e r c a n p r o v i d e t w o c o m p o n e n t s o f t h e
p h o t o t h e r m a l s i g n a l :
a ) t h e m a g n i t u d e and p h a s e .
b ) t h e i n - p h a s e and q u a d r a t u r e s i g n a l .
When o n l y t h e a m p l i t u d e a n d p h a s e o f t h e d e t e c t e d
s i g n a l i s m o n i t o r e d , t h e p h a s e i n f o r m a t i o n o f t h e
s i g n a l i s m o s t u s e f u l a s i t i s o n l y r e l a t e d t o t h e
t h e r m a l a n d g e o m e t r i c p r o p e r t i e s o f t h e s a m p l e . 1 When
t h e i n - p h a s e a nd q u a d r a t u r e c o m p o n e n t s a r e r e c o r d e d ,
t h e q u a d r a t u r e i s s e n s i t i v e t o s u b s u r f a c e t h e r m a l
s t r u c t u r e an d t h e i n - p h a s e c o m p o n e n t m a i n l y t o t h e
s u r f a c e o p t i c a l s t r u c t u r e .
A n o t h e r t y p e o f s i g n a l a n a l y s i s u s e d w i t h t h i s
t e c h n i q u e i s p h a s e a n g l e a d j u s t m e n t . H e r e t h e p h a s e o f
t h e r e f e r e n c e s i g n a l i s a d j u s t e d t o d e t e c t s e l e c t i v e l y
t h e p h o t o t h e r m a l s i g n a l w i t h a s p e c i f i e d p h a s e d e l a y .
I f l o c k - i n d e t e c t i o n i s d o n e d i g i t a l l y t h e n t h i s l a t t e r
m e t h o d o f s i g n a l a n a l y s i s e n a b l e s t h e u s e r t o
r e c o n s t r u c t a s u b s u r f a c e t h e r m a l im a g e o f t h e s a m p l e a t
a n y d e s i r a b l e d e p t h f r o m t h e s u r f a c e .
1 T h i s i s d i s c u s s e d i n d e t a i l i n s e c t i o n E . ^ . 1
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The s i m p l i c i t y o f t h e e x p e r i m e n t a l a p p a r a t u s and a
w e l l d e v e l o p e d t h e o r y h a v e p r o v i d e d t h e m a i n d r i v i n g
f o r c e f o r t h e r a p i d e x p l o i t a t i o n o f t h i s t e c h n i q u e
s i n c e i t s d e m o n s t r a t i o n f o r m a t e r i a l s t e s t i n g b y N o r d a l
and K a n s t a d and L u u k k a l a i n 1 9 8 0 C5D. R e a r s i d e C 6 , 2 3 1
and d i s p l a c e d d e t e c t i o n C7D s c h e m e s h a v e a l s o b e e n
i n v e s t i g a t e d . An a d v a n t a g e o f t h e f o r m e r d e t e c t i o n
sch em e i s a g r e a t e r d e p t h o f i n s p e c t i o n , a f e w
m i l l i m e t r e s , l i m i t e d o n l y b y t h e e x p e r i m e n t a l
s i g n a l - t o - n o i s e r a t i o . Two d i s a d v a n t a g e s o f t h i s
t r a n s m i s s i o n d e t e c t i o n m e t h o d a r e t h e r e q u i r e m e n t o f
a c c e s s t o t h e r e a r s u r f a c e and a l o s s i n t h e a b i l i t y t o
d e t e r m i n e t h e d e p t h o f a s u b s u r f a c e d e f e c t . T h i s
f o l l o w s f r o m t h e f a c t t h a t t h e s i g n a l - c h a n g e s r e c o r d e d
r e f l e c t o n l y a p r o j e c t i o n o f t h e i n t e r n a l t h e r m a l
s t r u c t u r e C63 i n a n a l o g y w i t h i m a g e s o b t a i n e d b y x - r a y
r a d i o g r a p h y .
When t h e h e a t i n g and I R d e t e c t i o n s p o t o n t h e s a m p l e
s u r f a c e a r e p a r t i a l l y d i s p l a c e d , t h e t e c h n i q u e i s
s e n s i t i v e t o t h e r m a l c h a n g e s p a r a l l e l t o t h e s u r f a c e
C7D and t h u s m o r e s u i t a b l e f o r d e t e c t i n g s u r f a c e
b r e a k i n g c r a c k s and t h e r m a l p r o p e r t y v a r i a t i o n s a l o n g
t h e s u r f a c e .
A r e c e n t d e v e l o p m e n t on t h e a b o v e b a s i c t e c h n i q u e i s
t h e p a r a l l e l d e t e c t i o n o f a l a r g e n u m b e r o f s a m p l e
p a i n t s w i t h a n IR v i d e o c a m e r a and d i g i t a l
p h a s e - s e n s i t i v e s i g n a l p r o c e s s i n g . R a p i d i n s p e c t i o n o f
l a r g e c o m p o n e n t a r e a s i s now f e a s i b l e . M o d u l a t i o n
f r e q u e n c i e s up t o 2 0 0 Hz h a v e b e e n d e m o n s t r a t e d w i t h
t h i s m e t h o d [ 3 9 , ^ 0 1 . T h e u p p e r l i m i t a t i o n on t h e
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m o d u l a t i o n f r e q u e n c y i s d e t e r m i n e d e i t h e r b y t h e
t h e r m a l i m a g e d i g i t i s a t i o n r a t e o r t h e p i x e l p r o c e s s i n g
r a t e o f t h e I R c a m e r a d e t e c t o r e l e m e n t .
1 . 3 . 2 PULSED PHOTOTHERMAL H EA T IN G
T he p u 1s e d p h o t o t h e r m a l t e c h n i q u e i s t h e m o s t w i d e l y
e x p l o i t e d o f a l l t h e p h o t o t h e r m a l m e t h o d s and h a s b e e n
r e a l i s e d i n two c o m m e r c i a l i n s t r u m e n t s ; L a s e r i n s p e c t
2 0 0 0 f r o m V a n z e t t i I n c . C313 and T h e r m a l w a v e i m p e d a n c e
s c a n n e r f r o m H a n f o r d E n g i n e e r i n g l a b o r a t o r y C 1 3 1 .
T h r e e s c h e m e s o f i n s p e c t i o n h a v e b e e n d e v e l o p e d w i t h
p u l s e d h e a t i n g : " p o i n t " h e a t i n g w i t h " p o i n t " d e t e c t i o n ,
l i n e h e a t i n g w i t h l i n e I R d e t e c t i o n and a r e a h e a t i n g
w i t h a r e a d e t e c t i o n b y an I R c a m e r a .
P O IN T H E A T IN G UIITH P O IN T INFRARED D ETE C TIO N
I n t h i s a r r a n g e m e n t , f i g u r e 1 . 3 a , s a m p l e h e a t i n g i s
p r o v i d e d b y a s h o r t p u l s e Ng*, N d - Y A G , o r COsa l a s e r .
T h e e v o l v i n g t r a n s i e n t t h e r m a l e m i s s i o n s i g n a l i s
d e t e c t e d b y a f a s t I R s e m i c o n d u c t o r d e t e c t o r , ( I n d i u m
a n t i m o n i d e i n t h e 3 - 5 Hm b a n d o r Cadmium m e r c u r y
t e l l u r i d e i n t h e 8 - 14 Hm b a n d ) . A l a r g e b a n d w i d t h
t r a n s i e n t r e c o r d e r i s u s e d f o r s i g n a l r e c o r d i n g and
a v e r a g i n g o v e r a nu m b er o f p u l s e s . M e a s u r e m e n t t i m e s
r a n g e f r o m a f e w m i l l i s e c o n d s f o r m e t a l s t o s e v e r a l
s e c o n d s f o r i n s u l a t o r s . Common a p p l i c a t i o n s r e p o r t e d
w i t h t h i s m e t h o d i n c l u d e t h e r a p i d d e t e c t i o n o f
s u b s u r f a c e d e f e c t s , t h e r m a l and o p t i c a l p r o p e r t y
d e t e r m i n a t i o n and a u t o m a t e d i n s p e c t i o n o f s o l d e r e d
j o i n t s .
L I N E H E A T IN G U I T H L I N E INFRARED DETECTIO N
A s c h e m a t i c i l l u s t r a t i o n o f t h i s t e c h n i q u e i s shown
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i n f i g u r e 1 . 3 b . A h o t a i r j e t o f 5 m i l l i s e c o n d p u l s e
d u r a t i o n i s u s e d t o h e a t t h e s a m p l e s u r f a c e . The
s a m p l e i s t h e n moved a s h o r t d i s t a n c e and t h e d e c a y i n g
t h e r m a l e m i s s i o n i s d e t e c t e d b y a l i n e IR s c a n n e r a t
two p r e d e t e r m i n e d t i m e i n t e r v a l s . S a m p l e t r a n s l a t i o n
i s r e q u i r e d t o a v o i d t h e r m a l e m i s s i o n i n t e r f e r e n c e f r o m
t h e h e a t s o u r c e . T h e I R s e n s o r s a m p l e s t h e s u r f a c e a t
a r a t e o f 2 5 6 l i n e s / s e c o n d and t h e d i g i t i s e d o u t p u t
i s a v e r a g e d o v e r a f i n i t e t i m e i n t e r v a l t o e n h a n c e t h e
s i g n a l t o n o i s e r a t i o . L a r g e s a m p l e a r e a s c a n be
i n s p e c t e d b y t h i s t e c h n i q u e b y c o n t i n u o u s l y s t e p p i n g
and p u l s e h e a t i n g t h e s a m p l e . T h e u s e o f l a s e r
h e a t i n g h a s y e t t o b e d e m o n s t r a t e d w i t h t h i s l i n e
s c a n n i n g t e c h n i q u e a nd m e a s u r e m e n t s h a v e o n l y b e e n
r e p o r t e d on t h e r m a l s p r a y c o a t i n g s C1 3 , A 1 - A 3 3 .
AREA H E A T IN G AND INFRARED CAMERA D E TEC TIO N
An I R c a m e r a i s a v e r s a t i l e t h e r m a l r a d i a t i o n
d e t e c t o r a l l o w i n g p o i n t , l i n e and a r e a d e t e c t i o n o f t h e
t h e r m a l r a d i a t i o n . I n a n a r e a s e n s i n g mode o f
o p e r a t i o n t h e c a m e r a o f f e r s t h e a b i l i t y t o m o n i t o r and
r e c o r d t r a n s i e n t t h e r m a l d i f f u s i o n e f f e c t s i n a s a m p l e
b y p a r a l l e l s c a n n i n g w i t h g o o d s p a t i a l , t e m p o r a l and
t e m p e r a t u r e r e s o l u t i o n . O p e r a t i n g a t v i d e o —f r a m e
r a t e s a t h e r m a l s c e n e c a n b e im a g e d i n 2 0 m i l l i s e c o n d s .
Two t y p e s o f t h e r m a l i m a g e r s h a v e b e e n e v a l u a t e d f a r
u s e w i t h t h i s mode o f h e a t i n g : c o o l e d s e m i c o n d u c t o r and
p y r o e l e c t r i c v i d i c o n c a m e r a . T h e l a t t e r p r o v i d e s room
t e m p e r a t u r e o p e r a t i o n and i s a c h e a p e r a l t e r n a t i v e t o
t h e s e m i c o n d u c t o r c a m e r a C 2 6 D .
An a r r a n g e m e n t o f t h i s a r e a s e n s i n g p u l s e d
t h e r m o g r a p h i c t e c h n i q u e i s sh own i n f i g u r e 1 . 3 c i n a
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t r a n s m i s s i o n mode o f o p e r a t i o n . H i g h e n e r g y f l a s h and
IR lam p s w i t h c o n v e n t i o n a l m i r r o r o p t i c s i s u s e d t o
u n i f o r m l y h e a t t h e s a m p l e . T h e t r a n s i e n t t h e r m a l
s i g n a l f r o m t h e s a m p l e i s t h e n r e c o r d e d by t h e c a m e r a
c o l l e c t i n g some 1 0 , 0 0 0 p o i n t m e a s u r e m e n t on t h e s a m p l e
e v e r y SO m i l l i s e c o n d s . A t t h e sam e t i m e t h e im a g e i s
r e c o r d e d on a v i d e o t a p e . T h e r e c o r d e d im a g e c a n t h e n
be a n a l y s e d v i s u a l l y b y p l a y i n g b a c k t h e i m a g e s a f r a m e
a t a t i m e and s i n g l e l i n e s f r o m t h e im a g e c a n be
e x t r a c t e d f o r m o r e q u a n t i t a t i v e s t u d y . Im ag e
p r o c e s s i n g t e c h n i q u e s i n c o r p o r a t i n g t r a n s i e n t t h e r m a l
d i f f u s i o n m o d e l s c a n a l s o b e r e a d i l y a p p l i e d t o t h e
t h e r m a l i m a g e s [ 1 5 - 1 7 , 2 6 - 5 8 ] .
1 . 3 . 3 STEP PHQTDTHERMAL H E A T IN G
S t e p i n t e n s i t y m o d u l a t i o n o f f e r s a n o t h e r v a r i a n t t o
t r a n s i e n t t h e r m a l t e c h n i q u e s . I t s a p p l i c a t i o n t o
t h e r m a l p r o p e r t y m e a s u r e m e n t s h a s s h o w n t h a t lo w p o w e r
la m p s ( r a t h e r t h a n p u l s e d l a s e r s ) c a n b e u s e d t o s t e p
e x c i t e t h e s a m p l e w i t h much r e d u c e d o v e r a l l h e a t i n g o f
t h e s a m p l e [ ^ , ^ 5 ] . A s c h e m a t i c i l l u s t r a t i o n o f a
s t e p h e a t i n g t e c h n i q u e u s i n g a l a s e r s o u r c e i s shown i n
f i g u r e 1 . A- . When m e a s u r e m e n t s t i m e s a r e l o n g , t h e
t r a n s i e n t e m i s s i o n c a n be c h o p p e d a t a h i g h f r e q u e n c y
and r e c o r d e d b y p h a s e s e n s i t i v e d e t e c t i o n . T h i s
r e m o v e s t h e n e e d o f t r a n s i e n t r e c o r d e r t o c a p t u r e t h e
s i g n a l . T h i c k n e s s and t h e r m a l r e s i s t a n c e m e a s u r e m e n t
on t h e r m a l b a r r i e r p l a s m a s p r a y e d c o a t i n g h a v e b e e n
r e p o r t e d by C i e l o and D a l l i a r e CA-6] u s i n g t h i s
t e c h n i q u e .
13
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1 . 3 . 4 COORDINATE MODULATION PHOTOTHERMAL HEATING
I n t h i s t e c h n i q u e h e a t i n g i s a l t e r n a t e d b e t w e e n two
a d j a c e n t s p o t s on t h e s a m p l e s u r f a c e a s show n i n f i g u r e
1 . 5 . P h a s e s e n s i t i v e IR d e t e c t i o n i s t h e n u s e d t o
m o n i t o r t h e t h e r m a l v a r i a t i o n b e t w e e n t h e h e a t e d s p o t s .
I f t h e s a m p l e p r o p e r t i e s a r e i d e n t i c a l a t t h e h e a t e d
r e g i o n s t h e n a n u l l s i g n a l w i l l b e o b t a i n e d . T h u s
m a k i n g t h e t e c h n i q u e s e n s i t i v e t o s m a l l v a r i a t i o n s i n
t h e t h e r m a l p r o p e r t i e s o f t h e s a m p l e d r e g i o n . L e t h o
e t a l CEO! h a v e i n v e s t i g a t e d t h i s t e c h n i q u e f o r
t h i c k n e s s m e a s u r e m e n t o f p l a s m a s p r a y e d t u n g s t e n
c a r b i d e on s t e e l . T h e i r r e s u l t s s h o w e d t h a t t h i c k n e s s
a r e s o l u t i o n o f £ 5 Hm i s p o s s i b l e w i t h t h i s c o a t i n g
s y s t e m .
1 . 3 . 5 SCANNING PHOTOTHERMAL H E A T IN G
By s c a n n i n g a l o c a l i s e d h e a t s o u r c e i n a r a s t e r
f a s h i o n on a s a m p l e s u r f a c e a n d d e t e c t i n g t h e t h e r m a l
r a d i a t i o n f r o m t h e h e a t e d s p o t , r a p i d i n s p e c t i o n o f
l a r g e s a m p l e a r e a c a n be m a d e , f i g u r e 1 . 6 . T h i s
a r r a n g e m e n t was w i d e l y e x p l o i t e d i n t h e l a t e 1 9 6 0 7s
u s i n g a s i n g l e e l e m e n t I R d e t e c t o r and e x t e r n a l o p t i c a l
s c a n n i n g t o f o c u s t h e h e a t e d s p o t o n t o t h e d e t e c t o r
e l e m e n t C 4 7 , 4 8 3 . The m o d e r n v e r s i o n o f t h i s t e c h n i q u e
u s e s t h e b u i l t i n o p t i c a l s c a n n i n g f a c i l i t i e s o f an IR
c a m e r a t o s e n s e t h e c h a n g i n g t h e r m a l e m i s s i o n f r o m t h e
s a m p l e [ 4 9 3 . S u b - s u r f a c e d e f e c t s and f a t i g u e c r a c k s
d e t e c t i o n h a s b e e n d e m o n s t r a t e d w i t h t h i s t e c h n i q u e
C 4 7 - 5 0 3 . To m a x i m i s e c o n t r a s t f r o m d e f e c t s an o p t im u m
s c a n n i n g s p e e d n e e d t o be p r e d e t e r m i n e d e x p e r i m e n t a l l y ,
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o r b y n u m e r i c a l m o d e l l i n g . S c a n n i n g t o o r a p i d l y w i l l
l e a d t o a r e d u c t i o n i n t h e s i g n a 1 - t o - n o i s e , t o im a g e
b l u r r i n g and p o o r r e s o l u t i o n .
1 . i* SUMMARY OF PTR NDE METHODS
T h e a b o v e p h o t o t h e r m a l I R t e c h n i q u e s o p e r a t e on a
p r i n c i p l e s i m i l a r t o u l t r a s o n i c p u l s e - e c h o m a t e r i a l s
t e s t i n g . S u b s u r f a c e i m p e r f e c t i o n s i n a m a t e r i a l s a r e
r e v e a l e d b y d e t e c t i o n o f t h e r e f l e c t e d t h e r m a l w a v e o r
p u l s e ( s e e s e c t i o n 2 . 2 ) . I n o p a q u e m a t e r i a l s w i t h
p u l s e d s u r f a c e h e a t i n g , t h e t i m e i n t e r v a l f o r t h e
d e l a y e d s i g n a l t o a p p e a r a t t h e s u r f a c e i s g i v e n by
L ^ / r x , w h e r e L i s t h e d e p t h o f t h e d e f e c t ( o r i n t e r f a c e )
an d oc t h e t h e r m a l d i f f u s i v i t y o f t h e m a t e r i a l . T h i s
s i m p l e r e l a t i o n s h i p sh o w s t h a t l o n g m e a s u r e m e n t t i m e s
w i l l b e r e q u i r e d f o r l o w d i f f u s i v i t y m a t e r i a l s ( i . e .
c e r a m i c s a n d p o l y m e r s ) a n d d e f e c t s d e e p i n t h e
m a t e r i a l . T h e same i n f e r e n c e s a l s o a p p l y t o t h e o t h e r
t h e r m a l m e t h o d s ( p e r i o d i c a n d s c a n n e d h e a t i n g ) s i n c e
a n y t h e r m a l p u l s e c a n b e d e c o m p o s e d i n t o w av e
c o m p o n e n t s t h r o u g h a F o u r i e r t r a n s f o r m a t i o n [ 5 1 3 .
T a b l e 1 . 2 s u m m a r i s e s t h e m a i n a d v a n t a g e s and
d i s a d v a n t a g e s o f a l l t h e PTR m e t h o d s d i s c u s s e d a b o v e .
T h e p r i m a r y a d v a n t a g e s o f t r a n s i e n t m e t h o d s o v e r
p e r i o d i c p u l s e t e c h n i q u e s a r e t h e i r s h o r t m e a s u r e m e n t s
t i m e s and c o m p l e t e s u b s u r f a c e t h e r m a l i n f o r m a t i o n i n a
s i n g l e h e a t i n g p u l s e . T h e i r d i s a d v a n t a g e s a r e t h e
r e q u i r e m e n t o f s i g n a l p r o c e s s i n g , n u m e r i c a l m o d e l l i n g
and e x t e n s i v e c o m p u t a t i o n a l s u p p o r t . I n c o n t r a s t ,
p e r i o d i c p u l s e h e a t i n g t e c h n i q u e s o f f e r s e v e r a l
i m p o r t a n t a d v a n t a g e s o v e r t r a n s i e n t m & t h o d s .
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P h a s e - s e n s i t i v e d e t e c t i o n removes s ig n a l <noise) components
t h a t are not a t the same f requency as the photothermal s i g n a l .
The output from the l o c k - i n a m p l i f i e r p ro v ides d i r e c t l y to the
user the s ig n a l ampl i tude and phase angle i n f o r m a t i o n .
The phase angle s ign a l i s s e n s i t i v e on ly to the samples’
thermal and geometr ic param eter .
Thermal d i f f u s i o n a n a ly s i s i s r e l a t i v e l y s imple f o r many NDT
p rab le m s.
F in e tuning o f the t e s t system is p o s s ib l e f o r optimum
performance by a d ju s t in g the modulat ion f req u en cy .
To o b t a i n s i m i l a r s i g n a l i n f o r m a t i o n w i t h t r a n s i e n t PTR
m e t h o d s i t w i l l b e n e c e s s a r y t o c o m p u t e t h e l o g a r i t h m i c
d e r i v a t i v e o f t h e t r a n s i e n t t h e r m a l s i g n a l .
1 . 4 . 1 S E L E C T IO N OF PTR TEC H N IQ U E
T h e c h o i c e o f w h i c h p a r t i c u l a r PTR t e c h n i q u e t o
a p p l y w i l l d e p e n d on t h e i n s p e c t i o n p r o b l e m . Some o f
t h e p a r a m e t e r s t h a t w i l l r e q u i r e c o n s i d e r a t i o n may b e :
a) the thermal d e g ra d a t io n temperature and the thermal
p r o p e r t i e s o f the m a t e r i a l ,
b) the type o f measurement req u i r e d
( i . e . th ickness gauging, d e f e c t d e t e c t i o n or imag in g) ,
c) component s i z e and geometry,
d) i n s p e c t io n speed,
e) system p o r t a b i l i t y , and
f ) economics.
F i g u r e 1 . 7 o u t l i n e s o n e s e l e c t i o n p r o c e d u r e i n
i d e n t i f y i n g t h e m o st a p p r o p r i a t e PTR m e t h o d f o r c o a t i n g
t h i c k n e s s m e a s u r e m e n t . T h e s e l e c t i o n c r i t e r i a i s b a s e d
on t h e m a g n i t u d e o f t h e t h e r m a l d e l a y t i m e d e f i n e d
a b o v e . F o r a r e l a t i v e l y t h i n a n d / o r h i g h l y c o n d u c t i v e
s u r f a c e c o a t i n g , t h e p e r i o d i c h e a t i ng t e c h n i q u e w i l l
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o f f e r e x c e l l e n t s i g n a 1- t o - n o i s e ( S / N ) r a t i o s and s h o r t
m e a s u r e m e n t t i m e s d u e t o t h e h i g h m o d u l a t i o n
f r e q u e n c i e s r e q u i r e d f o r t e s t i n g ( s e e s e c t i o n 2 . . 1 ) .
I f t h e c o a t i n g t h i c k n e s s i s l a r g e and i t s t h e r m a l
c o n d u c t i v i t y l o w , a t r a n s i e n t e x c i t a t i o n PTR s y s t e m i s
m o re s u i t a b l e a s m e a s u r e m e n t t i m e s w i t h a m o d u l a t e d PTR
t e c h n i q u e c a n b e l a r g e , t y p i c a l l y s e v e r a l 1 0 ’ s o f
s e c o n d s - I n t h e i n t e r m e d i a t e c a s e s t h e s e l e c t i o n
b e t w e e n t h e t h e v a r i o u s PTR t e c h n i q u e s w i l l n e e d t o be
d e t e r m i n e d e x p e r i m e n t a l l y .
T h e i n s p e c t i o n o f l a r g e c o m p o n e n t s a r e a s r e q u i r e s
t h e a p p l i c a t i o n o f an a r e a s e n s i t i v e PTR m e t h o d , i . e .
I R d e t e c t i o n w i t h e i t h e r I R l i n e s c a n n e r o r I R v i d e o
c a m e r a . T h e s e l e c t i o n o f t h e a p p r o p r i a t e PTR
t e c h n i q u e t h e n e s s e n t i a l l y f o l l o w s t h a t f o r c o a t i n g
t h i c k n e s s m e a s u r e m e n t s e x c e p t w h en v e r y t h i n s u r f a c e
l a y e r s a r e t o b e i n s p e c t e d . I n t h i s c a s e t h e m o v i n g
l i n e s o u r c e PTR t e c h n i q u e w i t h s y n c h r o n i s e d l i n e IR
w i l l n e e d t o b e i n v e s t i g a t e d C ^ 9 3 .
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Table 1 .1 : Advantages and d isadvantaqes o f thermographic and
photothermal ra d io m etr ic mater i a l s t e s t i n q .
Technique
Thermography
Photothermalrad io m et ry
Advantages
No a c t i v e h e a t in g necessary
Large area in sp ec t io n
Complex o b j e c t s
Severa l techniques a v a i l a b l e
Large area in s p e c t io n
Complex o b j e c t s
E m i s s iv i t y independent
Disadvantages
Surface e m i s s i v i t y var i at ions
Weak s e n s i t i v i t y to subsurface d e f e c t s
Sample h e a t in g r e q u i r e d
Laser hazard
Accurate thermal d i f f u s i o n models r e q u i r e d f o r quant i t a t ive a n a ly s i s
High s e n s i t i v i t y to subsurface d e f e c t s
Q u a n t i t a t i v e thermal a n a l y s i s
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Tab 1e 1 . g : Advantages and disadvantaqes o f PTR NDE te chn iq ues .
METHOD ADVANTAGES DISADVANTAGES
Ii
jPERIODIC
Simple te s t appara tus .
1
High noise re jec t ion.
iE m is s iv i ty independent.
IDepth p r o f i l i n g , thickness measurement and d efect d e te c t io n .
Thermal proper ty eva lua t ion.
High background heat i ng.
Depth p r o f i l i n g re q u i re s severa l frequency measurements.
1
PULSED
Minimum background h e a t i n g .
F as t .
Remote c a p a b i l i t y .
Complete subsurface in format ion in a s in g le measurement.
Thicknessmeasurement, de fec t d e te c t io n and thermal proper ty d e te rm in a t ion .
Extensive computer support requ ired fo r s ig na l processing and numerical a n a l y s i s .
Accurate thermal d i f f u s i o n model(s) needed fo r quanti t a t i v e a n a ly s is .
Signal averaging re quired to improve s i g n a l - t o noise r a t i o .
STEP
As above.
Reduced measurement t imes.
Smal ler dynamic temperature change.
As above
I
COORDINATEMODULATION
j
Simple te s t appara tus .
S e n s i t i v e to small changes in thermal propert i e s .
Comparative measurements o n ly .
1Uniform sur face o p t i c a l p r o p e r t i e s r e q u i r e d .
MOVINGSOURCE
j
F a s t .
Detect io n of f a t i g u e cracks and th i n f l 1ms.
Uniform sur face o p t ic a l p r o p e r t i e s requi r e d .
Optimum scanning speed needs to be determined fo r
! subsurface lnspec 1 1 on.
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FLAME TEMPERATURES 4,000 - 12, 1000 K
o° ooo °
CDATING MATERIAL
PLASMAFLAME
F i g u r e l a : A s c h e m a t i c
p l a s m a s p r a y i n g .
AIR DR INERT GAS ATMDSPHERE
SONIC VELOCITIES
o o
MOLTEN COATING PARTICLES
LdI—
COATINGLAYERS
i l l u s t r a t i o n o f c o a t i n g d e p o s i t i o n by
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METALS 8c CERAMICSALLOYS Ala D3 , Cr203
Al, Cu, Mo, w Zr02- Y20 3NlAl, Steels Z r0 2~ MgO
CERMETSNlCr-carbldej Nl-Graphlte, VC + Co
SURFACE COATING
METAL & ALLDYS Mo, NlAl M-CrAlY<M= Nt Co, Fe >
BOND COAT
SUBSTRATESTEELSSUPERALLOYS
LAYER THICKNESS
0,1 to 1 nm
^ 0.1 m
F i g u r e l b : F r e q u e n t l y u s e d m a t e r i a l s and t h e c o a t i n g / s u b s t r a t e
s y s t e m i n p l a s m a s p r a y i n g .
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SURFACE RDUGHNESS SURFACE BREAKINGCRACK
* SUBSURFACE• CRACKS
CDATING
DELAMINATIDN
PDRDSITYCLUSTERS
SUBSTRATE
F i g u r e l c : Some common d e f e c t s i n p l a s m a s p r a y e d c o a t i n g s .
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LIGHT CHOPPER SAMPLE
r o
oo
EMISSION
IR SENSOR
REF.SIGNAL
LOCK-INAMPLIFIER
LASER SOURCE
MICROCOMPUTER
SAMPLESCANNINGSYSTEM
Figure 1.2: A periodic PTR inspection system.
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N>
IR REFLECTING MIRRDR
SAMPLE
FILTERSEMICONDUCTORDETECTORREF.
SIGNAL
TRANSIENTRECORDER
PULSED LASER
MICROCOMPUTER
SAMPLESCANNINGSYSTEM
Figure 1.3a: A pulsed PTR instrumentation with spot illumination.
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SOURCE IR RADIATIDN SHEILD
IR LINE SCANNER
HOT AIR JET
SAMPLE
SAMPLE TRAVEL DIRECTION
AIR JET HEATER
SAMPLEDRIVER
DISPLAY ANDDATASTORAGE
L CONTROLLING ~ COMPUTER
IR SCANNER ELECTRONICS
F i g u r e 1 . 3 b : A p u l s e d PTR i n s t r u m e n t a t i o n w i t h l i n e h e a t i n g .
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TESTPIECEFLASHLAMP . MONITOR
INFRARED CAMERA 625 LINES PER FRAME
APPLICATION
FLASHCONTROL
POWER SUPPLY
MONITORVIDEO TIMERVIDEO TYPE
WRITERRECORDING VIDEO CASSETTE RECORDER
FIELD CONTROLMDNITDRDIAL-A-LINE
STRIPPERX-Y
RECORDERSCOPEANALYSIS 101
Figure 1.3c: A pulsed PTR transmission set-up with area heating.
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IR REFLECTING MIRROR
SAMPLE
LASER SOURCE SAMPLESCANNINGSYSTEM
LIGHTCHDPPERSTEP
PULSETRIGGER FILTER
SEMICONDUCTORDETECTDR
REF.SIGNAL
LOCK-INAMPLIFIER
MICROCOMPUTER
Figure 1 . **: A step heating PTR inspection system.
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SENSDR
BEAMDEFLECTDR
LDCK-INAMPLIFIERMICROCOMPUTER
LASER
SAMPLE
SAMPLE SCANNING SYSTEM
F i g u r e 1 . 5 : A c o o r d i n a t e m o d u l a t i o n PTR a r r a n g e m e n t .
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SYNC. PULSE IMAGEBUFFERANDDISPLAY
BEAMDEFLECTORMICROCOMPUTER
VIDEOSIGNALBEAM BLANKING
SIGNAL
CAMERA
A/OMODULATORLASER
SAMPLE
F i g u r e 1 . 6 : A s c h e m a t i c i l l u s t r a t i o n o f a m o v i n g s o u r c e PTR i n s p e c t i o n
s y s t e m . C4-9D
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MDVINGSOURCEPTR
HIGH OR LOWTHERMALCONDUCTIVITY
VERYTHIN
HIGH THERMAL CONDUCTIVITY
MODULATEDPTR
THIN PULSEDPTRCOATING
THICKNESS LOV THERMAL CONDUCTIVITY “
STEPPTR
PCKCOATING
PCKSUBSTRATE
HIGH THERMAL CONDUCTIVITY
MODULATED DR TRANSIENT PTR
THICKLOV THERMAL CONDUCTIVITY TRANSIENT PTR
F i g u r e 1 . 7 : A s e l e c t i o n g u i d e o f t h e m o s t a p p r o p r i a t e PTR i n s p e c t i o n
t e c h n i q u e f o r t h i c k n e s s m e a s u r e m e n t .
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C h a p t e r 2
P h o t h e r m a l R a d i o m e t r i c D e t e c t i o n T h e o r y
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CHAPTER E PHOTOTHERMAL R A D IO M E T R IC D E TE C T IO N THEORY
a. 1 IN TR OD U C TIO N
T h e t e c h n i q u e o f p h o t o t h e r m a l r a d i o m e t r y i n v o l v e s
m o d u l a t e d o p t i c a l h e a t i n g o f a s a m p l e and t h e d e t e c t i o n
o f e m i t t e d t h e r m a l i n f r a r e d ( I R ) r a d i a t i o n f r o m
s o m e w h e r e on t h e s a m p l e . T h e i n c r e a s e d b l a c k b o d y
t h e r m a l e m i s s i o n s i g n a l r e c o r d e d i n a p h o t o t h e r m a l
m e a s u r e m e n t c a n g e n e r a l l y b e g i v e n t h r o u g h an
e x p r e s s i o n l i k e C 5 2 1 :
( 2 . 1 a ) Signal^S x . 5 ^.S3S i » Sa> and S3 a r e s i g n a l c o n t r i b u t i o n t e r m s d e t e r m i n e d
r e s p e c t i v e l y b y t h e t e m p e r a t u r e and t h e r m a l p r o p e r t i e s
o f t h e s a m p l e , I R c o l l e c t i o n e f f i c i e n c y o f t h e t e s t
s y s t e m a nd t h e I R d e t e c t o r s e n s i t i v i t y . T h e s e t e r m s
c a n b e e x p r e s s e d a s f o l l o w s :
(2 .16) S x a3T
f e ( A . , r ) l / ( A , r ) d Xk
S 2** A radO JR J 7 m (kX')dX
S 3«D* .U h e r e
T is the ab so lu te temperature o f the sample,
X is the emission wave length ,
€( X »T ) is the IR e m i s s i v i t y o f the sample1,
W( X , T ) is the blackbody s p e c t r a l r a d i a n t e x c i t a n c e ,
cST is the induced temperature increment ,
A r«d is the thermal emission area on the sample,
R is the s o l i d angle over which the thermal
r a d i a t i o n is c o l l e c t e d ,
1 I g n o r i n g t h e d i r e c t i o n a l d e p e n d e n c e o f s u r f a c e t h e r m a l e m i s s i o n .
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T„,( X ) is the s p e c t r a l t ra n s m is s io n o f the IR
c o l l e c t i o n o p t i c s ,
D“ is the IR d e te c to r s e n s i t i v i t y .
I n t h e f o l l o w i n g p a r a g r a p h s a d e t a i l e d d i s c u s s i o n i s
g i v e n o f t h e t e r m S , w h i c h c o n t a i n s t h e t h e r m a l
e m i s s i o n c h a r a c t e r i s t i c s a n d t h e i n d u c e d s u r f a c e
t e m p e r a t u r e c h a n g e o f a s a m p l e f o l l o w i n g o p t i c a l
h e a t i n g . P a r t i c u l a r e m p h a s i s i s g i v e n t o o p a q u e\
l a y e r e d s t r u c t u r e s h a r m o n i c a l l y h e a t e d b y a l a s e r b e a m .
A w a v e d e s c r i p t i o n o f h e a t d i f f u s i o n i n a s a m p l e i s
i n t r o d u c e d a n d some common a p p 1 i c a t i o n s t o t h e r m a l NDT
a r e e x a m i n e d . T o p i c s d i s c u s s e d i n c l u d e t h e r e f l e c t i o n
and t r a n s m i s s i o n o f h e a t a t a n i n t e r f a c e and
i n t e r f e r e n c e a n d i n t e r f e r o m e t r y w i t h h e a t w a v e s . A
d i s c u s s i o n o f t h e t e r m s Se a n d S3 i s p r o v i d e d i n
c h a p t e r 3 .
5 . 1 . 1 THERMAL E M I S S I O N C H A R A C T E R IS T IC S
T h e s p e c t r a l d i s t r i b u t i o n o f s u r f a c e r a d i a n c e f r o m a
s a m p l e v a r i e s w i t h i t s t e m p e r a t u r e a n d c a n b e
r e p r e s e n t e d e x p l i c i t l y b y P l a n c k ’ s r a d i a t i o n
f u n c t i o n C 5 3 3 :
2 nhc2( 2 . 2 ) t / ( T , A) = --- ---
1
A5 L e x p f / i c /A / c T ) - 1 _f o r a n i d e a l b l a c k b o d y e m i t t e r . h , and k a r e
r e s p e c t i v e l y , t h e P l a n c k a n d B o l t z m a n n c o n s t a n t , c t h e
s p e e d o f l i g h t and T t h e a b s o l u t e t e m p e r a t u r e . T h e
i n c r e m e n t a l c h a n g e i n t h e r a d i a n c e w i t h c h a n g e s i n t h e
s a m p l e t e m p e r a t u r e , c o r r e s p o n d i n g t o t h e d e r i v a t i v e o f
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t h e P l a n c k ' s f u n c t i o n , i s g i v e n b y t h e e x p r e s s i o n :
a 1 / ( 7 , A . ) 2 n h * c 3 ( t i c ) 1
^ 2 , 3 ) a r " k T 2k * e X P U / c T j \ _ e x p ( h c / k f c T ) - 1 _
I n f i g u r e 2 . 1 and 2 . 2 t h e s e f u n c t i o n s a r e p l o t t e d f o r
d i f f e r e n t s a m p l e t e m p e r a t u r e s . F i g u r e 2 . 2 c o r r e s p o n d s
t o t h e m o d u l a t e d t h e r m a l IR e m i s s i o n s i g n a l d e t e c t e d i n
a p h o t o t h e r m a l m e a s u r e m e n t . F o r s a m p l e s h e a t e d t o n e a r
a m b i e n t t e m p e r a t u r e s p e a k t h e r m a l e m i s s i o n l i e s b e t w e e n
9 t o 10 Fm. A l s o , a t l o w e r w a v e l e n g t h s t h e t h e r m a l
e m i s s i o n d e c r e a s e s r a p i d l y a n d a t l o n g e r w a v e l e n g t h s
t h e d e c r e a s e i s g r a d u a l an d n e a r l y i n d e p e n d e n t o f
t e m p e r a t u r e . When t h e s e f u n c t i o n s a r e i n t e g r a t e d
a c r o s s t h e e m i s s i o n s p e c t r u m , t h e t o t a l r a d i a n c e i s
p r o p o r t i o n a l t o t h e f o u r t h p o w e r o f t h e t e m p e r a t u r e
( S t e f a n - B o 1 t z m a n n L a w ) . T h e i n c r e m e n t a l c h a n g e i n
r a d i a n c e w i t h t e m p e r a t u r e i s p r o p o r t i o n a l t o t h e t h i r d
p o w e r o f t h e s t e a d y s t a t e t e m p e r a t u r e o f t h e s a m p l e and
d i r e c t l y p r o p o r t i o n a l t o tfT f o r a s m a l l c h a n g e i n t h e
s a m p l e s u r f a c e t e m p e r a t u r e :
(2.4) 6W =6a [ ( r0 + Td<; + 67)4- ( r 0+ r dJ 4]
- 4 e o ( T 0 + T dc)36 T
T 0 i s t h e a m b i e n t s a m p l e t e m p e r a t u r e ; T dc i s t h e
s t e a d y s t a t e t e m p e r a t u r e r i s e o f t h e s a m p l e and cr =
5 . 6 7 x l O - 1 2 W cm ” 2 K“ 4 i s t h e S t e f a n - B o 1 t z m a n n
c o n s t a n t . T he c u b i c t e m p e r a t u r e d e p e n d e n c e o f <£W c a n be
e x p l o i t e d t o i n c r e a s e t h e s i g n a 1 - t o - n o i s e r a t i o o f t h e
d e t e c t e d s i g n a l . H o w e v e r , t h i s w i l l b e a t t h e e x p e n s e
o f an i n c r e a s e d c o h e r e n t n o i s e s i g n a l d u e t o c h a n g e s
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AT i n t h e s a m p l e ' s b a c k g r o u n d t e m p e r a t u r e :
6 1 / A T( 2 . 5 ) A W = d — A T = 3 6 W —
J 3 T T
E x a m i n a t i o n o f f i g u r e 2 . 2 sh o w s t h a t t h e t h i s n o i s e
s i g n a l w i l l b e r e d u c e d i f I R d e t e c t i o n i s a t l o n g IR
w a v e 1e n g t h s .
2 . 1 THERMAL WAVES
When a s u r f a c e i s s u b j e c t e d t o p l a n e h a r m o n i c
h e a t i n g , t h e e q u a t i o n d e s c r i b i n g t h e d i f f u s i o n o f h e a t
i n t o t h a t s a m p l e h a s a w a v e l i k e s o l u t i o n f o r t h e
t e m p e r a t u r e d i s t r i b u t i o n C54-3:
( 2 . 6 ) 7 ( x . < ) = ^ o ^ e x p T - x / f / - + J J .
T ( x , t ) i s t h e t e m p e r a t u r e r i s e a b o v e t h e e q u i l i b r i u m
a m b i e n t t e m p e r a t u r e , I 0 m a g n i t u d e o f t h e s u r f a c e h e a t
f l u x a n d F i s t h e t h e r m a l d i f f u s i o n l e n g t h
( 2 . 7 ) i i = a / n f
w i t h oc = t h e t h e r m a l d i f f u s i v i t y a nd f t h e m o d u l a t i o n
f r e q u e n c y . T h e t h e r m a l d i f f u s i v i t y i s e q u a l t o
( 2 . 8 ) a = k/pCw h e r e k i s t h e t h e r m a l c o n d u c t i v i t y , p t h e d e n s i t y and
C t h e s p e c i f i c h e a t c a p a c i t y . L i k e n o r m a l p r o p a g a t i n g
w a v e s , t h e t h e r m a l w a v e h a s an o s c i l l a t o r y s p a t i a l
d e p e n d e n c e o f t h e f o r m ’ e x p ( i k x ) ’ , w i t h a w a v e v e c t o r
g i v e n b y 1 / F . H o w e v e r , u n l i k e n o r m a l p r o p a g a t i n g
w a v e s , t h e t h e r m a l w a v e i s a l s o v e r y h e a v i l y damped
( e x p ( - x / H ) ) w i t h a d a m p i n g c o e f f i c i e n t 1 / F . I n o n e
t h e r m a l w a v e l e n g t h , 2 t t f , t h e a m p l i t u d e o f t h e t h e r m a l
wav e i s r e d u c e d b y a f a c t o r e x p ( - 2 T T ) = 0 . 0 0 1 9 . T h e
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t h e r m a l d i f f u s i o n l e n g t h c a n r a n g e f r o m a f e w
m i l l i m e t r e s (mm) a t lo w m o d u l a t i o n f r e q u e n c i e s t o
f r a c t i o n s o f mm a t h i g h e r m o d u l a t i o n f r e q u e n c i e s .
T a b l e 2 . 1 l i s t s t h e t h e r m a l p r o p e r t i e s and t h e r m a l
d i f f u s i o n l e n g t h s f o r v a r i o u s common e n g i n e e r i n g
m a t e r i a l s and t h e r m a l s p r a y c o a t i n g s .
The a b o v e p l a n e t h e r m a l w a v e e q u a t i o n c a n a l s o be
u s e d t o d e r i v e t h e t h e r m a l w a v e r e f l e c t i o n and
t r a n s m i s s i o n c o e f f i c i e n t a t a t h e r m a l b o u n d a r y ( s e e
a p p e n d i x 1 ) . F o r two h o m o g e n e o u s m e d i a i n p e r f e c t
t h e r m a l c o n t a c t t h e r e f l e c t i o n a n d t r a n s m i s s i o n
c o e f f i c i e n t f o r n o r m a l l y i n c i d e n t t h e r m a l w a v e s a r e
g i v e n b y t h e e q u a t i o n s [ 5 5 3 :
(2.9) * = 7 ^ : 7' = 7^ tl+o 1+6
where b = »/( P i C i f c i J
f o r t h e r m a l w a v e s i n c i d e n t f r o m m e d iu m o n e t o med ium
t w o . As an e x a m p l e , i f t h e t h e r m a l i m p e d a n c e m i s m a t c h
r a t i o ' b 7 b e t w e e n two c o n t a c t i n g s u r f a c e s i s a h a l f ,
t h e n a t h i r d o f t h e i n c i d e n t t h e r m a l e n e r g y i s
r e f l e c t e d and t w o - t h i r d s i s t r a n s m i t t e d .
I t i s i m p o r t a n t t o n o t e t h a t t h e s e t h e r m a l w a v e
r e f l e c t i o n c o e f f i c i e n t s a r e r e a l an d i n d e p e n d e n t o f t h e
m o d u l a t i o n f r e q u e n c y . T h i s i s n o t t h e c a s e , a s w i l l be
s e e n l a t e r , w hen t h e c o n t a c t b e t w e e n tw o m e d i a i s
p a r t i a l . I n t h i s s i t u a t i o n t h e s e c o e f f i c i e n t s b eco m e
c o m p l e x and f r e q u e n c y d e p e n d e n t .
E q u a t i o n 2 . 6 a l s o sho w s t h a t t h e s u r f a c e t e m p e r a t u r e
i s i n v e r s e l y p r o p o r t i o n a l t o t h e s q u a r e r o o t o f t h e
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m o d u l a t i o n f r e q u e n c y and t h e p h a s e l a g s t h e h e a t i n g
s o u r c e b y 4 5 d e g r e e s . T h i s i n d e p e n d e n c e o f t h e s u r f a c e
p h a s e a n g l e f r o m t h e m o d u l a t i o n f r e q u e n c y f o r a
s e m i - i n f i n i t e s a m p l e c a n b e u t i l i s e d i n n o r m a l i s i n g
e x p e r i m e n t a l p h a s e a n g l e d a t a f o r q u a n t i t a t i v e
a n a l y s i s .
g . g ONE D IM E N SIO N A L SURFACE TEMPERATURE EXP R E S S IO N S
When p e r i o d i c a l l y c h o p p e d l i g h t i l l u m i n a t e s an
o p a q u e s a m p l e t h e r e s u l t i n g s u r f a c e t e m p e r a t u r e
d i s t r i b u t i o n a s s u m i n g o n e d i m e n s i o n a l ( I D ) h e a t f l o w ,
c a n b e w r i t t e n a s a sum o f t h r e e t e m p e r a t u r e s C 5 6 3 :
( 2 . 1 0 ) T ( x ) = T 0 + T ( x ) d c - T ( x ) ae
w h e r e T0 i s t h e a m b i e n t t e m p e r a t u r e o f t h e s a m p l e , Tcic=
t h e s t e a d y s t a t e and T ^ t h e p e r i o d i c t e m p e r a t u r e o f
t h e s a m p l e d u e t o o p t i c a l h e a t i n g ( s e e a p p e n d i x 2 ) .
F o r a n o p a q u e s e m i - i n f i n i t e s a m p l e t h e r a t i o o f t h e
d c / a c s u r f a c e t e m p e r a t u r e c a n d i f f e r b y a n o r d e r o f
m a g n i t u d e a s show n i n t h e f o l l o w i n g e x a m p l e f o r a n LC1B
p l a s m a s p r a y c o a t i n g .
Let the coat in g o p t i c a l r e f l e c t i v i t y be 0 . 5 , o p t i c a l heat g e n e r a t in g e f f i c i e n c y n = l , la y e r th ic k n e s s 200 Fm, the in c id e n t l a s e r power P0 , o f 1 wat t over an a rea o f .65 mm r a d i u s . 2 The steady s t a t e sur face temperature can then be e v a lu a te d form:
( l - r ) f P a \ L x
\ r c r gJ k— = 8 . 5 C
and the p e r io d i c s u r face temperature a t a modula t ion frequency of 81 Hz
2 L a s e r beam r a d i u s c o r r e s p o n d s t o t h e A r g o n i o n l a s e r u s e d i n t h e i n v e s t i g a t i o n s .
3 A t t h i s f r e q u e n c y t h e . 2 mm l a y e r w i l l b e s e m i - i n f i n i t e t o t h e t h e r m a l w a v e .
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T a b l e 2 . 2 s u m m a r i s e s t h e p r i n c i p l e o n e d i m e n s i o n a l
s u r f a c e t e m p e r a t u r e e x p r e s s i o n s f o r t h e r m a l wave
i n s p e c t i o n o f s u r f a c e c o a t i n g s . R e w r i t i n g t h e p e r i o d i c
s u r f a c e t e m p e r a t u r e e x p r e s s i o n f o r an o p t i c a l l y o p a q u e
l a y e r on a t h i c k s u b s t r a t e a s :
1 + r e x p ( - 2 c r Z )(1 -r)/0(2.11) T ac2 k a
(1-r)/2k<y
1 - rexp(-2crZ)_ 2rexp(-2tfZ)
1 + 1 - rexp(-2crl)t h e p r e s e n c e o f a s u r f a c e l a y e r i s s e e n t o add a
c o r r e c t i o n t e r m t o t h e t e m p e r a t u r e t h a t w o u l d h a v e b e e n
o b t a i n e d f o r a s e m i - i n f i n i t e l a y e r . T h e m a g n i t u d e o f
t h e c o r r e c t i o n t e r m d e p e n d s o n t h e t h e r m a l wa ve
r e f l e c t i o n c o e f f i c i e n t j T , a t t h e c o a t i n g / s u b s t r a t e
i n t e r f a c e a n d o n t h e t h e r m a l t h i c k n e s s ( L / H ) .t
F u r t h e r e x p a n s i o n o f t h i s e q u a t i o n s h o w s t h a t t h e
s u r f a c e t e m p e r a t u r e i s c o m p o s e d o f many t h e r m a l w ave
r e f l e c t i o n s f r o m t h e c o a t i n g / s u b s t r a t e a n d t h e
c o a t i n g / g a s i n t e r f a c e s :
( l - O / .(2.12) T ac = 1 + 2 L r nexp ( -2n<fL' )rt- 12 k a
l h i s d e s c r i p t i o n o f t h e r m a l w a v e p r o p a g a t i o n i n t h e
s u r f a c e l a y e r ( o r l a y e r e d m e d i a ) i s a n a l o g o u s t o t h a t
o f o p t i c a l i n t e r f e r e n c e i n t h i n t r a n s l u c e n t f i l m s .
T h u s e q u a t i o n s 2 . 1 1 - 2 . 1 2 p h y s i c a l l y r e p r e s e n t t h e r m a 1
w av e i n t e r f e r e n c e i n a t h i n o p t i c a l l y o p a q u e f i l m C 5 7 I .
I t i s t h i s p h e n o m e n a t h a t a l l o w s t h e r m a l wave
t e c h n i q u e s t o b e u t i l i s e d a s a s e n s i t i v e
i n t e r f e r o m e t r i c m e t h o d f o r n o n - c o n t a c t t h i c k n e s s
m e a s u r e m e n t s .
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g . 3 THREE D IM E N S IO N A L SURFACE TEMPERATURE
EXPRESSIO NS
As m e n t i o n e d i n c h a p t e r 1 , l a s e r beam s a r e w i d e l y
u s e d f o r o p t i c a l h e a t i n g i n p h o t o t h e r m a l N D T . T h e
h e a t e d r e g i o n i s v e r y o f t e n a s m a l l s p o t on t h e s a m p l e
s u r f a c e and h e a t d i f f u s i o n c a n n o t b e s i m p l y r e g a r d e d a s
I D . T h e t e m p e r a t u r e d i s t r i b u t i o n now h a s a n a d d i t i o n a l
d e g r e e o f f r e e d o m . R a d i a l h e a t d i f f u s i o n i n now
p o s s i b l e . T h e s u r f a c e t e m p e r a t u r e o f t h e s a m p l e c a n b e
s e p a r a t e d i n t o t h r e e c o m p o n e n t s :
/2.13/ T(r,z) = T 0(r,2 ) + T dc(r,z)+Toe(r,z)w h e r e r i s t h e d i s t a n c e f r o m t h e c e n t r e o f t h e h e a t i n g
b e a m . A n u m b e r o f a n a l y t i c a l m e t h o d s h a v e b e e n
d e v e l o p e d t o s o l v e t h e t h r e e d i m e n s i o n a l ( 3 D ) t h e r m a l
d i f f u s i o n e q u a t i o n w i t h t h e e n d r e s u l t o f e v a l u a t i n g
t h e p e r i o d i c s u r f a c e t e m p e r a t u r e b y a n i n t e g r a l C 5 8 3 ,
s e r i e s s u m m a t i o n C 5 9 , 6 0 3 , o r a f a s t F o u r i e r t r a n s f o r m
C 6 1 3 . I n t a b l e 2 . 3 t h e s e r i e s r e p r e s e n t a t i o n o f t h e
c o m p l e x h a r m o n i c s u r f a c e t e m p e r a t u r e i s g i v e n f o r a
s e m i - i n f i n i t e o p a q u e s u b s t r a t e and a t h i n o p a q u e l a y e r
on a t h i c k s u b s t r a t e . I n b o t h c a s e s i t i s s e e n t h a t
t h e 3D s u r f a c e t e m p e r a t u r e i s c o m p o s e d o f I D s u r f a c e
t e m p e r a t u r e t e r m an d c o r r e c t i o n t e r m f o r t h e r a d i a l
d i f f u s i o n o f h e a t . I n s p e c t i o n o f t h e 3D s u r f a c e
t e m p e r a t u r e t e r m show s t h a t o n e c a n r e a d i l y w r i t e down
3D s u r f a c e t e m p e r a t u r e e x p r e s s i o n s b y r e p l a c i n g t h e ID
t h e r m a l w a v e v e c t o r , <x= ( j w / a ) 1 / 2 , w i t h ( 7 m 2 +
( jw /o c > ) 1 / 2 . One i m p o r t a n t c o n s e q u e n c e o f t h i s
s u b s t i t u t i o n i s t h e i n c r e a s e d d e c a y r a t e o f t h e s u r f a c e
t e m p e r a t u r e . F i g u r e s 2 . 3 a - c s u m m a r i s e t h e d e p t h d e c a y
o f a p l a n e t h e r m a l w a v e ( 2 . 3 a ) and t h e r a d i a l and d e p t h
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d e c a y o f t h e 3D t e m p e r a t u r e f i e l d ( 2 . 3 b , c ) . F o r a
p u r e l y ID h e a t f l o w t h e m a g n i t u d e o f t h e s u r f a c e
t e m p e r a t u r e d e c r e a s e s b y 1 / e i n a d i s t a n c e o f o n e
t h e r m a l d i f f u s i o n l e n g t h . T h e 3D s u r f a c e t e m p e r a t u r e
d e c a y s m ore r a p i d l y , d e c a y i n g by 1 / e i n a d i s t a n c e o f
H / 3 , f o r t h e t e s t p a r a m e t e r s shown i n f i g u r e 2 . 3 b .
W i t h l o c a l i s e d h e a t i n g a n d l o c a l i s e d IR d e t e c t i o n a
f u r t h e r c o m p l i c a t i o n i s i n t r o d u c e d i n i n t e r p r e t i n g t h e
r e c o r d e d p h o t o t h e r m a l s i g n a l . F i g u r e 2 . 3 d sho w s t h e
v a r i a t i o n o f t h e s i g n a l p h a s e w i t h o p t i c a l s p o t s i z e
and I R d e t e c t i o n a r e a f o r a n o p a q u e s e m i - i n f i n i t e
s a m p l e . ( I t i s a s s u m e d t h a t t h e h e a t i n g and I R
d e t e c t i o n s p o t a r e c o i n c i d e n t ) . T h e p h o t o t h e r m a l s i g n a l
i s t h e n c o m p u t e d f r o m a n i n t e g r a t i o n o f t h e s u r f a c e
t e m p e r a t u r e o v e r t h e e x t e n t o f t h e I R d e t e c t i o n r e g i o n .
F o r p o i n t IR d e t e c t i o n t h e p h a s e a n g l e i s p r e d i c t e d t o
show a p h a s e a d v a n c e a s t h e o p t i c a l s p o t s i z e i s
d e c r e a s e d ( c u r v e 1 ) . T h e p h a s e a n g l e a p p r o a c h e s t h e ID
v a l u e a t o p t i c a l - s p o t s i z e / H r a t i o > 2 0 . H e n c e , t o
a p p l y I D s u r f a c e t e m p e r a t u r e e x p r e s s i o n s t o i n t e r p r e t
e x p e r i m e n t a l p h a s e a n g l e d a t a t h e a b o v e c o n d i t i o n n e e d s
t o be s a t i s f i e d . W i t h an i n c r e a s e i n t h e I R s a m p l i n g
r e g i o n , c u r v e s 2-A- , t h e p h a s e a d v a n c e i s r e d u c e d and
r e t u r n s t o t h e v a l u e e x p e c t e d f o r I D h e a t f l o w , n a m e l y
—4-5 d e g r e e s . T h i s a d d i t i o n a l d e p e n d e n c e o f t h e p h a s e
a n g l e o n t h e o p t i c a l s p o t s i z e and t h e f i n i t e I R
d e t e c t i o n a r e a p r e s e n t s a d i f f i c u l t p r o b l e m s i n
i n t e r p r e t i n g e x p e r i m e n t a l p h a s e a n g l e d a t a
q u a n t i t a t i v e l y .
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g . * f A P P L I C A T I O N TO THERMAL SPRAY COATINGS
I n t h e f o l l o w i n g s e c t i o n s t h e t h e r m a l w a v e r e s p o n s e
f r o m o p t i c a l l y o p a q u e t h e r m a l s p r a y c o a t i n g s i s
e x a m i n e d . I t i s assum ed t h a t t h e s u r f a c e c o a t i n g ( s )
and t h e s u b s t r a t e h a v e u n i f o r m t h e r m a l p r o p e r t i e s and
I D h e a t f l o w c o n d i t i o n s a p p l y . S i g n a l v a r i a t i o n s u n d e r
3D h e a t d i f f u s i o n a r e a l s o c o n s i d e r e d . C o a t i n g
p a r a m e t e r s e x a m i n e d i n c l u d e : v a r i a t i o n s i n c o a t i n g
t h i c k n e s s , t h e r m a l p r o p e r t i e s , s u r f a c e r o u g h n e s s and
s u b s u r f a c e d e f e c t s .
5 . ^ . 1 COATING ON A SUBSTRATE
The e f f e c t s o n t h e s u r f a c e t e m p e r a t u r e a m p l i t u d e and
p h a s e a n g l e f r o m a t h i n o p a q u e c o a t i n g on a
s e m i - i n f i n i t e s u b s t r a t e a r e s h o w n n o r m a l i s e d a g a i n s t
t h e t h e r m a l t h i c k n e s s , L / H » a n d f o r d i f f e r e n t c o a t i n g /
s u b s t r a t e t h e r m a l w a v e r e f l e c t i o n c o e f f i c i e n t s i n
f i g u r e s 2 . 4 - a a n d b . T h e n o r m a l i s a t i o n i s w i t h r e s p e c t
t o t h e c o m p l e x s u r f a c e t e m p e r a t u r e f r o m a s e m i - i n f i n i t e
c o a t i n g . T h e s e two f i g u r e s r e p r e s e n t u n i v e r s a l
d i a g r a m s t h a t c a n b e u s e d t o p r e d i c t t h e v a r i a t i o n s o f
t h e p h o t o t h e r m a l s i g n a l a m p l i t u d e a nd p h a s e f r o m a n y
c o m b i n a t i o n o f a n o p a q u e c o a t i n g o n a s u b s t r a t e when
h e a t d i f f u s i o n i s I D . T h e m a i n e l e m e n t s o f t h e s e
a m p l i t u d e an d p h a s e d i a g r a m s a r e s u m m a r i s e d b e l o w .
1) The l a r g e r the d i f f e r e n c e s between the thermal e f f u s i v i t y
va lu es o f the coat ing and th e s u b s t r a t e (hence a la rg e
thermal wave r e f l e c t i o n c o e f f i c i e n t magnitude) the g r e a t e r
are the changes in the a m p l i tud e and phase o f the
photothermal s i g n a l .
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2) For a g iv en c o a t i n g / s u b s t r a t e r e f l e c t i o n c o e f f i c i e n t
changes in the co a t in g th ic k n e s s gen era te the locus
s p e c i f i e d f o r the c o a t i n g / s u b s t r a t e system, see f i g u r e
2 . 5 a .
3) Any v a r i a t i o n in the thermal p r o p e r t i e s o f the co a t in g and
/o r the s u b s t ra t e w i l l a l t e r the c o a t i n g / s u b s t r a te
thermal wave r e f l e c t i o n c o e f f i c i e n t to a d i f f e r e n t value
thus causing the phase ang le to s h i f t to a new r e f l e c t i o n
c o e f f i c i e n t locus, see f i g u r e 2 . 5 b .
**) Phase an gle measurements have th e advantages over ampl i tude
rec o rd in g o f g r e a t e r depth sens in g , up to 1.5x thermal
d i f f u s i o n le n g th , and being u n a f f e c t e d by v a r i a t i o n s in
the s u r f a c e o p t i c a l p r o p e r t i e s , a b s o r p t i v i t y and
e m i s s i v i t y , o f the sample. The l a t t e r p o i n t can be seen
e x p l i c i t l y by w r i t i n g the argument o f e q u a t io n 2 .11 [ 5 7 ] :
(2.14) A<j>= tan - 1 -2f exp(-2I/ji)sin(2Z//i)1 - r 2exp(-4I/*i)
or q u a l i t a t i v e l y through the phasor diagrams o f f i g u r e 2 . 6
S i n c e t h e r m a l w a v e i n t e r f e r e n c e e f f e c t s c a n o n l y b e
o b s e r v e d up t o 1 . 5 t i m e s t h e t h e r m a l d i f f u s i o n l e n g t h " 1* ,
t h e t e s t f r e q u e n c y f o r i n s p e c t i o n c a n a s a f i r s t
a p p r o x i m a t i o n b e d e t e r m i n e d b y s e t t i n g :
a( 2 . 1 5 ) L / i.i= 1 /
i t L
F o r a 2 5 0 Hm l a y e r o f A l ^ C ^ , L C 1 B , Z r Q G- Y a 0 3 , t h e t e s t
f r e q u e n c i e s a r e f o u n d t o b e 1 1 . 1 , 6 . ^ and 1 . 3 Hz
r e s p e c t i v e l y . I n g e n e r a l a l o w m o d u l a t i o n f r e q u e n c y
i s r e q u i r e d f o r i n s p e c t i n g l a r g e c o a t i n g t h i c k n e s s e s o r
lo w t h e r m a l d i f f u s i v i t y c o a t i n g s .
F i g u r e 2 . 7 sh o w s t h e t h e o r e t i c a l p h a s e a n g l e
A F o r t h e r m a l w a v e g e n e r a t i o n a nd d e t e c t i o n a t t h e s a m p l e s u r f a c e .
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v a r i a t i o n o f t h e s u r f a c e t e m p e r a t u r e when h e a t
d i f f u s i o n i n t h e s a m p l e i s t h r e e d i m e n s i o n a l . The
s u r f a c e c o a t i n g i s L C l t i and t h e s u b s t r a t e 3 1 6 s t a i n l e s s
s t e e l . As n o t e d e a r l i e r , when t h e l a s e r beam d i a m e t e r
i s s m a l l c o m p a r e d t o t h e t h e r m a l d i f f u s i o n l e n g t h ,
d e v i a t i o n s f r o m t h e I D p h a s e l o c u s o c c u r s , t h e
m a g n i t u d e o f w h i c h d e p e n d s on t h e r e l a t i v e r a t i o s o f
t h e a b o v e two d i m e n s i o n s and I R d e t e c t i o n a r e a
C 5 8 , 6 2 1 . F o r l a s e r beam d i a m e t e r s g r e a t e r t h a n 5 0 0
Hm, t h e p h a s e c u r v e s g e n e r a t e d f r o m t h e 3D and I D
s u r f a c e t e m p e r a t u r e e q u a t i o n s c o i n c i d e . I n g e n e r a l , t o
a p p l y I D t h e r m a l d i f f u s i o n a n a l y s i s i n PTR NDT a l a s e r
beam d i a m e t e r o f 2 0 t i m e s t h e l a y e r t h i c k n e s s i s
r e q u i r e d when p o i n t I R d e t e c t i o n u s e d . T h i s
r e q u i r e m e n t c a n b e r e l a x e d , a t t h e e x p e n s e o f r e d u c e d
i m a g e r e s o l u t i o n , i f t h e I R d e t e c t i o n s p o t on t h e
s a m p l e s u r f a c e i s i n c r e a s e d .
5 . *».2 COATING POROSI TY EFFECTS
L o c a l v a r i a t i o n s i n t h e c o a t i n g t h e r m a l p r o p e r t i e s
d u e t o p o r o s i t y c a n be m o d e l l e d b y r e p l a c i n g t h e b u l k
c o a t i n g t h e r m a l p a r a m e t e r s w i t h t h o s e c o r r e c t e d f o r
p o r o s i t y . F o r s p h e r i c a l p o r e s t h e c o r r e c t i o n t e r m s
a r e C 6 3 1 :
(2.16) pC “ (1 - /)pC , fc- (1~ ^ }(1 +0.5/)From t h e s e r e l a t i o n s h i p s i t i s s e e n t h a t t h e c o a t i n g
t h e r m a l e f f u s i v i t y c h a n g e s m o r e r a p i d l y w i t h i n c r e a s i n g
p o r o s i t y t h e s a m p l e ’ s t h e r m a l d i f f u s i v i t y :
l 2 ' 1 7 ) p C t ~ r H o ~ 5I / ) t ( , c t ) -
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w h e r e f i s t h e v o l u m e p o r o s i t y f r a c t i o n a nd s u f f i x o
r e f e r s t o t h e b u l k t h e r m a l p r o p e r t i e s . I n f i g u r e 2 . 8
a p l o t o f t h e n o r m a l i s e d p h a s e a n g l e v a r i a t i o n a g a i n s t
s q u a r e r o o t f r e q u e n c y f o r a 2 0 0 Hm LC1B c o a t i n g on 3 1 6
s t a i n l e s s s t e e l s a m p l e i s p r e s e n t e d w i t h d i f f e r e n t
p o r o s i t y f r a c t i o n s . UJi th i n c r e a s i n g c o a t i n g p o r o s i t y ,
t h e p h a s e a n g l e i s p r e d i c t e d t o i n c r e a s e w i t h r e s p e c t
t o t h e " z e r o " p o r o s i t y c o a t i n g v a l u e . T h i s p h a s e
a d v a n c e i s d u e t o t h e i n c r e a s e i n t h e t h e r m a l i m p e d a n c e
m i s m a t c h and h e n c e t h e t h e r m a l w a v e r e f l e c t i o n
c o e f f i c i e n t b e t w e e n t h e c o a t i n g a nd s u b s t r a t e ( s e e
e q u a t i o n 2 . 9 ) .
2 . . 3 SURFACE ROUGHNESS
T h e r m a l s p r a y c o a t i n g s h a v e i n h e r e n t l y r o u g h
a s - s p r a y e d s u r f a c e s . S u r f a c e r o u g h n e s s c a n r a n g e up
t o 2 5 Hm r m s , a l m o s t 10*/. o f t h e c o a t i n g t h i c k n e s s u s e d
i n many a p p l i c a t i o n s . I n a d d i t i o n t o t h e s u r f a c e
r o u g h n e s s t h e c o a t i n g / s u b s t r a t e i n t e r f a c e i s i r r e g u l a r
d u e t o t h e i n i t i a l r o u g h i n g o f t h e s u b s t r a t e t o p r o m o t e
c o a t i n g a d h e s i o n . To m o d e l t h e r m a l w a v e p r o p a g a t i o n
i n s u c h a s t r u c t u r e i t i s a s s u me d t h a t t h e ’ r o u g h ’
s u r f a c e s o f t h e c o a t i n g c a n b e r e p l a c e d b y a d i s c r e t e
l a y e r o f d i f f e r e n t t h e r m a l p r o p e r t i e s , a s shown i n
f i g u r e 2 . 9 . The s u r f a c e t e m p e r a t u r e o f s u c h a l a y e r e d
s a m p l e , w h e r e t h e s u r f a c e l a y e r i s o p t i c a l l y o p a q u e ,
c a n b e e v a l u a t e d b y a p p l y i n g t h e O s p a l - R o s e n c w a i g d e p t h
p r o f i l i n g t h e o r y C6^+l:
( 1 - r ' i r j l , ,( 2 . 1 8 ) 7' ac *7 InZ '[
4 3
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z [n = zC IZj,".! + Z„tanh u„ Z n + Zj," i tanhu.
w h e r e l a y e r n i s t h e n u mb e r o f s u r f a c e l a y e r s and t h ea r e
u p p e r m o s t l a y e r i s n u mber 1 . t h e t h e r m a l i n p u t
i m p e n d a n c e s .
C o n s i d e r f i r s t t h e e f f e c t s o f a t h e r m a l c o n d u c t i v i t y
v a r i a t i o n i n a c o a t i n g c h a n g i n g s t e p w i s e f r o m a v a l u e
o f 11 a t t h e s u b s t r a t e t o a v a l u e o f 1 a t t h e s u r f a c e .
L e t t h e c o a t i n g t h i c k n e s s b e 1 0 0 Hm. F i g u r e 2 . 1 0 a and
b show t h e c h a n g e s i n s i g n a l a m p l i t u d e a n d p h a s e a n g l e
w i t h r o o t f r e q u e n c y o f a 1 , 2 , a n d 8 l a y e r c o a t i n g
s t r u c t u r e . T h e f i g u r e sho ws t h a t w i t h i n c r e a s e d l a y e r s
and a m o r e g r a d u a l t h e r m a l c o n d u c t i v i t y c h a n g e t h e
t h e r m a l w a v e i n t e r f e r e n c e i s m o r e ’ d i f f u s e d ’ i n
c o m p a r i s o n t o t h e o n e l a y e r t h e r m a l s t r u c t u r e .
T h e t h e r m a l w a v e i n t e r f e r e n c e p a t t e r n f o r a m o d e l l e d
s u r f a c e r o u g h n e s s shown i n f i g u r e 2 . 9 i s shown i n
f i g u r e s 2 . 1 1 a - b f o r d i f f e r e n t t h e r m a l p r o p e r t i e s and
s u r f a c e r o u g h n e s s t h i c k n e s s . T h e p h a s e p l o t s
i l l u s t r a t e d i n t h e s e f i g u r e s a r e n o r m a l i s e d t o a
c o a t i n g t h i c k n e s s o f 100 Hm. F r o m t h e s e f i g u r e s t h e
f o l l o w i n g o b s e r v a t i o n s c a n b e s u m m a r i s e d .
1) W i t h i n c r e a s i n g f r e q u e n c y t h e t h e r m a l w a v e
i n t e r f e r e n c e e f f e c t s w i t h i n t h e s u r f a c e l a y e r
b e c o me i n c r e a s i n g l y a p p a r e n t a s sh o wn by t h e
p h a s e p e a k s i n t h e s e f i g u r e s . Two i n t e r f e r e n c e
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p e a k s a r e s e e n , t h e f i r s t f r o m t h e e f f e c t i v e
t h i c k n e s s o f t h e w h o l e c o a t i n g and s e c o n d l y f r o m
t h e s u r f a c e r o u g h n e s s l a y e r .
2 ) W i t h d e c r e a s i n g t h e r m a l c o n d u c t i v i t y o f t h e
s u r f a c e l a y e r f r o m a b u l k v a l u e o f 4 . ^ t o 2 . 2 W
/m K , t h e t h e r m a l w a v e i n t e r f e r e n c e p e a k s a r e
m o r e p r o n o u n c e d du e t o i n c r e a s i n g d i f f e r e n c e i n
t h e l a y e r / s u b s t r a t e t h e r m a l e f f u s i v i t y .
3 ) I n c r e a s i n g t h e t h i c k n e s s o f t h e s u r f a c e r o u g h n e s s
l a y e r t h e t h e r m a l w a v e i n t e r f e r e n c e p e a k s h i f t s
t o a l o w e r f r e q u e n c y . T h e m a g n i t u d e o f t h e
i n t e r f e r e n c e p e a k r e m a i n s u n c h a n g e d .
2 . 4 - . 4 - C O A T I N G / SUBSTRATE I NTERF ACE DEFECTS
S u b s u r f a c e d e f e c t s i n a c o a t e d c o m p o n e n t f a l l i n
e i t h e r o n e o f t h e f o l l o w i n g t wo c a t e g o r i e s . T h e d e f e c t
c a n b e a l o c a l i s e d r e g i o n o f c o m p l e t e s e p a r a t i o n o r
c o n s i s t s o f r e g i o n s i n p a r t i a l c o n t a c t C 6 5 , 6 6 1 . I n
b o t h c a s e s , t h e c o m p l e x s u r f a c e t e m p e r a t u r e , s e e t a b l e
2 . 2 , t a k e t h e same f o r m a s e q u a t i o n 2 . 1 1 b u t w i t h T
r e p l a c e d r e s p e c t i v e l y w i t h :
r 1 + r 2 e ~ 3 a * L*( 2 . 1 9 ) r = — i----- ? :-ia-L
i + r 1r 2e 22w h e r e
1 - b i 1 - 5 , 2( 2 . 2 0 ) r , - — - i a n d
l + 0 ',| I + 6 2
f o r t h e a i r g a p m o d e l , and
1 - b i + R'k2o 2< 2 - 2 1 > r = T ~ r — f i t - 51 b i + K k 2 o i
f o r t h e c o n t a c t r e s i s t a n c e m o d e l .
I n f i g u r e 2 . 1 2 t h e p h a s e v a r i a t i o n o f w i t h r o o t
f r e q u e n c y i s p r e s e n t e d f o r t h e a b o v e two d e f e c t s i n 3 1 6
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s t a i n l e s s s t e e l 0 . 5mm b e l o w t h e s u r f a c e f o r a r a n g e o f
a i r g a p t h i c k n e s s e s 53 and t h e r m a l c o n t a c t r e s i s t a n c e s .
T h e f i g u r e shows a c h a r a c t e r i s t i c p h a s e l o c u s f o r b o t h
d e f e c t t y p e s . A t l ow m o d u l a t i o n f r e q u e n c i e s t h e p h a s e
a n g l e shows an a d v a n c e w i t h r e s p e c t t o t h e d e f e c t f r e e
p h a s e c u r v e . W i t h i n c r e a s i n g f r e q u e n c y t h i s p h a s e
a d v a n c e t u r n s i n t o a p h a s e l a g . T h e s e t h e o r e t i c a l
c u r v e s a l s o p r e d i c t t h e f r e q u e n c y a t w h i c h a d e f e c t
b e c o m e s u n d e t e c t a b l e .
T h e s i m i l a r i t y o f t h e t h e r m a l w a v e p h a s e f o r b o t h
d e f e c t m o d e l s c a n b e s e e n e x p l i c i t l y by e x p a n d i n g t h e
r e f l e c t i o n c o e f f i c i e n t f o r l o w and h i g h f r e q u e n c y . A t
l o w m o d u l a t i o n f r e q u e n c i e s , t h e t h e r m a l w a v e v e c t o r s cr*
and (js a r e b o t h s m a l l and r r e d u c e s t o :
2 r i o t z 2 i—( 2 . 2 2 ) r « £ , e
f o r t h e a i r g a p m o d e l , and
JR k i cf i i——( 2 . 2 3 ) r **— - — £.g roccrlocyja)
f o r t h e t h e r m a l c o n t a c t r e s i s t a n c e m o d e l . A t h i g h
f r e q u e n c i e s b o t h e x p r e s s i o n s f o r F t e n d t o u n i t y a n d
a r e a l s o f r e q u e n c y i n d e p e n d e n t .
g - ^ - 5 DEFECT D ETEC TI ON S E N S I T I V I T Y
F i g u r e 2 . 1 3 and 2 . 1 ^ p l o t t h e p h a s e d i f f e r e n c e
( p h a s e a n g l e a t t h e d e f e c t m i n u s t h e p h a s e a t a d e f e c t
f r e e r e g i o n ) w i t h s q u a r e r o o t f r e q u e n c y f o r an a i r - g a p
t y p e d e f e c t i n c o a t e d o r b u l k m a t e r i a l s . T h e b u l k
S i n c l u d i n g g a s t h e r m a l c o n d u c t i v i t y c o r r e c t i o n a t s m a l l a i r gap t h i c k n e s s , s e e b e l o w .
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m a t e r i a l s c h o s e n a r e a l u m i n i u m a nd e p o x y r e s i n a s t h e y
h a v e an o r d e r o f m a g n i t u d e d i f f e r e n c e i n t h e t h e r m a l
e f f u s i v i t y w i t h r e s p e c t t o 3 1 6 s t a i n l e s s s t e e l , t h e
s u b s t r a t e m a t e r i a l i n t h e c o a t e d s i t u a t i o n . T h e c o a t e d
s t r u c t u r e s c o n s i s t o f a 0 . 5 mm s u r f a c e l a y e r o f
a l u m i n i u m , o r LC1B o r Y t t r i a s t a b i l i s e d z i r c o n i a on 3 1 6
s t a i n l e s s s t e e l .
C o n s i d e r i n g f i r s t t h e a i r g a p d e f e c t p l o t s o f f i g u r e
2 . 1 2 a n d 2 . 1 3 , when t h e a i r ga p t h i c k n e s s , L a »‘
a p p r o a c h e s t h e mean f r e e p a t h o f t h e a i r m o l e c u l e s , d ,
a c o r r e c t i o n f o r t h e g a s t h e r m a l c o n d u c t i v i t y m u s t be
ma d e . I n a p p e n d i x 3 t h e g a s c o n d u c t i v i t y c o r r e c t i o n
f a c t o r
(2.24) K a - K 0/ [ 1 + 7 7 )
i s d e r i v e d . d and F a r e t a k e n t o b e 0 . 1 5 Hm and 3
r e s p e c t i v e l y ( t h e a c c o m m o d a t i o n f a c t o r i m p l i c i t i n F i s
t a k e n t o b e 0 . 5 f o r b o t h s u r f a c e s ) . I n a d d i t i o n t o t h e
a b o v e d i s c u s s i o n on t h e d e f e c t p h a s e l o c u s t h e r e a r e
t h r e e o t h e r m a i n p o i n t s t o n o t e .
1) A i r gap d e f e c t s embedded i n h ig h th e r m a l e f f u s i v i t y
m a t e r i a l s ( e . g . a lu m in iu m ) w i l l be more r e a d i l y d e t e c t e d
th a n s i m i l a r s i z e d d e f e c t s i n low th e r m a l e f f u s i v i t y
m a t e r i a l s . T h is i s due t h e g r e a t e r d i f f e r e n c e i n the
t h e r m a l e f f u s i v i t y between t h e d e f e c t and host m a t e r i a l .
2 ) C o n t r a s t between d e f e c t s o f d i f f e r e n t t h i c k n e s s e s
d i m i n i s h e s in h ig h d i f f u s i v i t y m a t e r i a l due the r a p i d
approach o f th e r e f l e c t i o n c o e f f i c i e n t to u n i t y (o r the
s am p le / b ac k i n g r e f l e c t i o n c o e f f i c i e n t ) w i t h i n c r e a s i n g
d e f e c t t h i c k n e s s (see e q u a t i o n 2 . 1 9 ) .
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3) E s t i m a t i o n o f d e f e c t t h i c k n e s s become more d i f f i c u l t in
h ig h e f f u s i v i t y m a t e r i a l s due to c o n t r a s t s a t u r a t i o n .
5 . ^ . 6 THERMAL CONTACT R E S I ST A N C E
I n t h e p h a s e c u r v e s p r e s e n t e d i n f i g u r e 2 . 1 2
a r b i t r a r y v a l u e s o f t h e t h e r m a l c o n t a c t r e s i s t a n c e s
b e t w e e n t h e c o a t i n g and s u b s t r a t e w e r e u s e d t o
i l l u s t r a t e t h e p h a s e a n g l e v a r i a t i o n a t p a r t i a l l y
c o n t a c t i n g i n t e r f a c e s . I n t h i s s e c t i o n a d e t a i l e d
a n a l y s i s i s p r e s e n t e d f o r t h e c a l c u l a t i o n o f t h e r m a l
c o n t a c t r e s i s t a n c e s v a l u e s a t a r o u g h c o n t a c t i n g
i n t e r f a c e and i t s a p p l i c a t i o n t o t h e r m a l w a v e NDT o f
c o n t a c t i n g s u r f a c e s £ 6 7 3 .
T h e t h e r m a l c o n t a c t r e s i s t a n c e b e t w e e n r o u g h
s u r f a c e s i n c o n t a c t c a n b e r e l a t e d t o t h e t r u e c o n t a c t
a r e a b y a p p l y i n g a s t a t i s t i c a l d e s c r i p t i o n t o t h e
s u r f a c e t o p o g r a p h y C 6 8 D . I n t h e f o l l o w i n g a n a l y s i s
c e r t a i n a s s u m p t i o n s a r e m a d e :
i ) t h e t h e r m a l c o n t a c t r e s i s t a n c e a t a c o n t a c t i n g
s u r f a c e may b e d i v i d e d i n t o t wo c o m p o n e n t s ;
a) the th e rm a l r e s i s t a n c e due to c o n t a c t between s u r f a c e
a s p e r i t i e s ( t h e c o n s t r i c t i o n r e s i s t a n c e ) , Rm, and
b) t h e t h e rm a l r e s i s t a n c e due to t h e t r a p p e d f l u i d (gas ) l a y e r
between th e m at i ng s u r f a c e , R0 .
i i ) B o t h Rm and R^ a r e i n d e p e n d e n t o f e a c h o t h e r and
t h a t t h e t o t a l r e s i s t a n c e o f t h e i n t e r f a c e i s g i v e n
by
( 2 . 2 5 ) ( 1 ' 1 ^ 1RJ \ R mJ \ R J
4 8
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i i i ) The contact topography of the rough surface
a s s u m e s t h a t when two r o u g h s u r f a c e s ( r m s h and h o )
a r e p r e s s e d i n t o c o n t a c t , t h e s u r f a c e d e f o r m a t i o n
c a n be m o d e l l e d as b e i n g t h a t o f a r i g i d f l a t p l a n e
o n t o a s u r f a c e h a v i n g a c o m b i n e d r o u g h n e s s h,~=(h., .
+h;=> f~ ) , s e e f i g u r e 2 . 1 5 . F u r t h e r , t h e a s p e r i t i e s
o f t h e r o u g h s u r f a c e d e f o r m p l a s t i c a l l y w i t h
i n c r e a s i n g l o a d and t h a t a t a n y l o a d , t h e t r u e c o n t a c t
c o m p r o m i s e s a l a r g e n u m b e r o f e q u i - a r e a c i r c u l a r
c o n t a c t s o f r a d i u s r .
F o r a c o n t a c t s u r f a c e f o r m e d b e t w e e n a r i g i d f l a t
p l a n e a nd a r o u g h s u r f a c e h a v i n g a n o r m a l d i s t r i b u t i o n
o f c o n i c a l a s p e r i t i e s , t h e t h e r m a l r e s i s t a n c e Rm c a n
b e o b t a i n e d b y a p p l y i n g t h e r e l a t i o n s h i p s C693
f a l l o w s t h e p l a s t i c c o n t a c t t h e o r y . T h i s t h e o r y
(2.26) N n r
(2.27)
(2.28) R 1
m (2 N r k m)
where
A* i s the r e a l a r e a o f c o n t a c t ,
A0 i s t h e a p p a r e n t a r e a o f c o n t a c t ,
S i s th e a p p l i e d s t r e s s ,
P,„ i s th e har dness o f the d e f o r m in g m a t e r i a l ,
N i s th e number o f the c o n t a c t s p o t s p e r u n i t a r e a ,
u i s t h e d i s t a n c e between t h e mean p l a n e o f the
rough s u r f a c e and the p e r f e c t l y f l a t s u r f a c e ,
k„, is the harmonic mean the rm a l c o n d u c t i v i t y .
4 9
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Th e t h e r m a l r e s i s t a n c e , RSi(, c a n a s a f i r s t
a p p r o x i m a t i o n be w r i t t e n a s :
(2.29) R a = h c/ k gand t h e c o r r e s p o n d i n g c h a n g e i n t h e m a g n i t u d e o f t h e
t h e r m a l w a v e r e f l e c t i o n c o e f f i c i e n t , P , may be
e v a l u a t e d f r o m e q u a t i o n 2 . 8 0 a s s u m i n g o n e d i m e n s i o n a l
h e a t f l o w .
I n f i g u r e s 2 . 1 6 a a nd b , t h e v a r i a t i o n o f t h e
t h e r m a l c o n t a c t r e s i s t a n c e , f o r c o n t a c t s p o t s i n
v a c u u m a nd a i r , a g a i n s t t h e n o r m a l i s e d c o n t a c t a r e a
( A b/ A 0 ) a r e p l a t t e d u s i n g s u r f a c e r o u g h n e s s v a l u e s
o f 1 and 10 Hm rms a n d h a r m o n i c mean t h e r m a l
c o n d u c t i v i t y o f 64- and 1 W/m K . T h e s e f i g u r e s show
t h a t t h e t h e r m a l c o n t a c t r e s i s t a n c e d e c r e a s e s r a p i d l y
w i t h i n c r e a s i n g c o n t a c t a r e a r a t i o . T h e t h e r m a l
c o n t a c t r e s i s t a n c e i s l o w e r f o r c o n t a c t w i t h s mo o t h
s u r f a c e s and m a t e r i a l s w i t h h i g h t h e r m a l c o n d u c t i v i t y .
A i r p r e s e n t b e t w e e n t h e c o n t a c t i n g s u r f a c e s a l s o
r e d u c e s t h e t h e r m a l r e s i s t a n c e o f t h e j o i n t ; t h e
o v e r a l l r e d u c t i o n b e i n g d e p e n d a n t on t h e s p o t t h e r m a l
r e s i s t a n c e , Rm.
F i g u r e 2 . 1 7 a and b show t h e n o r m a l i s e d p h a s e a n g l e
v a r i a t i o n w i t h n o r m a l i s e d d e p t h ( d e p t h / t h e r m a l
d i f f u s i o n l e n g t h ) f o r d i f f e r e n t f r a c t i o n a l c o n t a c t a r e a
i n m i l d s t e e l and o p a q u e z i r c o n i a s a m p l e s -
a s s u m i n g t h e r m a l w a v e s b e i n g g e n e r a t e d a n d d e t e c t e d a t
t h e s u r f a c e . T h e s u r f a c e r o u g h n e s s o f t h e c o n t a c t i n g
f a c e s f o r t h e s e two p l o t s i s 1 Hm r m s . F o r an
e x p e r i m e n t a l p h a s e a n g l e n o i s e o f 1 d e g r e e , i t i s s e e n
f r o m t h e p l o t s t h a t f r a c t i o n a l c o n t a c t a r e a s up t o 0 . 3
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c a n be r e a d i l y d e t e c t e d b y t h e r m a l w a v e s f o r t h e s e
s a m p l e s . I t i s a l s o s e e n f r o m f i g u r e 2 . 1 7 b t h a t t h e
p r e s e n c e o f a i r b e t w e e n t h e c o n t a c t s u r f a c e o f l o w
c o n d u c t i v i t y m a t e r i a l r e d u c e s t h e d e t e c t a b i l i t y o f
t h i s i n t e r f a c e .
To c o m p a r e t h e s e n s i t i v i t y o f t h e r m a l and
u l t r a s o n i c w a v e s t o c o n t a c t i n g s u r f a c e s we a s s u m e t h a t
f o r c o m p a r a b l e r e s o l u t i o n b e t w e e n t h e t wo t e c h n i q u e s
t h a t t h e t h e r m a l d i f f u s i o n l e n g t h e q u a l s t h e u l t r a s o n i c
wa v e l e n g t h . T h i s a l l o w s t h e d e t e r m i n a t i o n o f t h e
a p p r o p r i a t e t h e r m a l w a v e t e s t f r e q u e n c y . N e x t i t i s
a ssumed t h a t s u i t a b l e n o i s e l e v e l b e s e t t o t h e
d e t e c t e d s i g n a l ; 1 d e g r e e p h a s e a n g l e n o i s e f o r t h e r m a l
w a v e s and a 1 dB s i g n a l c h a n g e f o r u l t r a s o n i c s .
F i g u r e 2 . 1 8 sh o ws t h e v a r i a t i o n o f t h e u l t r a s o n i c
r e f l e c t i o n c o e f f i c i e n t m a g n i t u d e , ( c o m p u t e d f r o m
e q u a t i o n 19 i n [ 6 9 3 ) , a g a i n s t t h e n o r m a l i s e d c o n t a c t
a r e a f o r a m i l d s t e e l s a m p l e w i t h a r ms i n t e r f a c e
r o u g h n e s s 1 Hm and 10 MH z . u l t r a s o n i c w a v e . I n
a t h r o u g h t r a n s m i s s i o n u l t r a s o n i c t e s t a 1 dB s i g n a l
c h a n g e c o r r e s p o n d s t o d e t e c t i n g a c o n t a c t a r e a r a t i o
o f a b o u t 0 . 1 . T h i s v a l u e i s s l i g h t l y l e s s t h e n t h e
c o n t a c t a r e a r a t i o p r e d i c t e d f o r t h e r m a l w a v e s o f
0 . 3 .
2 . 5 RESOLUTI ON AND D E F I N I T I O N OF SUBSURFACE
STRUCTURE
The p a r a m e t e r s w h i c h d e t e r m i n e t h e r e s o l u t i o n i n
m o d u l a t e d p h o t o t h e r m a l r a d i o m e t r y a r e :
a) the o p t i c a l h e a t i n g and IR d e t e c t i o n spot s i z e s ,
b) the dep th and geometry o f t h e s u b s u r f a c e s t r u c t u r e and,
c) the m o d u l a t i o n f r e q u e n c y .
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R e s o l u t i o n o f n e a r b y s t r u c t u r e s i s i m p r o v e d a s t h e
o p t i c a l h e a t i n g and I R d e t e c t i o n s p o t s i z e s a r e made
s m a l l e r t h e n t h e s u b s u r f a c e s t r u c t u r e . W i t h s o u r c e
l o c a l i s a t i o n t h e r e w i l l b e l i m i t e d i n t e r a c t i o n o f
s c a t t e r e d t h e r m a l wa v e s f r o m n e i g h b o u r i n g s t r u c t u r e s .
I n g l e h a r t e t a l . C7 0 ] h a v e s h o w n t h a t f o r o p t i c a l l y
o p a q u e s a m p l e s i m a g e r e s o l u t i o n i s i n d e p e n d e n t o f t h e
m o d u l a t i o n f r e q u e n c y , ( i . e . t h e r m a l w a v e l e n g t h ) f o r
s u b s u r f a c e t h e r m a l s t r u c t u r e s v e r y c l o s e t o t h e
s u r f a c e . I n t h i s ex t r e m e n e a r - f i e 1d l i m i t t h e i m a g e
r e s o l u t i o n i s t h e n d e t e r m i n e d b y t h e d e p t h o f t h e
s c a t t e r e r . T h e e x p l a n a t i o n f o r t h i s i s d u e t o t h e
f a c t t h a t t h e r e i s v e r y l i t t l e t h e r m a l w a v e s c a t t e r i n g
t o w a r d s t h e s u r f a c e . O n l y wh e n t h e s o u r c e a p p r o a c h e s
a l a t e r a l d i s t a n c e a p p r o x i m a t e l y e q u a l t o t h e d e p t h , i s
t h e r e a p p r e c i a b l e s c a t t e r i n g i n t h i s d i r e c t i o n 1 7 1 1 .
S i n c e t h e o p t i c a l w a v e l e n g t h u l t i m a t e l y d e t e r m i n e s t h e
mi n i mum o p t i c a l s p o t s i z e , t h e r e s o l u t i o n i n PTR i s
l i m i t e d by t h e o p t i c a l w a v e l e n g t h r a t h e r t h a n t h e I R
f o c a l s p o t .
When t h e s u b s u r f a c e d e f e c t i s f a r f r o m t h e s u r f a c e
b u t w i t h i n t h e t h e r m a l d i f f u s i o n l e n g t h , t h e l a t e r a l
r e s o l u t i o n i s d e t e r m i n e d by t h e t h e r m a l d i f f u s i o n
l e n g t h a s s u m i n g t h a t b o t h t h e h e a t e d and s e n s i n g s p o t
a r e much s m a l l e r t h e n t h i s l e n g t h . I m a g e w i d t h i n t h i s
n e a r - f i e 1d l i m i t w i l l b e d e p e n d e n t on t h e m o d u l a t i o n
f r e q u e n c y and d e f e c t g e o m e t r y C 7 2 - 7 ^ 1 . T h e o b s e r v e d
i m a g e w i d t h w i l l be l a r g e r t h e n t h e a c t u a l d e f e c t s i z e
d u e t o t h e r m a l wave d i f f r a c t i o n and good c o r r e l a t i o n o f
t h e o b s e r v e d i m a g e w i d t h w i l l o n l y b e o b t a i n e d a t h i g h
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f r e q u e n c i e s w h e r e i m a g e b l u r r i n g b y t h e r m a l w a v e
d i f f r a c t i o n i s r e d u c e d C75D. F i n a l l y , i f t h e o p t i c a l
s p o t s i z e i s much l a r g e r t h a n t h e t h e r m a l d i f f u s i o n
l e n g t h t h e l a t e r a l r e s o l u t i o n i s d e t e r m i n e d by o p t i c a l
s p o t s i z e . T h e d e p t h r e s o l u t i o n w i l l s t i l l b e s e t by
t h e t h e r m a l d i f f u s i o n l e n g t h . F i g u r e 2 . 1 9 p r o v i d e s a
summar y o f t h e v a r i o u s r e s o l u t i o n l i m i t s f o r t h e r m a l
w a v e NDT. B e s i d e s t h e a b o v e p a r a m e t e r s , r e s o l u t i o n
c a n a l s o b e l i m i t e d b y e n g i n e e r i n g d e t a i l s o f t h e
i n s p e c t i o n s y s t e m . I n p a r t i c u l a r t h e s t e p s i z e o f t h e
s a m p l e / o p t i c a l beam s c a n n i n g s y s t e m , f o c u s i n g l e n s
i m p e r f e c t i o n s a n d f i n i t e I R d e t e c t i o n s p o t s i z e .
2 . 6 SUMMARY
A d e t a i l e d a c c o u n t o f t h e t h e o r y f o r p h o t o t h e r m a l
r a d i o m e t r i c d e t e c t i o n and NDT h a s b e e n g i v e n a b o v e . T h e
t h e r m a l e m i s s i o n c h a r a c t e r i s t i c s , t h e r m a l w a v e
p r o p a g a t i o n a n d i n t e r a c t i o n w i t h t h e s u b s u r f a c e t h e r m a l
m i c r o s t r u c t u r e h a v e b e e n d i s c u s s e d i n r e l a t i o n t o
s u r f a c e c o a t i n g i n s p e c t i o n . T h e v a r i a b l e s d i c t a t i n g
t h e c h o i c e o f m o d u l a t i o n f r e q u e n c y f o r t h i c k n e s s
m e a s u r e m e n t s a n d d e f e c t d e t e c t i o n h a v e b e e n i d e n t i f i e d .
E x p e c t e d d e v i a t i o n s f r o m t h e s i m p l e o n e d i m e n s i o n a l
t h e o r y d u e t o h e a t d i f f u s i o n i n t h r e e d i m e n s i o n s h a v e
a l s o b e e n d i s c u s s e d . I n t h e f o l l o w i n g c h a p t e r s t h e
p r e d i c t i o n s o f t h e a b o v e t h e o r y a r e c o m p a r e d w i t h
e x p e r i m e n t a l r e s u l t s .
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Table 2 . 1 : Thermal p r o p e r t i e s o f some common m a t e r i a l s and plasma-sprayed c o a t in g s .
CJl-f*
i) M a t e r i a l
Densi t y S p e c i f i c h e a t
capac i t y
Thermal conduct i v i t y
Thermal d i f f u s i v i t y
x 10“ *
Thermal e f f u s i v i t y
x 10 6
Thermal d i f f u s i o n ( i n Hm)
le n g t h
1
I ..................... Kg /m3 J/Kg K W/m K m*2 / s ( J / m T- K) e s 1 Hz 16 Hz 64 Hz1j A luminium 2702 903 237 9 7 . 1 5 7 8 . 2 6 5560 1390 695
| M i l d s t e e l 7850 580 6 3 . 6 1 6 .5 2 9 8 . 6 0 2292 573..... .. ............. 2B7
! 316 S t a i n l e s s j s t e e l
8238 46B 1 3 .4 3 . 4 8 5 1 . 6 6 1052 263 131
i! T i t a n i u m 4500 522 2 1 . 9 9 . 3 2 5 1 . 4 4 1722 430 215
j_ Germanium
' S i l i c o n
5360 322 5 9 . 9 3 4 . 7 1 0 3 .4 0 3323 831 415
2330 712 1 4 8 . 0 8 9 . 2 2 4 2 . 3 6 5328 1332 666I
P l o y c r v s t a l - S l i n e Alu mina
3970 765 3 6 . 0 1 1 . 9 1 0 9 . 3 3 1946 487 243
|High d e n s i t y Gra phi te
1940 630 150 123 1 8 3 . 3 3 6257 1564 782
j Epoxy R es in
O !
in; ru; _ 1200 0 . 2 0_____ _____0 . 1 3 ____ !O
!m
|°ji! __ 203 51 25
j A i r 1 1005 0 . 0 2 5 2 4 . 9 0 . 0 0 0 0 2 5 2813 704 352
j PLASMA SPRAYED COATINGS ..... .....
1 ~ Alb-Oa 3540 6 . 3 5
ij
CD I
w H i
cu j; 1 8 . 5 8 , 833 208 1041 .......... • ...
|___ZrOa
j Z r O a -8 wt'/. Ya 0 3
5320 470 1 . 3 0 . 5 2 3 . 2 5 407 102 51
5670 491 0 . 7 2 0 . 2 6 1 . 8 8 288 72 36
[ Z r 0 H. - C r E.0:3 5410 475 1 . 4 0 0 . 5 5 3 . 5 6 418 105 52
1 N i - C r C a r b i d e i (LC1B)
6400 550 4 . 4 1 . 2 6 1 5 .3 6 633 158 79
! WC+12 wt*/. Co 12500 2 1 7 . 7 _____9.JE0_____ .... ...... 3 ______ 2 5 . 0 3 977 244 122
I N iC r A lY 6980 410 5 . 7 7 2 . 0 2 16.51 802 200 100
1 N i A l 1 8 . 4 4 . 6 7 3 . 6 1210 302 ; 151
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T a b l e 2 . 2 : One d i m e n s i o n a l s u r f a c e t e m p e r a t u r e e x p r e s s i o n s f o r
th e r m a l wave NDT o f opaque s u r f a c e c o a t i n c
S e m i - i n f i n i t e sol i d .
Th in c o a t i n g on a s e m i - i n f i n i t e s u b s t r a t e .
2 A r t a ,
y?C 1 - r ) l 2 ka
1 + r e x p ( - 2 o 1 L !) 1 - / ' e x p ( - 2 c r l L x)
r - ^ 2 ^ 2
k xo x
Aii— gap d e f e c t a t c o a t i n g / s u b s t r a t e i n t e r f a c e .
Rep la ce V above w i t h :
r r t -*-r2exp(-2or2Z2)1 + f 1/ , 2 e x p ( - 2 a 2 i 2 )
1 - b
F + bb2 3 ^ 3
I n t e r f a c e c o n t a c t r e s i s t a n c e .
R ep la ce r above w i t h :
1 - b t *+■ R k 2o 2r - 1 + bi *+■ R k 2o 2
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Tab l e 2 . 3 : S e r i es summat ion r e p r e s e n t a t i o n of the t h r ee
dimensional sur face temperature d i s t r i b u t i o n wi th Gaussian beam
i 1luminat i o n .
Generalterm
T„
r cJo, 7i
Opaque Semi- i n f i n i t e sol id
m-0
Thermal wave gen e r a t i o n term. Source i l l u m i n a t i o n term.
/ ( r ) = / 0e x p ( - 2 r a/ r * )
2 J l { y mr c) \ re x p ( - y ’ r ’ / 8 )
Given by J i (% m r c ) = 0Radius on sample a t which heat f l u x is zero .Zero and f i r s t order Bessel f unc t i on s r e s p e c t i v e l y ,
T. 12 k a ( m )
I f r V * 0 ( r ) = Tr — r
O C D - ^
2 \ r cJ m~o koim')
2
J-h- r c m • t mK C f m=l
Opaquet h i nc oat i ngon at h i c ks u b s t r a t e
r =1 -*■ r(m)exp(-2<r x(m)Li \
^icr^An)^ 1 - r ^ m ) e x p [ - 2 a Lt )
1 + r e x p ( - 2 a 1Ll )_ k i C f l ( \ - r e x p ( - 2 c r 1Z.l )) m- i
- r c -Tm m
Hrtm)b (m)
= J.(y~r ) ■ exp[-ylr l /a)/Jl(v*>rc)o * { m ) +
sample thermal d i f f u s i o n l engt h .: complex thermal wave r e f l e c t i o n c o e f f i c i e n t| = 1 - b ( m ) / 1 b ( m )
b( r n) = k 2o 2( m ) / k xa x(rr i )
56
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SP
EC
TR
AL
R
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CE
35
s.w
£3
£U>3.V/OootHX
25□25W A V E L E N G T H / um W A V E L E N G T H / um
F i g u r e 2 . 1 : S p e c t r a l e m i t t a n c e v e r s e s e m i s s i o n w a v e l e n g t h f o r
s a m p l e s t e m p e r a t u r e s o f 1) 2 0 0 , 2 ) 3 0 0 , 3 ) 3 2 0 and 4 ) 3 4 0 K.
F i g u r e 2 . 2 : D e r i v a t i v e p l o t o f t h e s p e c t r a l e m i t t a n c e f o r t h e
s a m p l e t e m p e r a t u r e s g i v e n i n f i g u r e 2 . 1
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NO
RM
. T
EM
P
□ 5N O R M A L I S E D D E P T H
O 5N O R M A L I S E D D E P T H
F i g u r e 2 . 3 a : A m p l i t u d e and p h a s e a n g l e v a r i a t i o n o f p l a n e t h e r m a l
w a v e s w i t h n o r m a l i s e d d e p t h , x / H -
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i o
-70O 1
1 O
LlIaDY-<aUJQ.2UJh-
J<n□<01
o 1
R / p R /p i
F i g u r e E . 3b : A m p l i t u d e and p h a s e a n g l e v a r i a t i o n o f t h e t h r e e
d i m e n s i o n a l s u r f a c e t e m p e r a t u r e a g a i n s t t h e n o r m a l i s e d r a d i a l
d i s t a n c e r / H - T h e s a m p l e i s m i l d s t e e l * 1 / e beam r a d i u s i s 0 . 5 mm
and t h e m o d u l a t i o n f r e q u e n c y i s 10 H z .
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TE
MP
ER
AT
UR
E
l O
-701□
l O
Z / p Z / p
F i g u r e 2 . 3 c : A m p l i t u d e and p h a s e a n g l e v a r i a t i o n o f t h e t h r e e
d i m e n s i o n a l s u r f a c e t e m p e r a t u r e a g a i n s t t h e n o r m a l i s e d d e p t h z / H .
T h e s a m p l e i s m i l d s t e e l , 1 / e beam r a d i u s i s 0 . 5mm and t h e
m o d u l a t i o n f r e q u e n c y i s 10 H z .
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PH
AS
E
AN
GLE
C
DE
G
l O
- 5 020O
2 R //J
F i g u r e 2 . 3 d : P h a s e a n g l e v a r i a t i o n o f t h e t h r e e d i m e n s i o n a l
s u r f a c e t e m p e r a t u r e a g a i n s t t h e n o r m a l i s e d p a r a m e t e r , 2 R / n > f o r
v a r i o u s i n f r a r e d d e t e c t i o n s p o t d i a m e t e r s o f 1) p o i n t , 2 ) ^ mm
and 3 ) 8 mm. T h e s a m p l e i s a l u m i n i u m and l a s e r beam 1 / e r a d i u s
i s 1 . 5 mm.
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50-0-9
- 0-6
- 0 - 3
0-3
0-6
0-9
-50O 3
0-9
_ \0*60-3
-0-3
- 0-6
-0-9
O 3L / y u L / / J
F i g u r e 2 . 4 - : N o r m a l i s e d t h e r m a l w a v e i n t e r f e r e n c e p l o t s s h o w i n g t h e
v a r i a t i o n o f t h e a m p l i t u d e , f i g . 2 . 4 a and p h a s e a n g l e , f i g . 2 . 4 b ,
a g a i n s t t h e t h e r m a l t h i c k n e s s , l_/H> f o r v a r i o u s c o a t i n g / s u b s t r a t e
t h e r m a l w a v e r e f l e c t i o n c o e f f i c i e n t .
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PHAS
E AN
GLE
FIG. 2.5 a FIG. 2.5 b
INCREASING COATING THICKNESS
THERMAL THICKNESS
C O A T I N G / S U B S T R A T E
L O C U S
l±JID2<U
<XCL
THICKNESSTHERMAL
DEFECT PHASE LOCUS
F i g u r e 2 . 5 : S c h e m a t i c i l l u s t r a t i o n o f t h e c h a n g e i n t h e o b s e r v e d
p h a s e a n g l e w i t h c h a n g e s i n t h e c o a t i n g t h i c k n e s s f i g . 2 . 5 a , and
i n t e r f a c e d e f e c t , f i g . 2 . 5 b .
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CD-P*
□ P T I C A L
H E A T I N G
HEAT D I F F U S I O N
S E M I - I N F I N I T E S U B S T R A T E
F i g u r e 2 . 6 a :
t h e s u r f a c e
A p h a s o r r e p r e s e n t a t i o n o f
p h o t o t h e r m a 1 s i g n a l f o r a
s e m i - i n f i n i t e o p a q u e s a m p l e .
C O A T I N G
S U B S T R A T E
Y THERMAL
N E T
P H A S E
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R E G I O N
F i g u r e 2 . 6 b : P h a s o r d i a g r a m i l l u s t r a t i n g t h e d e v e l o p m e n t o f t h e
f i n a l p h o t o t h e r m a l f o r an o p a q u e c o a t i n g on a s u b s t r a t e , ( l e f t ) ,
a n d t h e i n v a r i a n c e o f t h e n e t p h a s e a n g l e o f t h i s s i g n a l d u e t o
i n c r e a s e d l i g h t a b s o r p t i o n a t a ’ d a r k e r ’ r e g i o n on t h e s a m p l e
s u r f a c e ( r i g h t ) .
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F i g u r e 2 . 7 : P h a s e a n g l e v a r i a t i o n w i t h r o o t f r e q u e n c y f o r
d i f f e r e n t d i a m e t e r l a s e r s p o t s i z e s 1) i n f i n i t e , 2 ) 2 mm, and 3 ) <+
mm. P h a s e v a l u e s a r e t a k e n a t t h e c e n t r e o f t h e l a s e r b e a m .
T h e s a m p l e i s a 1 0 0 Fm LC1B c o a t i n g on s t a i n l e s s s t e e l .
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f r e q u e n c y p l o t f o r a 2 0 0 urn LC1B c o a t i n g on s t a i n l e s s s t e e l .
1) 0 , 2 ) 10 a nd 3 ) 2 0 */. p o r o s i t y .
r o o t
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SURFACE LAYERSURFACE ROUGHNESS
COATINGCOATING
INTERFACE LAYERINTERFACE ROUGHNESS
SUBSTRATE SUBSTRATE
F i g u r e 2 . 9 : S c h e m a t i c r e p r e s e n t a t i o n o f s u r f a c e r o u g h n e s s w i t h a
d i s c r e t e l a y e r o f u n i f o r m t h i c k n e s s and t h e r m a l p r o p e r t i e s .
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100 un
9l .
□ 2 0SQRT. FREQUENCY
F i g u r e 2 . 1 0 : A m p l i t u d e andf r e q u e n c y o f a l a y e r e d s a m p l e c o n d u c t i v i t y . L a y e r t h i c k n e s s t h e r m a l c o n d u c t i v i t y o f 9 and
9
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p h a s e a n g l e v a r i a t i o n w i t h r o o t e x h i b i t i n g s t e p c h a n g e s i n t h e r m a l i s 100 Fm. T h e s u b s t r a t e h a s a t h e s u r f a c e l a y e r o f 1 U) / ( m K ) .
Top d i a g r a m s hows t h e t h e r m a l c o n d u c t i v i t y v a l u e s when t h e 1 0 0 Fm l a y e r i s d i v i d e d i n 2>^+ and 8 e q u a l p a r t s . T h e h e a t c a p a c i t y o f a l l l a y e r s a r e e q u a l .
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c o a t i n g t h i c k n e s s i n c l u d i n g t h e r o u g h s u r f a c e l a y e r i s a 1 0 0 Hm.
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F i g u r e 2 . 1 2 a a nd b : N o r m a l i s e d a m p l i t u d e a n d p h a s e a n g l e
v a r i a t i o n w i t h r o o t f r e q u e n c y f o r a i r - g a p t h i c k n e s s e s 1) 0 . 1 , 2 )
1 , 3 ) 10 a n d 4-) 1 0 0 Hm 0 . 5 mm b e l o w t h e s u r f a c e i n b u l k 3 1 6
s t a i n l e s s s t e e l . H e a t f l o w i s o n e d i m e n s i o n a l .
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v a r i a t i o n w i t h r o o t f r e q u e n c y f o r t h e r m a l c o n t a c t r e s i s t a n c e s o f
1) 4 E - 6 , 2 ) 4 E - 5 , 3 ) 4E-4- a n d 4 ) 4 E - 3 mf~ K /W 0 . 5 mm b e l o w t h e
s u r f a c e i n b u l k 3 1 6 s t a i n l e s s s t e e l . H e a t f l o w i s o n e
d i mens i o n a 1 .
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t h i c k n e s s e s 1) 0 . 1 , 2 ) 1 , 3 ) 10 and 100 Hm 0 . 5mm b e l o w t h e
s u r f a c e i n b u l k a l u m i n i u m and e p o x y . H e a t f l o w i s o n e
d i mens i o n a 1 .
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a i r - g a p t h i c k n e s s e s 1) 0 . 1 , 2 ) 1 , 3 ) 10 and *+) 1 0 0 Fm 0 . 5mm b e l o w
t h e s u r f a c e i n a ) a l u m i n i u m , b ) LC1B and c ) Y i t t r i a s t a b i l i s e d
Z i r c o n i a on s t a i n l e s s s t e e l . H e a t f l o w i s o n e d i m e n s i o n a l .
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RIGID FLAT SURFACE
RDUGH SURFACENORMAL DISTRIBUTION OF CONICAL PEAKS
F i g u r e 2 . 1 5 : C o n t a c t b e t w e e n r e a l s u r f a c e s m o d e l l e d a s b e i n g d u e
t o f l a t t e n i n g o f c o n i c a l p e a k s . C683
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i n c r e a s i n g f r a c t i o n a l c o n t a c t a r e a . A= c o n t a c t i n a i r , V=
c o n t a c t i n v a c u u m . F i g u r e 2 . 1 6 a c o n t a c t i n m i l d s t e e l and 2 . 1 6 b
c o n t a c t i n z i r c o n i a .
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N O R M . L E N G T H N O R M . L E N G T H
F i g u r e 2 . 1 7 : P l o t s o f t h e t h e r m a l w a v e p h a s e a n g l e v a r i a t i o n w i t h
n o r m a l i s e d d e p t h a nd f r a c t i o n a l c o n t a c t a r e a o f 1) 0 . 1 , 2 ) 0 . 2 and
3 ) 0 . 5 o f p a r t i a l l y c o n t a c t i n g i n t e r f a c e s i n m i l d s t e e l , f i g .
2 . 1 7 a , a n d z i r c o n i a , f i g . 2 . 1 7 b , w i t h a r o u g h n e s s o f 1 Hm. A=
c o n t a c t i n a i r , V= c o n t a c t i n v a c u u m .
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c o e f f i c i e n t m a g n i t u d e w i t h f r a c t i o n a l c o n t a c t a r e a i n m i l d s t e e l
s a m p l e o f r o u g h n e s s 1 Fm and a n u l t r a s o n i c f r e q u e n c y o f 10 MHz .
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C h a p t e r 3
E x p e r i m e n t a l D e s c r i p t i o n
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CHAPTER 3 EXPER I MENTA L D E S C R I P T I O N
3 . 1 PHOTOTHERMAL SYSTEM
A s t u d y o f f i g u r e 1 . 2 sho ws t h a t t h e r e a r e
e s s e n t i a l l y s i x b a s i c c o m p o n e n t s i n a m o d u l a t e d
p h o t o t h e r m a l NDT s y s t e m . A l a s e r s o u r c e ) a beam
m o d u l a t o r , an I R s e n s o r , a l o c k - i n a n a l y s e r , a
c o n t r o l l i n g c o m p u t e r and a s a m p l e ( o r l i g h t beam)
s c a n n i n g u n i t . T h e m e a s u r e m e n t s r e p o r t e d i n s e c t i o n
4 . 1 u s e d a 5 w a t t c o n t i n u o u s w a v e A r g o n i o n l a s e r C 7 6 ]
f o r s a m p l e h e a t i n g and a s e c t o r e d b l a d e m e c h a n i c a l
c h o p p e r f o r beam m o d u l a t i o n [ 7 7 3 . T h e h a r m o n i c t h e r m a l
e m i s s i o n f r o m t h e s a m p l e w e r e d e t e c t e d b y a M u l l a r d s
7GS p y r o e l e c t r i c d e t e c t o r [ 7 8 3 and d e m o d u l a t e d u s i n g a n
EG&G 5 2 0 6 t wo p h a s e l o c k - i n a n a l y s e r [ 7 9 3 . An IBM PC
XT m i c r o c o m p u t e r c o n t r o l l e d t h r o u g h a n I E E E 4 8 8
i n t e r f a c e , t h e d a t a a c q u i s i t i o n and s a m p l e t r a n s l a t i o n
[ 8 0 3 i n h o r i z o n t a l a nd v e r t i c a l d i r e c t i o n s u s i n g
i n t e r p r e t e d b a s i c c o m p u t e r c o d e . A r o t a t i n g t a b l e
p r o v i d e d m a n u a l c o n t r o l o v e r t h e a n g u l a r p o s i t i o n i n g o f
t h e s a m p l e . T h e I R d e t e c t o r , s a m p l e t r a v e l l i n g and
r o t a t i o n s t a g e s w e r e m o u n t e d on an o p t i c a l b e n c h and
t h e w h o l e s e t - u p , i n c l u d i n g p a r t o f t h e l a s e r h e a d ,
w e r e e n c l o s e d i n a l i g h t t i g h t box t o c o m p l y w i t h l a s e r
s a f e t y r e q u i r e m e n t s C 8 1 J .
To p r e v e n t t h e g e n e r a t i o n o f c o h e r e n t s i g n a l n o i s e
b y t h e a b s o r p t i o n o f s c a t t e r e d / r e f l e c t e d l a s e r l i g h t
a t t h e I R d e t e c t o r w i n d o w , a d i e l e c t r i c i n t e r f e r e n c e
f i l t e r [ 8 2 3 was u s e d t o s e l e c t i v e l y r e f l e c t a way t h e
i n c i d e n t l a s e r r a d i a t i o n and t r a n s m i t t h e I R . F i g u r e s
79
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3 . 1 a and b show t h e r e f l e c t a n c e and t r a n s m i t t a n c e
s p e c t r a o f t h i s i n t e r f e r e n c e f i l t e r and t h e d e t e c t o r
w i n d o w m a t e r i a l i n t h e o p t i c a l and I R r e g i o n .
3 . 2 DETECTOR SEL ECT I ON
The I R d e t e c t o r may b e c h o s e n a c c o r d i n g t o i t s
s p e c t r a l , t e m p o r a l , and n o i s e c h a r a c t e r i s t i c s , i t s
o p e r a t i n g t e m p e r a t u r e and r o b u s t n e s s . F o r room
t e m p e r a t u r e i n s p e c t i o n o f m a t e r i a l s , 3 0 0 K, t h e m a i n
s p e c t r a l r e q u i r e m e n t i s t h a t t h e I R d e t e c t o r e l e m e n t i s
s e n s i t i v e t o w a v e l e n g t h s g r e a t e r t h a n 3 Fm, as shown i n
f i g u r e 2 . 2 . T h e t e m p o r a l r e q u i r e m e n t s , e s p e c i a l l y f o r
e v a l u a t i n g l o w d i f f u s i v i t y m a t e r i a l s , a r e t h a t t h e
d e v i c e h a s l o w e l e c t r i c a l n o i s e a t l o w f r e q u e n c i e s (<
1 0 0 H z ) . T h e I R d e t e c t o r s h o u l d a l s o h a v e a
s u f f i c i e n t l y f a s t r e s p o n s e t i m e ( < 0 . 0 0 1 s e c o n d ) so t h a t
t h e d e t e c t e d s i g n a l f o l l o w s t h e m o d u l a t e d e m i s s i o n
s i g n a l . T h e f o r m e r r e q u i r e m e n t i s u n u s u a l f o r mo st
e l e c t r o n i c a p p l i c a t i o n s b u t i s n e c e s s a r y i n PTR a s l ow
m o d u l a t i o n f r e q u e n c i e s a r e r e q u i r e d f o r i n s p e c t i n g
t h i c k a n d / o r l o w t h e r m a l d i f f u s i v i t y c o a t i n g s . A l ow
n o i s e p r e a m p l i f i e r i s an e s s e n t i a l r e q u i r e m e n t o f t h e
I R d e t e c t o r .
T he n o i s e p r o p e r t i e s o f I R d e t e c t o r s a t a f r e q u e n c y
t a r e g i v e n by t h e n o r m a l i s e d D e t e c t i v i t y , D~ i n cm
Hz 1 /vs- W -l , w h i c h de t e r m i n e s t h e no i s e - e q u i va 1 e n t - p o w e r
NER C 0 3 1 :
( 3 . 1 ) N E P = ^ n " 2D
F o r t h e d e t e c t o r - s a m p 1e g e o m e t r y shown i n f i g u r e 3 . 2 ,
80
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t h e e x p r e s s i o n f o r t h e m i n i m u m d e t e c t a b l e t e m p e r a t u r e
c a n b e p u t i n t h e f o r m :
(3.2) 6 T ~ N E P . ----- ----- .------ —4 eoTlAr** T m( X ) s i n 3e o
T h i s e q u a t i o n a s s u m e s t h a t t h e I R d e t e c t o r i s
s e n s i t i v e t o a l l w a v e l e n g t h s . T h e f i r s t t e r m i n
e q u a t i o n 3 . 2 sh ows t h e d e p e n d e n c e o f d e t e c t o r
p a r a m e t e r s , t h e s e c o n d t e r m a c c o u n t s f o r t h e t o t a l
e m i s s i o n f r o m t h e s a m p l e a nd t h e t h i r d t e r m t h e IR
c o l l e c t i o n e f f i c i e n c y . H e n c e t o d e t e c t t h e s m a l l e s t
t e m p e r a t u r e p e r t u r b a t i o n , a l o w NEP v a l u e ( o r h i g h D *
) i s r e q u i r e d f o r t h e d e t e c t o r , h i g h e m i s s i v i t y f o r
t h e s a m p l e a n d h i g h c o l l e c t i o n e f f i c i e n c y f o r t h e I R
o p t i c s . I n t h i s s t u d y an e l l i p s o i d a l m i r r o r was
e v a l u a t e d t o a s s e s s t h e i m p r o v e m e n t i n t h e I R
c o l l e c t i o n e f f i c i e n c y a n d d e t e r m i n e a n y p r a c t i c a l
p r o b l e m s i n i t s u s a g e . I n t a b l e 3 . 1 a su mmar y i s
p r e s e n t e d o f t h e p r i n c i p l e c h a r a c t e r i s t i c s o f t h e A r g o n
i o n l a s e r , t h e I R d e t e c t o r and t h e e l l i p s o i d a l
c o 1 l e c t o r .
3 . 3 SEMI - CONDUCTOR LASER
I n a d d i t i o n t o t h e a b o v e e x p e r i m e n t a l s e t - u p , a
G a A l A s s e m i - c o n d u c t o r l a s e r was s t u d i e d f o r i t s
a p p l i c a t i o n a s a s a m p l e h e a t s o u r c e . F i g u r e 3 . 3 show
a s c h e m a t i c b l o c k d i a g r a m o f t h e l a s e r s y s t e m , M o d e l
7 2 0 0 - Y 2 , a c q u i r e d f r o m S p e c t r a P h y s i c s [ 8 5 ] . T h i s
u n i t c o n s i s t e d o f two o f t h e a b o v e l a s e r d i o d e s w i t h
t h e i r o u t p u t f e d i n t o a . 2 5 mm d i a m e t e r o p t i c a l f i b r e .
The l a s e r e m i s s i o n f r o m t h e d i o d e s l i e s i n t h e n e a r I R
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r e g i o n , 8 1 0 - 8 2 0 n m. C o u p l e d w i t h t h i s l a s e r
r a d i a t i o n t h e r e i s a l s o i n c o h e r e n t e m i s s i o n i n t h e
v i s i b l e r e d r e g i o n , 6 3 0 n m . A h i g h q u a l i t y c u r r e n t
s o u r c e d r i v e s t h e l a s e r d i o d e s and a t h e r m o e l e c t r i c
c o o l i n g s y s t e m i s e m p l o y e d t o p r e v e n t d i o d e da ma ge f r o m
o v e r h e a t i n g and s t a b i l i s e l a s e r e m i s s i o n . Th e
c o n t i n u o u s w a v e p o w e r o u t p u t e m e r g i n g f r o m t h e f i b r e
end c o u l d b e v a r i e d b e t w e e n z e r o and 0 . 5 w a t t .
P r o v i s i o n i s a l s o p r o v i d e d f o r e x t e r n a l l y m o d u l a t i n g
t h e l a s e r e m i s s i o n and t h e w h o l e a s s e m b l y i s p a c k a g e d
i n t o a s i z e no l a r g e r t h a n a n A t p a g e w i t h a d e p t h o f
10 cms .
The i n v i s i b i l i t y o f t h e l a s e r r a d i a t i o n p r e s e n t t wo
p r a c t i c a l p r o b l e m s i n i t s u s a g e ; l o c a t i n g t h e r a d i a t i o n
on t h e s a m p l e a nd o p e r a t o r s a f e t y . T h e f i r s t p r o b l e m
i s p a r t l y o v e r c o m e b y m a k i n g u s e o f t h e v i s i b l e " r e d "
e m i s s i o n f r o m t h e l a s e r . T h e r e d e m i s s i o n c a n be
r e a d i l y s e e n wh e n i t i s i n c i d e n t on a w h i t e s u r f a c e .
A l t e r n a t i v e l y a n I R f l u o r e s c e n t c a r d c a n a l s o b e u s e d .
The s e c o n d p r o b l e m o f o p e r a t o r s a f e t y i s d i s c u s s e d
b e l o w , b o t h f o r t h i s l a s e r a n d t h e a r g o n i o n l a s e r .
3. *» LASER SAFETY
S a f e t y r e q u i r e m e n t s o f l a s e r p r o d u c t s a nd s y s t e m s ,
and f o r u s e r s i s c o v e r e d b y t h e B S ^ 8 0 3 ( p a r t 1 , 2 and
3 , 1 9 8 3 ) r e g u l a t i o n . B o t h l a s e r r a d i a t i o n s i f v i e w e d
by t h e u n p r o t e c t e d e y e ( d i r e c t l y o r t h r o u g h s p e c u l a r
r e f l e c t i o n s ) c a n l e a d t o p e r m a n e n t b l i n d n e s s . T h i s i s
d i r e c t l y d u e t o t h e 10'",; f o l d i n c r e a s e i n e n e r g y d e n s i t y
f o c u s e d on t h e r e t i n a by t h e e y e . F o r t h e I R l a s e r t h e
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e y e d a ma g e c a n b e r e t i n a l b u r n s o r l e a d t o c a t a r a c t s .
U l i t h a r g o n i o n l a s e r r a d i a t i o n t h e r e i s p o t e n t i a l f o r
p h o t o c h e m i c a l a n d t h e r m a l r e t i n a l i n j u r y t o t h e e y e and
a l s o t o s k i n b u r n s a t h i g h l a s e r p o w e r s .
l o c o m p l y w i t h t h e s a f e t y r e q u i r e m e n t s f o r t h e two
l a s e r s , b o t h t h e s e l a s e r s w e r e o p e r a t e d i n a c l o s e d
room and p r o t e c t i v e e y e g o g g l e s w e r e w o r n t o a t t e n u a t e
t h e l a s e r r a d i a t i o n b y an o p t i c a l d e n s i t y o f 13 ( 10 13
r e d u c t i o n o f i n c i d e n t r a d i a t i o n ) .
3 - 5 SAMPLE AND MEASUREMENT D E T A I L S
T h e e x p e r i m e n t a l i n v e s t i g a t i o n r e p o r t e d i s d i v i d e d
i n t o t h r e e p a r t s * . An e v a l u a t i o n o f t h e p h o t o t h e r m a l
s y s t e m b a s e d on t h e A r g o n i o n l a s e r t o t h e s e n s i t i v i t y
o f t h e d e t e c t e d s i g n a l t o s a m p l e and d e t e c t o r s e t - u p ,
M e a s u r e m e n t s o n c o a t e d s a m p l e s t o a s s e s s t h e e f f e c t s o fand-
s u r f a c e r o u g h n e s s and s u b s u r f a c e d e f e c t s , ^ M e a s u r e m e n t s
o f c o a t i n g t h i c k n e s s u s i n g t h e s e m i - c o n d u c t o r l a s e r f o r
s a m p l e h e a t i n g .
Th e m a t e r i a l s s t u d i e d i n t h e s e i n v e s t i g a t i o n s a r e as
f o l l o w s . LC1B ( N i c k e l - c h r o m e c a r b i d e ) , f i n e and c o a r s e
p l a s m a s p r a y e d c o a t i n g s a nd h i g h d e n s i t y n u c l e a r
g r a p h i t e f o r s u r f a c e r o u g h n e s s s t u d i e s . As s p r a y e d and
s u r f a c e p o l i s h e d LC1B c o a t i n g s f o r d e f e c t d e t e c t i o n
s t u d i e s b y p h o t o t h e r m a l and u l t r a s o n i c m e t h o d s . A i r
gap d e f e c t s i n m i l d s t e e l / s t a i n l e s s s t e e l and m i l d
s t e e l / m i l d s t e e l d i f f u s i o n b o n d e d p l a t e s . C o n t a c t i n g
s u r f a c e d e t e c t i o n w i t h p r e s s e d a l u m i n i u m p l a t e s .
F i g u r e s 3 . ^ - 3 . 7 p r o v i d e a d e t a i l e d summary o f t h e
s a m p l e s u s e d i n t h e a b o v e t e s t s and t a b l e 3 . 2 l i s t s t h e
e x p e r i m e n t s u n d e r t a k e n .
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Tab le 3 .1 Laser » IR d e t e c t o r and e l l i p s o i d a l m i r r o r d e t a i I s
Argon ion l aser
Laser power
Wavelength range
l / e 2 beam diameter
Beam di vergence
IR de t e c t o r
Dimension
Sensing element
Element s i z e
Det ect or window
Respons i v i t y
Noise Eq u i va l e n t
Power
D* D e t e c t i v i t y
Operat ing v o l t a g e
0 to 6 Watt i n m u l t i - l i n e mode
^88 to 51*t nm
1. 3 mm
0 . 0 0 5 rad i an s
C y l i n d r i c a l shape 25 mm i n diameter
and 100 mm in l eng t h .
Ana l i ne doped t r i - g l y c i n e
su l pha t e
2 x 2 mm
Bloomed germanium 20 mm in
d i a m e t e r .
IE 5 v o l t s / w a t t
7 . 7 E - l l Wa t t / J Hz
2 . 6 E 9 cm / w a t t / -J Hz
9 v o l t s DC
E l l i p o s i d a l m i r r o r d e t a i l s ,
£
1 PRIMARY FDCUSa
abcde
12.1 mm25.4 mm59.2 mm74.4 mm 102,8 mm
2 SECONDARY FOCUS
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Table 3 . 5 : Exper im enta1 i n v e s t i q a t i o n summary.
System e v a l u a t i o n
E l i m i n a t i n g IR r a d i a t i o n from the l a s e r tube.
Signal and phase v a r i a t i o n wi t h l a s e r power and beam di ameter .
Signal and phase v a r i a t i o n wi t h sample or d e t e c t o r r o t a t i o n .
E f f e c t s o f r e f l e c t e d l aser l i g h t on s i gna l and phase
measurements.
Signal and phase v a r i a t i o n wi t h l a s e r power using the
e l l i p s i o d a l m i r r o r c o l l e c t o r
Sur face roughness study
Signal and phase measurements on LC1B f i n e and rough c o a t i n gs .
Signal and phase measurements on g r a p h i t e .
Defect study
Photothermal and u l t r a s o n i c measurements on LC1B "de f ec t "
samples.
Phase angle v a r i a t i o n wi th d e f e c t depth and width in d i f f u s i o n
bonded d e f e c t samples.
Phase angle measurements on p a r t i a l l y con t ac t i n g i n t e r f a c e s .
Semiconductor l aser study
Signal and phase angle measurements wi t h l ase r power
Signal and phase angle v a r i a t i o n wi th f i b r e head p o s i t i o n i n g .
Measurements o f coat i ng t h ickness on an LC1B coa t i ng .
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Z REFLECTION
(RELA
TIVE)
10 —
100 t
3. \ a . .F> cj 3 . \ b
453^ ~ 7
488 514 ^ 536 / nnLASER EMISSIDN LINES.
100
z□t— I
(/) 50>— i
zcI—
-7 10 12
WAVELENGTH / urn
F - i g u r e 3 . 1 : O p t i c a l and i n f r a r e d r e f l e c t a n c e and t r a n s m i t t a n c e
s p e c t r a a t t h e i n f r a r e d d e t e c t o r w i n d o w m a t e r i a l * c u r v e A , and t h e
i n t e r f e r e n c e r e f l e c t a n c e f i l t e r , c u r v e B.
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00"sj
INCIDENT LASER BEAM
IR DETECTOR .
SOLIDANGLEIRCOLLECTION
F i g u r e 3 . 2 : S c h e m a t i c i l l u s t r a t i o n o f t h e s a m p l e and I R d e t e c t o r
g e o m e t r y .
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0000
FIBER OPTIC CABLE
FAN
LASERDIODEASSEMBLY
POWERSUPPLY
DIODEDRIVERBOARD
CONTROL PANEL
LASER DIODE CHARACTERSTICS
LASER POWER TEM 0.5 w
BEAMDIVERGANCE 30 Deg.
EMISSIONWAVELENGTH 820 nrn
FIBERDIAMETER 0.25 m
DIODE DRIVE CURRENT 0.5 Anp
LASER DIODE LIFE TIME (30 C) SOOOOh
F i g u r e 3 . 3 : A b l o c k d i a g r a m o f t h e l a s e r d i o d e s y s t e m m o d u l e and
beam c h a r a c t e r i s t i c s .i
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FIG, 3.4a FIG, 3,4b
ooCO
8 10
LC1B COATING
316 STAINLESS STEEL
F i g u r e 3 . 4 a : A s c h e m a t i c o f LC1B s t e p c o a t i n g t h i c k n e s s s a m p l e .
S a m p l e w i d t h 3 5 mm, s u b s t r a t e 3 mm t h i c k 3 1 6 s t a i n l e s s s t e e l and
l e n g t h 2 0 c m s . ( Th i c l ^c - ss *** T£tou&cindi'h i ^ c h . )
F i g u r e 3 . 4 b : A s c h e m a t i c i l l u s t r a t i o n o f s u b s u r f a c e s q u a r e d e f e c t s
i n LC1B c o a t e d s a m p l e . S p e c i m e n d i m e n s i o n a s a b o v e , c o a t i n g
t h i c k n e s s a r o u n d 2 0 0 Hm. D e f e c t s 10 mm s q u a r e a n d s e p a r a t e d b y 10
mm.
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2 A L U M I N A
G R O U N D S U R F A C E
2 0 0 ' G R I T '
P A P E R F I N I S H
coo
SAV-CUTPROFILE
' W V N A AGRAPHITE GRAPHITE
F i g u r e 3 . 5 : G r a p h i t e r o u g h n e s s s a m p l e g e o m e t r y . S a m p l e 1
s q u a r e s e c t i o n b l o c k » 1 0 0 mm l o n g .
0 mm
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TOP VIEW
CD
1 0 MM
5 M M5 M M
2 MM 3 MM
SIDEVIEW
TOP PLATE
BOTTOM PLATE
SPARK ERODED DISC CRATERS IN BOTTOM PLATE
F i g u r e 3 . 6 : S c h e m a t i c i l l u s t r a t i o n o f d i f f u s i o n b o n d e d d e f e c t t e s t
s a m p l e . S u b s t r a t e 10 mm t h i c k * 7 5 mm w i d e 1 5 0 mm l o n g . S u r f a c e
l a y e r d i f f u s i o n b o n d e d t o s u b s t r a t e a nd m a c h i n e d down t o r e q u i r e d
t h i c k n e s s .
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2 mm
CDro
A L UMI N I UM P L A T E A L U M I N I U M PL A T E F L A T B O T T O M DRI LLED HOLE
\P R E S S E D C O N T A C T M I C R O M E T E R PIN HEAD
5 mm
6 mm
P R E S S E D C O N T A C TM I C R O M E T E R PIN HEAD
F i g u r e 3 . 7 : A s c h e m a t i c i l l u s t r a t i o n o f t h e s a m p l e s e t - u p u s e d t o
s t u d y t h e d e t e c t a b i l i t y o f c o n t a c t i n g s u r f a c e s b y t h e r m a l w a v e s .
L e f t , a 2 mm t h i c k a l u m i n i u m p l a t e p r e s s e d i n t o c o n t a c t w i t h a
m i c r o m e t e r p i n h e a d . R e a r s u r f a c e p o l i s h e d t o a 2 Fm a l u m i n a
f i n i s h . R i g h t , s u b s u r f a c e c o n t a c t w i t h i n a p a r t i a l l y f l a t b o t t o m
d r i l l e d h o l e i n a 5 mm t h i c k a l u m i n i u m p l a t e .
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C h a p t e r 4
E x p e r i m e n t a l R e s u l t s
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CHAPTER 4 EXPERI MENTAL RESULTS
4 . 1 SYSTEM E VALU AT I ON
F i g u r e 4 . 1 s h o w s a s c h e m a t i c i l l u s t r a t i o n o f t h e
g e n e r a l r a d i a t i o n s c e n e v i e w e d by an I R d e t e c t o r i n a
p h o t o t h e r m a l NDT s y s t e m . I n a d d i t i o n t o t h e o p t i c a l l y
g e n e r a t e d t h e r m a l e m i s s i o n a t t h e s a m p l e ) t h e r e c a n be
t h r e e o t h e r s o u r c e s o f I R r a d i a t i o n .
a) From the hot plasma tube o f the argon ion l a s e r .
b) S i gna l genera ted by r e f l e c t e d l a s e r l i g h t absorbed
a t the d e t e c t o r window/ o p t i c s .
c) N a t ur a l background thermal r a d i a t i o n f rom the
sample and sur roundi ngs .
S t e p s m u s t b e t a k e n t o e l i m i n a t e o r m i n i m i s e t h e
d e t e c t i o n o f t h e s e s o u r c e s . P h a s e s e n s i t i v e d e t e c t i o n
w i l l d i s c r i m i n a t e a g a i n s t t h e d e t e c t i o n o f i n c o h e r e n t
s i g n a l c o m p o n e n t s s u c h a s t h o s e a r i s i n g - f rom b a c k g r o u n d
v a r i a t i o n s i n t h e r m a l r a d i a t i o n . R e d u c t i o n o f t h e
o t h e r I R c o m p o n e n t s r e q u i r e s p e c i a l a t t e n t i o n and
m e t h o d s a v a i l a b l e t o p r e v e n t t h e i r d e t e c t i o n a r e
d e s c r i b e d i n s e c t i o n 4 . 1 . 1 . P h o t o t h e r m a l s i g n a l
v a r i a t i o n s w i t h l a s e r p o w e r , s a m p l e and d e t e c t o r s e t - u p
a r e d i s c u s s e d i n 4 . 1 . 2 - 3 . T h e f i n d i n g s o f t h e s y s t e m
e v a l u a t i o n a r e d i s c u s s e d i n 4 . 1 . 4 .
4 . 1 . 1 REMOVAL OF UNWANTED INFRARED S I G N A L SOURCES
INFRARED E M I S S I O N FROM THE LASER
W a t e r c o l u m n s o f l e n g t h 2 , 4 , 5 , 6 , 8 and 10 c e n t i m e t r e s
w e r e u se d t o i n v e s t i g a t e t h e r e d u c t i o n o f I R e m i s s i o n
f r o m t h e l a s e r b y a b s o r p t i o n . T h e e x p e r i m e n t a l
a r r a n g e m e n t u s e d i s shown s c h e m a t i c a 1 1 y i n f i g u r e 4 . 2 a .
L a s e r e m i s s i o n was p a s s e d t h r o u g h t h e w a t e r c o l u m n and
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a l l o w e d t o i l l u m i n a t e t h e d e t e c t o r w i n d o w / f i l t e r . The
i n c i d e n t l a s e r p o w e r u s e d was 3 w a t t and t h e m o d u l a t i o n
f r e q u e n c y 10 H z . T h e c h a n g e i n s i g n a l a m p l i t u d e and
p h a s e a n g l e w i t h i n c r e a s i n g w a t e r c o l u m n l e n g t h was
m o n i t o r e d and t h e r e s u l t s o b t a i n e d a r e sho wn i n f i g u r e
<^.2b. B o t h t h e s i g n a l a m p l i t u d e and p h a s e a n g l e
d e c r e a s e d w i t h i n c r e a s i n g w a t e r c o l u m n l e n g t h and
s a t u r a t e d a t c o l u m n l e n g t h s g r e a t e r t h a n A- cm. The
s a t u r a t i o n o f t h e p h a s e a n g l e w i t h i n c r e a s i n g w a t e r
c o l u m n l e n g t h s u g g e s t t h a t t h e d i r e c t I R c o m p o n e n t f r o m
t h e l a s e r t u b e h a s b e e n r e d u c e d o r e l i m i n a t e d . The
p r e s e n c e o f a r e s i d u a l s i g n a l e v e n when a l a s e r l i g h t
r e f l e c t i o n f i l t e r i s u s e d s t r o n g l y c o n f i r m t h e
g e n e r a t i o n o f a s e c o n d a r y s i g n a l a t t h e d e t e c t o r I R
o p t i c s . H e n c e t h e d i r e c t r e f l e c t i o n o f l a s e r r a d i a t i o n
on t o t h e I R o p t i c s mu s t b e a v o i d e d . I n a l l o f t h e
s u b s e q u e n t m e a s u r e m e n t s r e p o r t e d b e l o w a 5 cm w a t e r
c o l u m n was u s e d t o r e d u c e t h e I R r a d i a t i o n f r o m t h e
l a s e r .
REFLECTED LASER L I GH T
T h e g e n e r a t i o n o f a s e c o n d a r y c o h e r e n t s i g n a l b y t h e
a b s o r p t i o n o f r e f l e c t e d l a s e r l i g h t a t t h e d e t e c t o r
w i n d o w c a n b e r e d u c e d by r o t a t i n g t h e s a m p l e t o r e f l e c t
away t h e l a s e r l i g h t o r by e m p l o y i n g s u i t a b l e o p t i c a l
f i l t e r ( s ) t o s e l e c t i v e l y r e f l e c t a w a y t h e l a s e r l i g h t
and t r a n s m i t t h e I R . Th e e f f e c t o f s a m p l e s u r f a c e
r e f l e c t i v i t y i s i l l u s t r a t e d i n f i g . <4.3 a , w h i c h i s a
t r a c e o f t h e v a r i a t i o n o f t h e p h o t o t h e r m a l p h a s e a n g l e
a c r o s s a t e s t p i e c e c o m p r o m i s i n g o f l o w r e f l e c t i v i t y
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g r a p h i t e and h i g h r e f l e c t i v i t y t i t a n i u m . T h e s h a r p
d r o p o f 2 0 d e g r e e s i n t h e p h a s e a n g l e wh e n g o i n g f r o m
g r a p h i t e t o t i t a n i u m i s c a u s e d b y t h e h i g h r e f l e c t i v i t y
o f t h e t i t a n i u m s u r f a c e . I n t r o d u c i n g an i n t e r f e r e n c e
o p t i c a l f i l t e r t o r e f l e c t a wa y t h e l a s e r l i g h t t h e l i n e
t r a c e sh own i n f i g . ^ . 3b i s o b t a i n e d , s h o w i n g t h e
e x p e c t e d p h a s e a n g l e b e h a v i o u r on b o t h t y p e s o f
s u r f a c e s t o b e i n d e p e n d e n t o f s a m p l e o p t i c a l c o n d i t i o n .
I n f i g u r e ^ . 3c t h e i m p r o v e m e n t i n r e j e c t i n g t h e
r e f l e c t e d l a s e r l i g h t b y s a m p l e r o t a t i o n i s p r e s e n t e d
w i t h o u t t h e u s e o f a f i l t e r .
F r om t h e s e m e a s u r e m e n t s i t i s c l e a r t h a t t h e a b o v e
m e a s u r e s s i g n i f i c a n t l y r e d u c e s e c o n d s i g n a l g e n e r a t i o n
a t t h e d e t e c t o r and i n p r a c t i c e b o t h m e a s u r e s s h o u l d b e
t a k e n when i n s p e c t i n g r e f l e c t i v e s u r f a c e s .
*f. 1 . 2 LASER POUER LEVEL
F i g u r e 4- .^ sh ows t h e v a r i a t i o n o f t h e p h o t o t h e r m a l
s i g n a l w i t h i n c i d e n t l a s e r p o w e r . T h e m e a s u r e m e n t s a r e
made on a 2 5 0 Fm LC1B c o a t i n g a t a m o d u l a t i o n f r e q u e n c y
o f 10 H z . T h e i n t e r f e r e n c e f i l t e r was a l s o u s e d .
B e l o w l a s e r p o w e r s o f 3 w a t t t h e s i g n a l v a r i a t i o n i s
s e e n t o be l i n e a r . F o r l a s e r p o w e r s a b o v e 3 w a t t t h e
s i g n a l shows a n o n - l i n e a r v a r i a t i o n . A c u r v e f i t
a n a l y s i s p r e d i c t s t h a t t h e s i g n a l v a r i a t i o n f o l l o w s a
c u r v e o f t h e f o r m :
( 4 . 1 ) Signal ~ al 0 + cl Iw h e r e a , b , c a r e c o n s t a n t s and I 0 i s t h e i n c i d e n t l a s e r
p o w e r . T h i s e q u a t i o n f o l l o w s d i r e c t l y f r o m e q u a t i o n
2 . A- and t h e s u r f a c e t e m p e r a t u r e e x p r e s s i o n s d e v e l o p e d
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i n a p p e n d i x 2 . T h e p h a s e a n g l e a p p e a r s t o show l i t t l e
v a r i a t i o n w i t h l a s e r p o w e r w i t h i n t h e e x p e r i m e n t a l
n o i s e o f h a l f a d e g r e e . I t a l s o r e m a i n s u n c h a n g e d i n
t h e n o n - l i n e a r s i g n a l v a r i a t i o n r e g i o n . T he r i s e i n
p h a s e a n g l e a t l a s e r p o w e r o f 1 w a t t i s d u e t o a p o o r
s i g n a l t o n o i s e r a t i o a t t h i s p o w e r l e v e l .
T he v a r i a t i o n o f p h o t o t h e r m a l s i g n a l w i t h o p t i c a l
s p o t s i z e i s s hown i n f i g u r e ^ . 5 a f o r a . 2 5 0 Hm LC1B
c o a t i n g on s t a i n l e s s s t e e l a t a f r e q u e n c y o f 10 H z . A
c o n v e r g i n g l e n s o f f o c a l l e n g t h o f 2 5 cm was u s e d t o
v a r y t h e o p t i c a l s p o t s i z e . T h e m e a s u r e d p h a s e a n g l e
s h owe d a n a d v a n c e a s t h e l a s e r s p o t was b r o u g h t i n t o
f o c u s . T h e p h a s e a n g l e v a r i a t i o n s f o l l o w a p a t t e r n
s i m i l a r t o t h a t shown i n f i g u r e 2 . 3 d c u r v e 1 , w h i c h
p l o t s t h e t h e o r e t i c a l p h a s e v a r i a t i o n w i t h t h e
n o r m a l i s e d p a r a m e t e r o p t i c a l s p o t s i z e / t h e r m a l
d i f f u s i o n l e n g t h .
C h a n g e s i n t h e o p t i c a l s p o t s i z e w i l l a l s o a f f e c t
t h e p h a s e - t h i c k n e s s c a l i b r a t i o n c u r v e a n d h e n c e l e a d t o
i n c o r r e c t t h i c k n e s s m e a s u r e m e n t s . M e a s u r e m e n t s o f t h e
p h a s e v a r i a t i o n w i t h c o a t i n g t h i c k n e s s f o r d i f f e r e n t
beam d i a m e t e r s i s shown i n f i g u r e ^ . 5 b . T h e s a m p l e was
a LC1B c o a t i n g on s t a i n l e s s s t e e l , t h e t e s t f r e q u e n c y
10 Hz a nd a l a s e r p o w e r o f 3 w a t t . D e c r e a s i n g t h e
o p t i c a l s p o t s i z e n o t o n l y s h i f t s t h e p h a s e - t h i c k n e s s
c a l i b r a t i o n c u r v e i n t o an a d v a n c e b u t a l s o r e d u c e s t h e
m a g n i t u d e o f t h e o v e r a l l p h a s e c h a n g e . T h e e x p l a n a t i o n
f o r t h e p h a s e a d v a n c e h a s b e e n d i s c u s s e d a b o v e . The
r e d u c t i o n o f t h e t o t a l p h a s e c h a n g e i s r e l a t e d t o ; a )
t h e t h r e e d i m e n s i o n a l f l o w o f h e a t i n t h e s a m p l e w i t h
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small beam diameters and, b) changes in the thermal
p r o p e r t i e s o f t h e c o a t i n g . F i g u r e 4 . 5 c sh ows a
t h e o r e t i c a l p l o t o f t h e p h a s e a n g l e v a r i a t i o n w i t h
c o a t i n g t h i c k n e s s and d i f f e r e n t o p t i c a l s p o t d i a m e t e r s
f o r a LC1B c o a t i n g o n s t a i n l e s s s t e e l . The t h e r m a l
p r o p e r t i e s o f t h e c o a t i n g a r e a s s u m e d t o b e u n c h a n g e d
a t a l l t h e o p t i c a l s p o t d i a m e t e r s and t h e p h a s e v a l u e
p l o t t e d i s t h e v a l u e a t t h e c e n t r e o f t h e h e a t i n g b ea m .
T he g e n e r a l p h a s e v a r i a t i o n i n t h i s f i g u r e a g r e e
q u a l i t a t i v e l y w i t h t h o s e o b t a i n e d e x p e r i m e n t a l l y . T h e
m a i n d i s a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l and
e x p e r i m e n t a l d a t a i s t h e m a g n i t u d e o f t h e t o t a l p h a s e
c h a n g e a t t h e s m a l l e r o p t i c a l s p o t d i a m e t e r . I n t h e
t h e o r e t i c a l p l o t t h i s p h a s e d i f f e r e n c e i s o n l y t wo
d e g r e e s c o m p a r e d t o n e a r l y t e n d e g r e e s f o r t h e
e x p e r i m e n t a l d a t a . T h i s l a r g e p h a s e d i f f e r e n c e i s
m o s t l i k e l y t o b e r e l a t e d t o c h a n g e s i n t h e c o a t i n g
t h e r m a l p r o p e r t i e s d u e t h e i n c r e a s e d l i g h t beam
i n t e n s i t y w i t h beam f o c u s i n g . T h i s v a r i e s f r o m a n
i n c i d e n t l a s e r p o w e r o f 3 w a t t d e p o s i t e d o n a s p o t o f 2
mm d i a m e t e r down t o a s p o t o f 0 . 4 mm d i a m e t e r . T h i s
c o r r e s p o n d , r o u g h l y , t o a s t e a d y s t a t e t e m p e r a t u r e
c h a n g e f r o m 2 0 t o 4 5 0 K, a s s u m i n g h e a t g e n e r a t i n g
e f f i c i e n c y o f u n i t y and 50*/. l i g h t a b s o r p t i o n .
E L L I P S O I D A L COLLECTOR
I n f i g u r e 4 . 6 t h e v a r i a t i o n o f t h e p h o t o t h e r m a l
s i g n a l w i t h i n c i d e n t l a s e r p o w e r c a n be s e e n u s i n g an
e l l i p s o i d a l m i r r o r c o l l e c t o r . C o m p a r i n g t h i s w i t h
f i g u r e 4 . 4 , u s i n g t h e m i r r o r c o l l e c t o r h a s r e s u l t e d i n
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a 3 0 f o l d i n c r e a s e i n t h e d e t e c t e d s i g n a l .
M e a s u r e m e n t s a t l a s e r p o w e r s down t o 5 0 m i l l i w a t t was posV»t).
w i t h a p h a s e n o i s e o f o n e d e g r e e . S i g n a l a m p l i t u d e
v a l u e s a t t h i s p o w e r l e v e l c o r r e s p o n d e d t o t h o s e
o b t a i n e d w i t h o u t t h e c o l l e c t o r a t a l a s e r p o w e r o f 1
w a t t . The p h a s e a n g l e s h o w e d l i t t l e v a r i a t i o n f o r
l a s e r p o w e r s g r e a t e r t h a n 2 w a t t s b u t was o b s e r v e d t o
f a l l b y 4 d e g r e e s w i t h d e c r e a s i n g l a s e r p o w e r . The
r e a s o n f o r t h i s l a r g e c h a n g e i n t h e p h a s e a n g l e a t l o w
p o w e r l e v e l s i s u n c l e a r .
A l t h o u g h t h e d e t e c t e d s i g n a l was g r e a t e r when u s i n g
t h e c o l l e c t o r t h e r e w e r e p r o b l e m s wh en r e f l e c t i v e
s u r f a c e s w e r e e x a m i n e d . F i g u r e A . 7 s h o ws t h e o b s e r v e d
p h a s e v a r i a t i o n w i t h s a m p l e r o t a t i o n f o r b u l k g r a p h i t e
and t i t a n i u m . T h e p h a s e a n g l e s f r o m b o t h s u r f a c e s a r e
n o t t h e same d e s p i t e t h e u s e o f t h e i n t e r f e r e n c e
r e f l e c t i o n f i l t e r . S a m p l e r o t a t i o n a p p e a r s t o h e l p
t h e p h a s e a n g l e on t h e t i t a n i u m s u r f a c e t o a p p r o a c h
t h a t on t h e g r a p h i t e s u r f a c e , b u t t h e r e i s s t i l l a
p h a s e d i f f e r e n c e o f n e a r l y 10 d e g r e e s b e t w e e n t h e
samp 1e s .
I n f i g u r e 4 . 8 t h e r e p r o d u c i b i 1 i t y o f t wo c o n s e c u t i v e
l i n e s c a n t r a c e s a r e p r e s e n t e d a c r o s s a t h i c k n e s s s t e p
on a n LC1B c o a t i n g u s i n g t h i s s y s t e m . T h e l a s e r p o w e r
was a 1 0 0 m i l l i w a t t and t h e c h o p p i n g f r e q u e n c y 10 H z .
I n f i g u r e 4 . 9 t h e p h a s e c h a n g e a c r o s s t h e t h i c k n e s s
s t e p w i t h v a r y i n g l a s e r p o w e r i s p r e s e n t e d s h o w i n g i t s
i n v a r i a n c e w i t h i n c r e a s i n g l a s e r p o w e r .
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4 . 1 . 3 SAMPLE AND DETECTOR R OTAT I ON
A f u r t h e r e x p e r i m e n t a l p a r a m e t e r t h a t n e e d s t o b e
e v a l u a t e d i s t h e a n g u l a r p o s i t i o n i n g o f t h e s a m p l e /
d e t e c t o r . I n f i g u r e 4 . 1 0 t h e v a r i a t i o n o f t h e
p h o t o t h e r m a l s i g n a l w i t h s a m p l e r o t a t i o n and f i x e d
d e t e c t o r p o s i t i o n i s s h o w n . ( M e a s u r e m e n t s w i t h o u t t h e
e l l i p s o i d a l c o l l e c t o r . ) A t t h e z e r o d e g r e e p o s i t i o n
t h e l a s e r beam i s n o r m a l t o t h e s a m p l e s u r f a c e . As
t h e s a m p l e i s r o t a t e d b o t h t h e s i g n a l a m p l i t u d e and
p h a s e a n g l e sho w a maximum b e t w e e n —2 0 and - 1 0 d e g r e e .
I n t h i s o r i e n t a t i o n t h e s a m p l e i s o b s e r v e d t o b e n o r m a l
t o t h e d e t e c t o r . T h e p h a s e a n g l e v a r i a t i o n a r o u n d t h e
p e a k i s l e s s t h a n o n e d e g r e e f o r a s a m p l e r o t a t i o n o f ±
2 0 d e g r e e s . F i g u r e 4 . 1 1 s h o w s t h e s i g n a l a m p l i t u d e
and p h a s e v a r i a t i o n w i t h d e t e c t o r r o t a t i o n . A g a i n t h e
p h a s e a n g l e c h a n g e s v e r y l i t t l e w h e n t h e d e t e c t o r i s
r o t a t e d b y a s much a s 2 5 d e g r e e s .
F i g u r e 4 . 1 2 a shows t h e p h a s e d i f f e r e n c e w i t h s a m p l e
r o t a t i o n a c r o s s a s t e p t h i c k n e s s c h a n g e on a LC1B
c o a t i n g s a m p l e f r o m 1 5 0 - 2 0 0 Fm. T y p i c a l l i n e s t r a c e s
a r e s hown i n f i g u r e 4 . 1 2 b f o r v a r i o u s s a m p l e r o t a t i o n
a n g l e s . T h e s e m e a s u r e m e n t s a l s o show t h a t w i t h i n t h e
e x p e r i m e n t a 1 n o i s e , t h e p h a s e s t e p s o b s e r v e d a r e
u n a f f e c t e d b y s a m p l e r o t a t i o n .
4 . 1 . 4 D I S C U S S I O N
The r e s u l t s r e p o r t e d a b o v e show t h a t many
n o n - t h e r m a l v a r i a b l e s i n f l u e n c e t h e p h a s e a n g l e o f t h e
d e t e c t e d s i g n a l .
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a) IR emission from the l a s e r .
b) Re f l e c t e d l ase r l i g h t .
c) Sample / d e t e c t o r r o t a t i o n .
d) O p t i c a l spot s i z e .
T h e s e v a r i a b l e s c a n make c a l i b r a t i o n c u r v e s u n r e l i a b l e
and h i n d e r q u a n t i t a t i v e a n a l y s i s . T h e f i r s t t wo
v a r i a b l e s l e a d t o a c o h e r e n t n o i s e s i g n a l and t h e l a s t
t wo a r e d e p e n d a n t on t h e e x p e r i m e n t a l s e t - u p . I n
4 . 1 . 1 s i m p l e m e a s u r e s w e r e o u t l i n e d t o r e d u c e o r
e l i m i n a t e p h a s e v a r i a t i o n s a s s o c i a t e d w i t h ( a ) and ( b ) .
I n a p r a c t i c a l s y s t e m s p e c i a l d i c h o r i c f i l t e r s w i l l
n e e d t o b e u s e d i n s e p a r a t i n g t h e o p t i c a l and I R
c o m p o n e n t f r o m t h e i l l u m i n a t i o n s o u r c e .
I n 4 . 1 . 2 - 3 t h e m a g n i t u d e o f p h a s e v a r i a t i o n s l i k e l y
t o b e e x p e c t e d w i t h o p t i c a l s p o t s i z e and s a m p l e /
d e t e c t o r p o s i t i o n i n g e r r o r s w e r e d e t e r m i n e d . T h e
r e l a t i v e p o s i t i o n i n g o f t h e s a m p l e / I R d e t e c t o r h a d
l i t t l e e f f e c t on t h e p h a s e a n g l e p r o v i d e d t h a t t h e
a n g u l a r p o s i t i o n i n g v a r i a t i o n s w e r e m a i n t a i n e d l e s s
t h a n 2 0 d e g r e e s . T h e l a r g e s t v a r i a t i o n s i n t h e p h a s e
a n g l e r e s u l t e d w i t h c h a n g e s i n t h e o p t i c a l s p o t s i z e a s
t h i s d i m e n s i o n be c a me c o m p a r a b l e w i t h t h e t h e r m a l
d i f f u s i o n l e n g t h , 2 0 0 pm. I t was n o t e d t h a t a s l o n g a s
t h e l a s e r beam d i a m e t e r i s i n e x c e s s o f 2 mm t h e p h a s e
a n g l e r e m a i n s c o n s t a n t .
T h e e m p l o y m e n t o f an e l l i p s o i d a l m i r r o r c o l l e c t o r
r e s u l t e d i n a 3 0 f o l d i n c r e a s e i n t h e I R d e t e c t i o n
e f f i c i e n c y . T h e l a r g e s o l i d a n g l e o f I R c o l l e c t i o n ,
0 . 6 ' 7 o f t h e c o l l e c t o r c o m p a r e d t o 0 . 0 0 1 6 o f t h e u n a i d e d
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d e t e c t o r , i s t h e p r i m a r y r e a s o n f o r t h e i n c r e a s e i n
d e t e c t i o n e f f i c i e n c y . T h e s e f i g u r e s s u g g e s t an
e x p e c t e d i n c r e a s e i n t h e d e t e c t e d s i g n a l o f n e a r l y ^ 0 0 .
T h i s h a s n o t b e e n r e a l i s e d d u e t o p o s s i b l e h i g h
r e f l e c t i o n l o s s e s a t t h e d e t e c t o r w i n d o w / f i l t e r f o r
r a d i a t i o n i n c i d e n t a t a n g l e s r e m o v e d f r o m t h e n o r m a l .
H e n c e o n l y a l i m i t e d f r a c t i o n o f t h e c o l l e c t e d I R
r a d i a t i o n i s f o c u s e d on t o t h e I R d e t e c t o r e l e m e n t . To
r e g a i n . t h e l o s t s i g n a l i t w i l l b e n e c e s s a r y t o
c o l l i m a t e t h e i n c i d e n t r a d i a t i o n so t h a t i t i s n o r m a l l y
i n c i d e n t a t t h e I R d e t e c t o r .
W i t h t h i s i m p r o v e m e n t i n I R d e t e c t i o n e f f i c i e n c y
l a s e r p o w e r s down t o 5 0 m i l l i w a t t w e r e s u f f i c i e n t f o r
t h i c k n e s s m e a s u r e m e n t s on L C1B t y p e c o a t i n g s . T h i s
p o w e r r a n g e i s w e l l w i t h i n t h e c a p a b i l i t i e s o f
c o m m e r c i a l l o w p o w e r e d g a s l a s e r s a n d r e c e n t l y , h i g h
p o w e r e d s e m i - c o n d u c t o r l a s e r . C u r r e n t t e c h n o l o g y
o f f e r s c o n t i n u o u s w a v e o u t p u t o f 1 w a t t C 8 5 1 . I n
s e c t i o n m e a s u r e m e n t s a r e p r e s e n t e d on t h i c k n e s s
g a u g i n g o f LC1B c o a t i n g u s i n g a n e a r I R l a s e r d i o d e f o r
s a m p l e h e a t i n g .
• 5 SURFACE ROUGHNESS
I n t h i s s e c t i o n m e a s u r e m e n t s a r e r e p o r t e d t o a s s e s s
t h e e f f e c t s o f s u r f a c e r o u g h n e s s on t h e p h a s e a n g l e o f
t h e p h o t o t h e r m a l s i g n a l . M e a s u r e m e n t s a r e f i r s t
r e p o r t e d f r o m a s - s p r a y e d ' f i n e 7 and ' c o a r s e 7 LC1B
c o a t i n g s t o d e t e r m i n e t h e m a g n i t u d e o f p h a s e a n g l e
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v a r i a t i o n s 1 . D a t a i s a l s o p r e s e n t e d f r o m b u l k h i g h
d e n s i t y n u c l e a r g r a p h i t e w i t h i t s s u r f a c e r o u g h e n e d
w i t h e m e r y p a p e r o r mesa c u t .
4 . 2 - 1 LC1B F I N E AND ROUGH COATI NGS
T h e e f f e c t s o f s u r f a c e r o u g h n e s s on t h e m e a s u r e d
p h a s e a n g l e on p l a s m a s p r a y e d LC1B c o a t i n g s w i t h
d i f f e r e n t t h i c k n e s s a r e s h o wn i n f i g u r e 4 . 1 3 a - d f o r
m o d u l a t i o n f r e q u e n c i e s o f 1 0 , 2 5 , 3 6 , and 6 4 Hz
r e s p e c t i v e l y . I n a l l c a s e s t h e p h a s e a n g l e m e a s u r e d on
t h e r o u g h c o a t i n g shows a p h a s e a n g l e a d v a n c e w i t h
r e s p e c t t o t h e v a l u e s o b t a i n e d on t h e s m o o t h c o a t i n g .
T h e p h a s e d i f f e r e n c e b e t w e e n t h e r o u g h a nd f i n e
s u r f a c e s r i s e s t o a p e a k a s t h e c o a t i n g t h i c k n e s s
i n c r e a s e s a n d a p p e a r s t o s a t u r a t e w i t h i n c r e a s i n g
f r e q u e n c y . I n f i g u r e 4 . 1 4 t h e p h a s e d i f f e r e n c e b e t w e e n
t h e r o u g h a n d s m o o t h s a m p l e a r e p l o t t e d a g a i n s t r o o t
f r e q u e n c y . T h e p h a s e m e a s u r e m e n t s a r e f r o m a 10 mm
l i n e a v e r a g e on a n o m i n a l 2 5 0 Hm c o a t i n g t h i c k n e s s . On
r e m o v i n g t h e s u r f a c e r o u g h n e s s b y p o l i s h i n g ( a 6 0 0
e m e r y p a p e r f i n i s h ) t h e p h a s e a n g l e m e a s u r e d on t h i s
s u r f a c e c o r r e l a t e d w e l l , s e e f i g . 4 . 1 5 , t o t h a t
m e a s u r e d o n t h e s mo o t h a s - s p r a y e d s a m p l e .
4 . 2 . 2 GR A P H I T E SAMPLES
I n f i g u r e 4 . 1 6 t h e p h a s e a n g l e d i f f e r e n c e w i t h r o o t
f r e q u e n c y f r o m a 2 0 0 g r i t f i n i s h and a mesa s a w - t o o t h
c u t g r a p h i t e s u r f a c e a r e p r e s e n t e d . T h e s e s a m p l e
s u r f a c e c o n d i t i o n s r e p r e s e n t t h e w i d e s t d i f f e r e n c e i n
1 F i n e and c o a r s e r e f e r t o t h e c o a t i n g p o w d e r t y p e u s e d t o d e p o s i t t h e c o a t i n g .
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the surface roughness and the surface thermal
p r o p e r t i e s . T h e p h a s e d i f f e r e n c e d a t a o f f i g u r e 4 . 1 6
i s o b t a i n e d f r o m l i n e t r a c e m e a s u r e m e n t s a c r o s s a f l a t
and r o u g h r e g i o n on a s a m p l e . S a m p l e l i n e t r a c e s
a c r o s s t h e s e s u r f a c e s a r e sh o wn i n f i g u r e 4 . 1 6 c f o r a
t e s t f r e q u e n c y o f 7 H z . F o r t h e s a w - t o o t h g r a p h i t e
s a m p l e t h e r o u g h n e s s p e a k s a p p e a r t o b e w e l l r e s o l v e d ,
□n f u r t h e r i n v e s t i g a t i o n i t was f o u n d t h a t t h e o p t i c a l
s p o t s i z e d e t e r m i n e d t h e m a g n i t u d e o f t h e p h a s e p e a k s
a n d t h e i r r e s o l u t i o n . To c o v e r t h e f r e q u e n c y r a n g e
shown i n t h e s e f i g u r e s a c a d m i u m m e r c u r y t e l l u r i d e
( CMT) I R d e t e c t o r w i t h a g e r m a n i u m l e n s was u s e d f o r
s i g n a l d e t e c t i o n . T h e i n c i d e n t l a s e r p o w e r was 5
w a t t s . As w i t h t h e LC1B c o a t i n g s s a m p l e s , t h e p h a s e
d i f f e r e n c e b e t w e e n t h e r o u g h s u r f a c e a n d f l a t ( l H
a l u m i n a f i n i s h ) s h o w s a n a d v a n c e . T h e p h a s e a d v a n c e i s
a l s o d e p e n d e n t o n t h e m o d u l a t i o n f r e q u e n c y . T h e p e a k
p h a s e a d v a n c e o b s e r v e d on b o t h s a m p l e i s a r o u n d 2 5 - 2 9
d e g r e e s . ( T h e e r r o r b a r s s hown i n t h e f i g u r e s a r e
t h o s e f r o m a l i n e a v e r a g e o f 15 mm on t h e r o u g h s u r f a c e
and a r e n o t a s s o c i a t e d w i t h e l e c t r o n i c n o i s e i n t h e
m e a s u r e m e n t s y s t e m ) .
The d a t a o f f i g u r e 4 . 1 6 b was f i t t e d t o t h e
t h e o r e t i c a l p h a s e c u r v e s g e n e r a t e d b y m o d e l l i n g t h e
s a w - t o o t h r o u g h n e s s p r o f i l e a s a l a y e r o f f i n i t e
t h i c k n e s s and d i f f e r i n g t h e r m a l p r o p e r t i e s . F i g u r e
4 . 1 7 shows t h e f i t t i n g o b t a i n e d . T h e l a y e r t h i c k n e s s
u s e d i s t h e r o o t mean s q u a r e s u r f a c e r o u g h n e s s and t h e
t h e r m a l p r o p e r t i e s a r e u s e d a s t h e f i t t i n g p a r a m e t e r s .
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A s s u m i n g t h a t t h e d a t a f i t s t h e t h e o r e t i c a l p h a s e c u r v e
f o r a r e f l e c t i o n c o e f f i c i e n t o f - 0 . 6 5 , t h e n t h e
e f f e c t i v e t h e r m a l p r o p e r t y v a l u e s i n d i c a t e d i n t h e
f i g u r e a r e o b t a i n e d . T h e mesa r o u g h n e s s p r o f i l e
b e h a v e s a s t h o u g h t h e t h e r m a l e f f u s i v i t y o f t h e s u r f a c e
h a s b e e n r e d u c e d by a f a c t o r o f 5 .
T h e p h a s e a d v a n c e on t h e s e g r a p h i t e r o u g h n e s s
s a m p l e s w e r e a l s o f o u n d t o b e d e p e n d a n t on l a s e r
p o w e r . W i t h i n c r e a s i n g l a s e r p o w e r t h e p h a s e a d v a n c e
on t h e s a m p l e i n c r e a s e d . S a m p l e r o t a t i o n h a d l i t t l e
e f f e c t on t h e o b s e r v e d p h a s e a d v a n c e on t h e s e g r a p h i t e
s a m p l e s . T h e s e o b s e r v a t i o n s a r e s u m m a r i s e d i n f i g u r e
4 . 1 8 .
* f . 5 . 3 D I S C U S S I O N
T h e a b o v e m e a s u r e m e n t s s ho w t h a t s u r f a c e r o u g h n e s s
i n d u c e s a p h a s e i n c r e a s e r e l a t i v e t o t h a t m e a s u r e d on
a n o m i n a l l y f l a t s u r f a c e . On a r o u g h LC1B c o a t i n g a
p h a s e a d v a n c e o f 2 - 3 d e g r e e s was m e a s u r e d . On a
r o u g h e n e d g r a p h i t e s u r f a c e t h e p h a s e a d v a n c e was a s
h i g h a s 2 5 - 3 0 d e g r e e s . T h e s e i n i t i a l o b s e r v a t i o n s
s u g g e s t t h a t t h e s c a l e o f t h e s u r f a c e r o u g h n e s s and i t s
t h e r m a l p r o p e r t i e s d i c t a t e t h e m a g n i t u d e o f t h e p h a s e
a d v a n c e . A d e t a i l e d s t u d y on t h e g r a p h i t e r o u g h n e s s
s a m p l e s a l s o showed t h a t t h e p h a s e a d v a n c e i s d e p e n d e n t
on t h e m o d u l a t i o n f r e q u e n c y , l a s e r p o w e r and s p o t s i z e .
P h a s e d a t a o b t a i n e d f r o m LC1B r o u g h n e s s s a m p l e s
sh owed a c l o s e s i m i l a r i t y t o t h e t h e o r e t i c a l p h a s e
v a r i a t i o n m o d e l l e d i n f i g u r e 2 . 1 1 i n w h i c h t h e s u r f a c e
r o u g h n e s s i s r e p r e s e n t e d by a f i n i t e l a y e r o f w e l l
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d e f i n e d t h i c k n e s s and r e d u c e d t h e r m a l c o n d u c t i v i t y . A
s i m i l a r a n a l y s i s o f t h e p h a s e d a t a f r o m t h e mesa
g r a p h i t e r o u g h n e s s s a m p l e was a l s o p o s s i b l e w i t h t h e
c o n c l u s i o n t h a t t h e r m a l e f f u s i v i t y o f t h e s u r f a c e l a y e r
ha d b e e n r e d u c e d by a f a c t o r o f f i v e .
T h i s s u r f a c e r o u g h n e s s s t u d y h a s r e v e a l e d t h e
a b s e n c e o f a p h a s e l a g a t a r o u g h s u r f a c e . A p h a s e
l a g may b e e x p e c t e d i f o n e c o n s i d e r p h a s e v a r i a t i o n s
f r o m t h e e d g e s , c o r n e r s a n d mesa s t r u c t u r e s o n t h e
s a m p l e s u r f a c e s a m p l e s C 8 6 J . A n u m e r i c a l a n a l y s i s i s
r e q u i r e d t o d e t e r m i n e w h e t h e r a p h a s e l a g o r a n a d v a n c e
i s e x p e c t e d a t a r o u g h s u r f a c e . A d i f f i c u l t y w i t h t h e
t e s t s a m p l e s u s e d a b o v e i s t h a t b o t h t h e s u r f a c e
t o p o g r a p h y and s u r f a c e t h e r m a l p r o p e r t i e s w e r e a l t e r e d
w i t h p o l i s h i n g / r o u g h e n i n g . T h i s m a k e s i t i m p o s s i b l e
t o c o r r e l a t e t h e o b s e r v e d p h a s e a n g l e c h a n g e s w i t h
s u r f a c e t o p o g r a p h y o n l y . F o r t h e s a m p l e s s t u d i e d h e r e
i t a p p e a r s t h a t t h e s u r f a c e t h e r m a l p r o p e r t i e s c h a n g e s
a r e c o n t r i b u t i n g s i g n i f i c a n t l y t o t h e p h a s e a d v a n c e s
o b s e r v e d .
. 3 DEFECTS
S u b s u r f a c e d e f e c t s h a v e a c h a r a c t e r i s t i c p h a s e
r e s p o n s e w i t h i n c r e a s i n g f r e q u e n c y n a m e l y a p h a s e
a d v a n c e a t l ow f r e q u e n c i e s t o a p h a s e l a g a t h i g h
f r e q u e n c i e s . I n t h i s s e c t i o n m e a s u r e m e n t s a r e
r e p o r t e d on m a n u f a c t u r e d d e f e c t s a m p l e s t o a s s e s s t h e
p h o t o t h e r m a l t e c h n i q u e f o r s u b s u r f a c e d e f e c t
c h a r a c t e r i s a t i o n and t h e d e t e c t i o n o f c o n t a c t i n g
i n t e r f a c e s . T h e p h o t o t h e r m a l s y s t e m i s a l s o c o m p a r e d
w i t h u l t r a s o n i c m e a s u r e m e n t s .
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* + . 3 . 1 SQUARE DEFECTS I N LC1B COATI NGS
PHOTOTHERMAL I N V E S T I G A T I O N
I n f i g u r e ^+.19 5 0 mm l i n e s c a n t r a c e s a r e p r e s e n t e d
a c r o s s t h e d e f e c t s i n p o l i s h e d a nd a s - s p r a y e d LC1B
c o a t i n g a t a f r e q u e n c y o f 8 H z . T h e l i n e t r a c e s a r e a t
t h e p o s i t i o n s i n d i c a t e d i n f i g u r e ^ . 2 0 . T a b l e . 1
p r o v i d e s a s u mma r y o f t h e p h a s e v a r i a t i o n o v e r t h e
d e f e c t r e g i o n s . I n b o t h s a m p l e s d e f e c t s A , B and D
w e r e r e a d i l y d e t e c t a b l e . D e f e c t C f a i l e d t o be
d e t e c t e d . A p h a s e i n c r e a s e o f a b o u t 1 . 5 d e g r e e s was
o b s e r v e d a t t h e d e f e c t s i t e s . T h e d e f e c t s f o u n d i n
t h e p o l i s h e d s a m p l e showed up m o r e s t r o n g l y t h a n t h o s e
d e t e c t e d o n t h e a s s p r a y e d s a m p l e . To d e t e r m i n e
w h e t h e r t h e p h a s e i n c r e a s e a t t h e d e f e c t s i t e i s d u e t o
a d h e s i o n d e f i c i e n c i e s a f r e q u e n c y r e s p o n s e o f d e f e c t A
i n t h e a s - s p r a y e d and B a n d D i n t h e p o l i s h e d s a m p l e s
w e r e e x a m i n e d . F i g u r e 4- . 21 s h o w s l i n e t r a c e s o f t h e
p h a s e v a r i a t i o n s o f t h e s e d e f e c t s w i t h f r e q u e n c y . Th e
a b s e n c e o f a p h a s e l a g w i t h i n c r e a s i n g f r e q u e n c y
s u g g e s t s t h a t t h e s e p h a s e v a r i a t i o n s a r e n o t d u e t o
s u b s u r f a c e a d h e s i o n d e f e c t s . T h e p h a s e a d v a n c e a t t h e
d e f e c t i s m o r e i n d i c a t i v e o f l o c a l i s e d s u b s u r f a c e
t h e r m a l p r o p e r t y c h a n g e p r o b a b l y d u e t o i n c r e a s e d
p o r o s i t y . T h i s a s s e r t i o n was v e r i f i e d by o p t i c a l
m i c r o s c o p y , f i g u r e * f . 2 2 , w h e r e s i g n i f i c a n t v a r i a t i o n i n
t h e l o c a l m i c r o s t r u c t u r e b e t w e e n s i t e s r e m o t e and
w i t h i n t h e d e f e c t r e g i o n s w e r e o b s e r v e d .
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ULT RASONI C I N V E S T I G A T I O N
An u l t r a s o n i c e x a m i n a t i o n CB7D o f t h e a s - s p r a y e d
d e f e c t s a m p l e was a l s o u n d e r t a k e n t o c o m p a r e i t s
p e r f o r m a n c e w i t h t h e p h o t o t h e r m a l t e c h n i q u e i n s e n s i n g
t h e s e d e f e c t s i t e s . M e a s u r e m e n t on t h e s a m p l e w e r e
made d i f f i c u l t d u e t o s a m p l e c u r v a t u r e n e a r t h e d e f e c t
r e g i o n s . F i g u r e 4 . 2 3 s h o ws l i n e s c a n t r a c e s o f s i g n a l
a t t e n u a t i o n a c r o s s t h e ’ d e f e c t 7 r e g i o n s i n t h e
p o l i s h e d , f i g . 4 . 2 3 a , a n d a s - s p r a y e d , f i g . 4 . 2 3 b ,
s a m p l e . O n l y d e f e c t s A a n d B i n t h e a s - s p r a y e d s a m p l e
s h o w e d s i g n i f i c a n t p e r t u r b a t i o n i n t h e s i g n a l v a r i a t i o n
a c r o s s t h e d e f e c t r e g i o n s . A d e c r e a s e i n s i g n a l
a t t e n u a t i o n r a t h e r t h e n a n i n c r e a s e was o b s e r v e d a c r o s s
t h e d e f e c t s i t e s . T h e d e c r e a s e i n s i g n a l a t t e n u a t i o n
may b e e x p l a i n e d a s b e i n g d u e t o t h e p r e s e n c e o f w a t e r
i n t h e p o r o u s m i c r o s t r u c t u r e w h i c h w i l l r e s u l t i n l o w e r
i m p e d a n c e m i s m a t c h l o s s e s o f t h e t r a n s m i t t e d u l t r a s o n i c
b e a m .
B o t h t h e p h o t o t h e r m a l a n d t h e u l t r a s o n i c
m e a s u r e m e n t s i n d i c a t e t h e a b s e n c e o f i n t e r f a c e d e f e c t s
i n t h e s e s a m p l e s . T h e r e i s h o w e v e r a l o c a l i s e d c h a n g e
i n t h e c o a t i n g m i c r o s t r u c t u r e .
4 . 3 . 2 D I F F U S I O N BONDED DEFECT SAMPLES
W i t h t h e d i f f i c u l t y i n p r o d d c i n g c o m p l e t e l y
d e l a m i n a t e d d e f e c t s i n p l a s m a s p r a y e d c o a t i n g s , d e f e c t s
i n d i f f u s i o n b o n d e d m i l d s t e e l / m i l d s t e e l ( M S / M S ) and
m i l d s t e e l / s t a i n l e s s s t e e l ( M S / S S ) s a m p l e s w e r e
s t u d i e d . D e t a i l s o f s a m p l e g e o m e t r y and d e f e c t s i z e s
a r e s u m m a r i s e d i n f i g u r e 3 . 6 .
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I n f i g u r e 4 . 2 4 l i n e s c a n t r a c e s t h r o u g h t h e c e n t r e
o f 10 and 5 mm d e f e c t i n MS/ MS s a m p l e ( s a m p l e n o . 4 )
a r e p r e s e n t e d a t s e v e r a l m o d u l a t i o n f r e q u e n c i e s . T h e
s a m p l e s u r f a c e was l i g h t l y d a r k e n e d w i t h s o o t f r o m a
c a n d l e f l a m e t o i n c r e a s e l i g h t a b s o r p t i o n and t h e r m a l
e m i s s i o n . T h e t r a c e s p r e s e n t e d show a p h a s e l a g a t t h e
d e f e c t . T h e m a g n i t u d e o f p h a s e l a g g o e s t h r o u g h a
maximum w i t h i n c r e a s i n g f r e q u e n c y and d i s a p p e a r s i n t h e
s a m p l e p h a s e n o i s e a t h i g h e r f r e q u e n c i e s . T h i s t y p e o f
p h a s e v a r i a t i o n i s c h a r a c t e r i s t i c o f s u b s u r f a c e
a d h e s i o n d e f e c t s .
F i g u r e 4 . 2 5 sh ows a p l o t o f t h e p h a s e d i f f e r e n c e 22
w i t h r o o t f r e q u e n c y o f t h e 5 and 10 mm d e f e c t d i a m e t e r
i n MS/MB f i t t e d t o t h e o r e t i c a l d e f e c t p h a s e l o c i u s i n g
l i t e r a t u r e v a l u e s f o r t h e t h e r m a l p r o p e r t i e s o f m i l d
s t e e l a n d a i r . T h e t h e o r e t i c a l c u r v e s a r e g e n e r a t e d
a s s u m i n g o n e d i m e n s i o n a l h e a t f l o w a nd a i r - g a p d e f e c t s
o f f i n i t e t h i c k n e s s . T h e d a t a a p p e a r s t o b e a g o o d f i t
a t h i g h m o d u l a t i o n f r e q u e n c i e s f o r b o t h d e f e c t
d i a m e t e r s , 5 a nd 10 mm. A t l o w f r e q u e n c i e s h o w e v e r ,
t h e r e i s a s i g n i f i c a n t d e p a r t u r e f r o m t h e o n e
d i m e n s i o n a l d e f e c t p h a s e l o c u s w i t h t h e 5 mm d i a m e t e r
d e f e c t . T h e i t e r a t i v e f i t t i n g t e c h n i q u e u s e d p r e d i c t s
t h e d e f e c t d e p t h t o b e a r o u n d 9 0 0 Hm and d e f e c t
t h i c k n e s s g r e a t e r t h a n o r e q u a l t o 1 0 0 Hm. T h e d e f e c t
d e p t h i s i n good a g r e e m e n t w i t h t h e t h i c k n e s s
m e a s u r e m e n t p r o v i d e d w i t h t h e t e s t s a m p l e o f 1 mm.
F u r t h e r l i n e t r a c e s f r o m d e f e c t s o f d i f f e r e n t
d i a m e t e r a r e p r e s e n t e d i n f i g u r e 4 . 2 6 a - d f o r a M S / SS
2 phase d i f f e r e n c e = phase at d e f ec t minus phase away from d e f e c t .
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s a m p l e ( s a m p l e n o . 3 ) and a c o m p o s i t e p h a s e d i f f e r e n c e
a g a i n s t r o o t f r e q u e n c y p l o t i s c o m p i l e d i n f i g u r e 4 . 2 7 .
U i t h d e c r e a s i n g d e f e c t d i a m e t e r t h e p h a s e d i f f e r e n c e a t
t h e d e f e c t b e c o m e s mo r e p o s i t i v e a n d t h e r e i s p o o r
c o r r e s p o n d e n c e o f t h e o b s e r v e d p h a s e m e a s u r e m e n t t o
t h a t o f t h e o n e d i m e n s i o n a l d e f e c t m o d e l . T h i s
d e p a r t u r e o f t h e e x p e r i m e n t a l d a t a f r o m t h e one
d i m e n s i o n a 1 d e f e c t p h a s e c u r v e i s d u e p r i n c i p a 1 l y t o
t h e t h r e e d i m e n s i o n a l d i f f u s i o n o f h e a t a t low
m o d u l a t i o n f r e q u e n c i e s . A t t h e s e l o w f r e q u e n c i e s t h e
t h e r m a l d i f f u s i o n l e n g t h b e c o m e s l a r g e ( f e w m i l l i m e t r e s
) and l a t e r a l h e a t d i f f u s i o n c a n no l o n g e r be
n e g l e c t e d . A t h r e e d i m e n s i o n a l h e a t d i f f u s i o n a n a l y s i s
p r o v i d e s t h e p h a s e l o c i s h o w n i n f i g u r e 4 . 2 8 f o r t h e
p h a s e a n g l e v a r i a t i o n a t t h e s u r f a c e o f t h e a b o v e
d e f e c t s a m p l e w i t h d i f f e r e n t o p t i c a l s p o t d i a m e t e r s 3 .
T h e d e p a r t u r e o f t h e p h a s e a n g l e a t l o w m o d u l a t i o n
f r e q u e n c i e s i s c l e a r l y s h o w n i n t h i s f i g u r e a s i s t h e
d e p e n d e n c e on h e a t i n g beam d i a m e t e r .
4 . 3 . 3 THERMAL CONTACT R E S I S T A N C E
I n f i g u r e 4 . 2 9 l i n e t r a c e s a r e p r e s e n t e d o f t h e
p h a s e d i f f e r e n c e b e t w e e n c o n t a c t i n g a n d n o n - c o n t a c t i n g
s u r f a c e s d e m o n s t r a t i n g t h e a b i l i t y o f p h o t o t h e r m a l
t e c h n i q u e i n d e t e c t i n g c o n t a c t i n g s u r f a c e s . The
c o n t a c t g e o m e t r y f o r b o t h f i g u r e s i s s hown f i g u r e 3 . 7 .
I n b o t h c a s e s t h e s u b s u r f a c e c o n t a c t i s r e a d i l y v i s i b l e
and t h e p h a s e c h a n g e a t t h e c o n t a c t i s p o s i t i v e . T h i s
c a n be e x p l a i n e d q u a l i t a t i v e l y a s i l l u s t r a t e d
3 In the phase p l o t o f f i g u r e ^ . 2 8 no a ccount has been taken o f hea t d i f f u s i o n around the d e f e c t .
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s c h e m a t i c a l l y i n f i g u r e 4 . 3 0 . U l i t h o u t c o n t a c t t h e
p h a s e a n g l e r e c o r d e d r e p r e s e n t s a d e f e c t o f i n f i n i t e
c o n t a c t r e s i s t a n c e . W i t h c o n t a c t ) t h e t h e r m a l c o u p l i n g
b e t w e e n t h e s a m p l e s s i g n i f i c a n t l y r e d u c e s t h i s
r e s i s t a n c e a n d t h e c o n t a c t p h a s e c u r v e i s f o r c e d i n t o
a n a d v a n c e r e l a t i v e t o t h e no c o n t a c t p h a s e l o c u s . I t
i s t h e d i f f e r e n c e o f t h e s e p h a s e c u r v e s w h i c h p r o v i d e s
t h e p o s i t i v e p h a s e c h a n g e s h own i n f i g u r e <+. 2 9 .
^ . 3 . ^ D I S C U S S I O N
T h e a b o v e i n v e s t i g a t i o n s show c l e a r l y t h e
s e n s i t i v i t y o f t h e t h e r m a l w a v e t e c h n i q u e f o r d e t e c t i n g
m a t e r i a l p o r o s i t y , i n t e r f a c e d e f e c t s a nd p r e s s e d
c o n t a c t s . A c o m p a r i s o n b e t w e e n u l t r a s o n i c and
p h o t o t h e r m a l m e a s u r e m e n t s a p p e a r t o s u g g e s t t h a t t h e
t h e r m a l w a v e t e c h n i q u e i s m o r e s e n s i t i v e i n d e t e c t i n g
a b n o r m a l s u b s u r f a c e c o n d i t i o n s t h e n u l t r a s o n i c s . T h i s
a s p e c t o f t h e s t u d y r e q u i r e s f u r t h e r i n v e s t i g a t i o n s a s✓
t h e u l t r a s o n i c r e s p o n s e o f t h e ' s q u a r e d e f e c t ' s a m p l e s
w e r e o n l y s t u d i e d a t o n e a r b i t r a r y t e s t f r e q u e n c y o f 5
MHz .
P h a s e a n g l e m e a s u r e m e n t s on t h e d i f f u s i o n b o n d e d
d e f e c t s a m p l e s o f v a r y i n g d i a m e t e r and d e p t h i l l u s t r a t e
t h e c a p a b i l i t y a n d l i m i t a t i o n s f o r q u a n t i t a t i v e
s u b s u r f a c e d e f e c t c h a r a c t e r i s a t i o n . To a n a l y s e t h e
p h a s e a n g l e d a t a a t l o w f r e q u e n c i e s a n u m e r i c a l m o d e l
n e e d s t o be d e v e l o p e d w h i c h t a k e s i n t o a c c o u n t t h e
f i n i t e w i d t h and t h i c k n e s s o f t h e d e f e c t , t h e o p t i c a l
h e a t i n g and I R d e t e c t i o n s p o t s i z e s on t h e s a m p l e .
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4 . 4 SEMI - CONDUCTOR LASER D I ODE SYSTEM EVALUATI ON
I t was n o t e d i n s e c t i o n 4 . 1 . 4 t h a t t h e u s e o f an
e l l i p s o i d a l m i r r o r c o l l e c t o r r e s u l t e d i n a 3 0 f o l d
i n c r e a s e i n t h e d e t e c t e d s i g n a l . I t was a l s o
d i s c u s s e d t h a t t h i s i m p r o v e m e n t i n t h e I R c o l l e c t i o n
e f f i c i e n c y w o u l d a l l o w much l o w e r l a s e r p o w e r s t o be
u s e d f o r s a m p l e h e a t i n g . I n t h e f o l l o w i n g s e c t i o n s
m e a s u r e m e n t s a r e r e p o r t e d on t h e u s e o f a n o p t i c a l
f i b r e c o u p l e d s e m i c o n d u c t o r l a s e r d i o d e f o r s a m p l e
h e a t i n g . F i g u r e 4 . 3 1 s h o ws a s c h e m a t i c i l l u s t r a t i o n o f
t h e e x p e r i m e n t a l s e t - u p u s e d f o r e v a l u a t i n g t h e l a s e r
d i o d e NDT s y s t e m .
4 . 4 . 1 LASER POUIER LEVEL STUDY
I n f i g u r e 4 . 3 2 t h e s i g n a l a m p l i t u d e a nd p h a s e
v a r i a t i o n w i t h l a s e r p o w e r i s s h o w n . T h e m o d u l a t i o n
f r e q u e n c y was 10 Hz a n d t h e s a m p l e a 2 5 0 Hm t h i c k LC1B
c o a t i n g on s t a i n l e s s s t e e l . A l i n e a r c h a n g e i n s i g n a l
a m p l i t u d e w i t h l a s e r p o w e r i s o b s e r v e d b e t w e e n 0 . 0 5 a n d
0 . 3 W a t t . S i g n a l l e v e l s r e c o r d e d a r e r o u g h l y a f a c t o r
o f 3 l o w e r when c o m p a r e d w i t h t h e v a l u e s o b t a i n e d w i t h
t h e a r g o n i o n l a s e r . T h e p h a s e a n g l e sh o ws a s m a l l
v a r i a t i o n w i t h l a s e r p o w e r a n d t h e p h a s e n o i s e i s l e s s
t h a n 0 . 5 d e g r e e s f o r l a s e r p o w e r a b o v e 0 . 1 5 W a t t .
S I GN AL AMPLI TUDE AND PHASE ANGLE V A R I A T I O N
WITH F I B R E HEAD P O S I T I O N I N G
W i t h o p t i c a l f i b r e c o u p l i n g o f l a s e r e m i s s i o n t h e
h e a t e d s p o t on t h e s a m p l e s u r f a c e c a n b e l o c a t e d i n a
v a r i e t y o f p o s i t i o n w i t h r e s p e c t t o t h e a r e a s e n s e d by
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t h e I R d e t e c t o r . An a s s e s s m e n t i s t h e r e f o r e n e c e s s a r y
t o d e t e r m i n e t h e e f f e c t s o f f i b r e p o s i t i o n i n g on t h e
d e t e c t e d p h o t o t h e r m a l s i g n a l . I n f i g u r e 4 . 3 3 t h e
s i g n a l a m p l i t u d e and p h a s e v a r i a t i o n w i t h t h e d i s t a n c e
o f t h e f i b r e h e a d f r o m t h e s a m p l e i s p l o t t e d . The
s i g n a l a m p l i t u d e i n i t i a l l y r i s e s a nd t h e n f a l l w i t h
i n c r e a s i n g d i s t a n c e a s t h e f i b r e h e a d i s moved away
f r o m t h e s a m p l e s u r f a c e . T h e i n i t i a l r i s e o f t h e
s i g n a l i s d u e t o t h e d e t e c t o r b e i n g a b l e t o ’ s e e ’ mo r e
o f t h e h e a t e d a r e a a s t h e f i b r e h e a d i s r e t a r d e d . The
s i g n a l d e c a y a n d i n c r e a s i n g p h a s e l a g a s t h e f i b r e h e a d
i s f u r t h e r r e t a r d e d f r o m t h e s a m p l e s u r f a c e i s m a i n l y
d u e t o i n c r e a s e s i n t h e l a s e r s p o t d i a m e t e r on t h e
s a m p l e s u r f a c e a s a r e s u l t o f beam d i v e r g e n c e . A t v e r y
s h o r t d i s t a n c e s f r o m t h e s a m p l e s u r f a c e t h e s p o t s i z e
c a n b e e x p e c t e d t o b e t h a t o f t h e o p t i c a l f i b r e
d i a m e t e r ) 2 5 0 Fm. T h i s d i a m e t e r i s a p p r o x i m a t e l y e q u a l
t o t h e t h e r m a l d i f f u s i o n l e n g t h i n t h e c o a t i n g o f 2 0 0
Fm a t 10 H z . A s i m i l a r p h a s e b e h a v i o u r was a l s o n o t e d
i n s e c t i o n 4 . 1 . 2 , f i g u r e 4 . 5 , w h e r e t h e a r g o n i o n l a s e r
beam d i a m e t e r i s v a r i e d .
F i g u r e 4 . 3 4 shows t h e v a r i a t i o n o f s i g n a l a m p l i t u d e
and p h a s e a n g l e a s t h e f i b r e h e a d i s moved t h r o u g h t h e
I R d e t e c t i o n s p o t h o r i z o n t a l l y . T h e s i g n a l a m p l i t u d e
c h a n g e i s s y m m e t r i c a b o u t t h e d e t e c t i o n s p o t b u t t h e
p h a s e a n g l e c h a n g e i s a s y m m e t r i c . T h e r e a s o n f o r t h i s
i s d u e t o a c o v e r i n g o f t h e d e t e c t i o n s p o t b y t h e
o p t i c a l f i b r e h e a d as i t i s moved o v e r t h e r e g i o n
s a m p l e d by t h e I R d e t e c t o r ( s e e f i g . 4 . 3 1 ) . M o v i n g t h e
f i b r e h e a d i n a v e r t i c a l d i r e c t i o n t h r o u g h t h e
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d e t e c t i o n s p o t , t h e d a t a sho wn i n f i g u r e 4 . 3 5 a r e
o b t a i n e d . I n t h i s c a s e b o t h s i g n a l a m p l i t u d e and p h a s e
a n g l e show t h e e x p e c t e d s y m m e t r i c d i s t r i b u t i o n a b o u t
t h e d e t e c t i o n s p o t .
• 3 LC1B COATING TH I CKN ESS MEASUREMENTS
I n f i g u r e 4 . 3 6 a and b p h a s e a n g l e l i n e s c a n t r a c e s
a r e p r e s e n t e d f o r m e a s u r e m e n t s on LC1B c o a t i n g s a t 10
a n d S5 H z , r e s p e c t i v e l y , u s i n g a l a s e r p o w e r o f . 3
W a t t . A l s o s h o w n a n t h e s e f i g u r e s a r e t h e
c o r r e s p o n d i n g t r a c e s o b t a i n e d w i t h a r g o n i o n l a s e r
h e a t i n g . T h e l a t t e r t r a c e s a r e s l i g h t l y d i s p l a c e d
v e r t i c a l l y f o r c l a r i t y . T h e r e i s e x c e l l e n t
r e p r o d u c i b i 1 i t y w i t h c o n s e c u t i v e t r a c e s o b t a i n e d w i t h
t h e s e m i c o n d u c t o r l a s e r a nd a l s o a c l o s e m a t c h t o t h e
d a t a o b t a i n e d w i t h t h e a r g o n i o n l a s e r s y s t e m . T h e
’ n o i s y 7 a p p e a r a n c e o f t h e l i n e t r a c e s o b t a i n e d w i t h t h e
s e m i c o n d u c t o r l a s e r i s b e l i e v e d t o b e a s s o c i a t e d w i t h
t h e f i n e r s p o t s i z e u s e d f o r s a m p l e h e a t i n g .
4 . 4 . 4 D I S C U S S I O N
T h e s e i n i t i a l m e a s u r e m e n t s w i t h t h e l a s e r d i o d e
s y s t e m c l e a r l y d e m o n s t r a t e t h e s u c c e s s i n u s i n g s u c h a
l a s e r s o u r c e f o r s a m p l e h e a t i n g . T h e t h i c k n e s s
m e a s u r e m e n t s o b t a i n e d a r e v e r y s i m i l a r t o t h o s e
o b t a i n e d w i t h t h e a r g o n i o n l a s e r . W i t h t h e f o c u s e d
I R d e t e c t i o n s y s t e m u s e d h e r e a c a r e f u l c o n t r o l o v e r
t h e I R d e t e c t i o n and t h e i l l u m i n a t i o n s p o t on t h e
s a m p l e i s r e q u i r e d . T h e r e r e l a t i v e p o s i t i o n s on t h e
s a m p l e n ee d t o b e m a i n t a i n e d f i x e d t o a v o i d p h a s e a n g l e
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v a r i a t i o n s o f t h e t y p e i l l u s t r a t e d i n f i g u r e s
4 . 3 3 - 4 . 3 5 .
A p r a c t i c a l d i f f i c u l t y i n t h e u s a g e o f t h e l a s e r
s y s t e m was t h e a l i g n m e n t o f t h e l a s e r i l l u m i n a t i o n
( w h i c h i s i n v i s i b l e w i t h p r o t e c t i v e e y e g o g g l e s ) w i t h
t h e I R d e t e c t i o n s p o t on t h e s a m p l e . T h e l a t t e r i s
d e t e r m i n e d by m a x i m i s i n g t h e d e t e c t e d p h o t o t h e r m a l
s i g n a l w i t h f i n e a d j u s t m e n t s o f t h e v e r t i c a l and
a n g u l a r p o s i t i o n i n g o f t h e I R d e t e c t o r . F o r a
p r a c t i c a l s y s t e m a s e t - u p i n w h i c h t h e o p t i c a l and I R
d e t e c t i o n s p o t a r e c o i n c i d e n t i s v e r y d e s i r a b l e .
4 . 5 INFRARED DETECTOR E V A L U A T I O N .
I n t h e f o l l o w i n g p a r a g r a p h s m e a s u r e m e n t s a r e
p r e s e n t e d o f t h e i n f r a r e d d e t e c t o r f r e q u e n c y r e s p o n s e ,
t h e p h o t o t h e r m a l f r e q u e n c y r e s p o n s e o f b u l k t i t a n i u m
a n d a LC1B c o a t i n g a n d t h e p h a s e a n g l e n o i s e o f t h e
d e t e c t i o n s y s t e m .
4 . 5 . 1 INFRARED DETECTOR FREQUENCY RESPONSE.
F i g u r e 4 . 3 7 a and b show r e s p e c t i v e l y , t h e s i g n a l
a n d p h a s e r e s p o n s e w i t h f r e q u e n c y o f t h e p y r o e l e c t r i c
TGS i n f r a r e d d e t e c t o r o b t a i n e d when v i e w i n g c h o p p e d
t h e r m a l r a d i a t i o n f r o m a s o l d e r i n g i r o n a t a
t e m p e r a t u r e o f 2 0 0 C t h r o u g h a 10 mm a p e r t u r e . The
f r e q u e n c y r a n g e c o v e r e d i s f r o m 10 t o 8 8 0 H z . A t
f r e q u e n c i e s l e s s t h a n 2 5 Hz t h e s i g n a l v a r i a t i o n
a p p e a r s t o s a t u r a t e . W i t h i n c r e a s i n g f r e q u e n c y t h e
s i g n a l d e c a y s v e r y r a p i d l y a t a r a t e a p p r o x i m a t e 1 y
p r o p o r t i o n a l t o i n v e r s e c u b e f r e q u e n c y . T h e p h a s e
114
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a n g l e v a r i a t i o n a l s o s hows a l a r g e c h a n g e . T h e r a t e o f
c h a n g e b e i n g r a p i d b e t w e e n 10 and 5 0 0 Hz a nd t e n d i n g t o
s a t u r a t e f o r f r e q u e n c i e s g r e a t e r t h a n 5 0 0 H z .
4 . 5 . 2 PHOTOTHERMAL FREQUENCY RESPONSE .
T h e a b o v e f r e q u e n c y m e a s u r e m e n t s c a n be u s e d t o
o b t a i n t h e p h o t o t h e r m a l f r e q u e n c y r e s p o n s e o f a t e s t
s a m p l e . F i g u r e s ^ . 3 B a and b show r e s p e c t i v e l y , t h e
n o r m a l i s e d s i g n a l and p h a s e v a r i a t i o n o f a 10 mm t h i c k
t i t a n i u m and a 2 5 0 Hm t h i c k LC1B c o a t i n g on s t a i n l e s s
s t e e l . T h e i n c i d e n t l a s e r p o w e r was 4 w a t t a n d t h e I R
d e t e c t o r was s c r e e n e d b y t h e l a s e r l i g h t r e f l e c t i o n
f i l t e r . T h e n o r m a l i s e d s i g n a l d a t a was o b t a i n e d b y
e v a l u a t i n g t h e r a t i o o f t h e o b s e r v e d s i g n a l v a l u e t o
t h a t o f t h e d e t e c t o r f r e q u e n c y r e s p o n s e s i g n a l . The
p h a s e d a t a i s o b t a i n e d b y a s u b t r a c t i o n o f t h e m e a s u r e d
s a m p l e p h a s e a n g l e w i t h t h a t o f t h e d e t e c t o r p h a s e a t
t h e c o r r e s p o n d i n g f r e q u e n c y . T h e n o r m a l i s e d s i g n a l
v a r i a t i o n f o r b o t h s a m p l e s show t h a t t h e p h o t o t h e r m a l
d e c a y s a s i n v e r s e l y p r o p o r t i o n a l t o s q u a r e r o o t
f r e q u e n c y . T h e p h a s e a n g l e v a r i a t i o n i s s e e n t o b e
f l a t a t h i g h f r e q u e n c i e s and i n c r e a s e s a t l o w
f r e q u e n c i e s .
4 . 5 . 3 PHASE ANGLE NOI SE
F i g u r e 4 . 3 9 sho ws t h e o b s e r v e d p h a s e n o i s e w i t h
f r e q u e n c y m e a s u r e d a t a s p o t on a LC1B c o a t i n g f r o m 2 0 0
m e a s u r e m e n t s i n a t i m e p e r i o d o f 5 m i n u t e s . T h e p h a s e
n o i s e i s s e e n t o be b e t w e e n 0 . 1 and 0 . 5 d e g r e e s and
i n c r e a s e s w i t h i n c r e a s i n g f r e q u e n c y . I n t h e s e
115
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m e a s u r e m e n t s i t was n o t e d t h a t f o r s i g n a l v a l u e s b e l o w
0 . 2 m i l l i v o l t s t h e p h a s e n o i s e c a n b e i n e x c e s s one
d e t e c t a b l e s i g n a l o f a p p r o x i m a t e l y 5 0 m i c r o v o l t s c o u l d
be m e a s u r e d b y t h e l o c k - i n a m p l i f i e r . I n t h i s c a s e t h e
p h a s e n o i s e r e c o r d e d u s i n g a 3 s e c o n d t i m e c o n s t a n t was
i n e x c e s s o f 5 d e g r e e s .
4 . 5 . 4 D I S C U S S I O N .
T h e s h a r p v a r i a t i o n s o f t h e d e t e c t o r f r e q u e n c y
r e s p o n s e i s d u e t o t h e c l o s e m a t c h o f t h e t i m e
c o n s t a n t s o f t h e d e t e c t o r s i g n a l r e s p o n s i v i t y C 7 8 , 8 3 3 .
A b a s i c e x p r e s s i o n f o r s i g n a l f r e q u e n c y r e s p o n s e o f a
p y r o e l e c t r i c d e t e c t o r e x c l u d i n g p o s t d e t e c t i o n
e l e c t r o n i c a m p l i f y i n g c i r c u i t s t a k e s t h e f o r m :
w h e r e t e a nd t -t a r e r e s p e c t i v e l y , t h e e l e c t r i c a l and
t h e r m a l t i m e c o n s t a n t s f o r t h e i n f r a r e d d e t e c t o r C 8 3 3 .
' A * i s a c o n s t a n t f o r t h e d e t e c t o r a nd r e p r e s e n t s t h e
p y r o e l e c t r i c , t h e r m a l and p h y s i c a l p r o p e r t i e s o f t h e
f r e q u e n c y , a s i g n a l v a r i a t i o n i n v e r s e l y p r o p o r t i o n a l t o
p o s s i b l e r e a s o n f o r t h i s d i s c r e p a n c y may be d u e t o t h e
n e g l e c t i n e q u a t i o n 4 . 2 o f t h e m o d i f i c a t i o n o f t h e
d e g r e e . U i t h o u t a n y l a s e r i l l u m i n a t i o n no s i g n a l was
d e t e c t a b l e b y t h e l o c k - i n a m p l i f i e r . A mi n i mum
(4.2) Signal« A to
d e t e c t o r e l e m e n t . T h i s e q u a t i o n p r e d i c t s a t h i g h
f r e q u e n c y . T h e i s i n d i s a g r e e m e n t w i t h t h e o b s e r v e d
s i g n a l d e c a y r a t e o f i n v e r s e c u b e f r e q u e n c y . A
s i g n a l f r e q u e n c y r e s p o n s e w i t h a s s o c i a t e d s i g n a l
a m p l i f y i n g c i r c u i t s . T h e s e c i r c u i t s a r e w i d e l y u s e d
116
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t o b o o s t t h e v o l t a g e r e s p o n s i v i t y o f t h e i n f r a r e d
d e t e c t o r s a t t h e e x p e n s e o f a l i m i t e d f r e q u e n c y
r e s p o n s e C7 BD .
T h e i n v e r s e s q u a r e r o o t f r e q u e n c y v a r i a t i o n o f t h e
p h o t o t h e r m a l s i g n a l f o r t h e t i t a n i u m and LC1B c o a t i n g
i n d i c a t e s t h a t t h e s e s a m p l e a r e b e h a v i n g a s
s e m i - i n f i n i t e o p a q u e m e d i a . T h i s f r e q u e n c y v a r i a t i o n
o f t h e p h o t o t h e r m a l s i g n a l f o l l o w s t h a t p r e d i c t e d , s e e
t a b l e 2 . 2 , b y t h e o n e h e a t d i f f u s i o n t h e o r y . A n o t h e r
p r e d i c t i o n o f t h i s t h e o r y i s p h a s e a n g l e i n d e p e n d e n c e
w i t h f r e q u e n c y . T h i s b e h a v i o u r a p p e a r s t o b e
s a t i s f i e d w i t h t h e e x p e r i m e n t a l d a t a a t f r e q u e n c i e s
a b o v e H z . A t f r e q u e n c i e s l o w e r t h a n t h i s t h e
n o r m a l i s e d p h a s e a n g l e d a t a sh o ws a n i n c r e a s e . T h e s e
i n c r e a s e a r e d u e t o t wo d i f f e r e n t r e a s o n s . F o r t h e
t i t a n i u m s a m p l e t h e p h a s e i n c r e a s e i s r e l a t e d t o t h r e e
d i m e n s i o n a l h e a t d i f f u s i o n e f f e c t s , i n p a r t i c u l a r w i t h
t h e i n c r e a s e i n t h e t h e r m a l d i f f u s i o n l e n g t h w i t h
d e c r e a s i n g f r e q u e n c y r e l a t i v e t o t h e l a s e r s p o t s i z e .
F o r t h e c o a t i n g s a m p l e t h e p h a s e i n c r e a s e d u e t o
t h e r m a l w a v e i n t e r f e r e n c e i n t h e c o a t i n g . As d i s c u s s e d
i n s e c t i o n 2 . 4 - a p h a s e a n g l e i n c r e a s e w i l l b e o b t a i n e d
f r o m c o a t i n g s y s t e m s i n w h i c h t h e c o a t i n g / s u b s t r a t e
r e f l e c t i o n c o e f f i c i e n t i s n e g a t i v e , i . e a c o a t i n g w i t h
i t s t h e r m a l e f f u s i v i t y l o w e r t h a n t h a t o f t h e
s u b s t r a t e .
117
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LASER ILLUMINATION
R E F L E C T E D
V I S I B L E
A N D I R
R A D I A T I D N
(VISIBLE AND INFRARED CDMPDNENTS)
V 7
INFRAREDDETECTOR
EMMITED IR RADIATION
SECOND SIGNAL GENERATION
DETECTORELEMENTDETECTOR WINDOW '
BACKGROUNDTHERMALRADIATION
TEST SPECIMEN
THERMAL DIFFUSION ZONE
F i g u r e ^ . 1 : R a d i a t i o n s c e n e v i e w e d b y t h e i n f r a r e d d e t e c t o r .
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SIG
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8 012
COLUMN OF WATER / cm COLUMN OF WATER / cm
F i g u r e 4 . 2 : T o p : A t r a n s m i s s i o n p h o t o t h e r m a l s e t - u p . 1 ) A r g o n i o nL a s e r , 2 ) L i g h t c h o p p e r , 3 ) w a t e r i n r e c t a n g u l a r c o n t a i n e r , and 4 )i n f r a r e d d e t e c t o r .B o t t o m : M e a s u r e d s i g n a l a n d p h a s e v a r i a t i o n w i t h w a t e r c o l u m n l e n g t h f o r l a s e r l i g h t n o r m a l l y i n c i d e n t on t h e d e t e c t o r w i n d o w ( A ) , and on t h e i n t e r f e r e n c e r e f l e c t a n c e f i l t e r < B ) .
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co
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Graphife Tifanium
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Graphife Tifanium
F i g u r e ^ . 3 a : P h a s e a n g l e t r a c e a c r o s s a g r a p h i t e and
t i t a n i u m s u r f a c e w i t h o u t l a s e r l i g h t s c r e e n i n g .
b ) As a b o v e b u t w i t h i n t e r f e r e n c e f i l t e r f i t t e d t o t h e
i n f r a r e d d e t e c t o r .
c ) As f i g . ^ . 3 a a b o v e b u t w i t h s a m p l e r o t a t e d t o r e f l e c t
a way t h e s c a t t e r e d l a s e r l i g h t f r o m t h e i n f r a r e d
d e t e c t o r .
120
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SIG
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L A S E R POW ER / W a t t
F i g u r e 4-. ^ : P h o t o t h e r m a l s i g n a l v a r i a t i o n w i t h i n c i d e n t l a s e r
p o w e r on a LC1B c o a t i n g s a m p l e on 3 1 6 s t a i n l e s s s t e e l a t a
m o d u l a t i o n f r e q u e n c y o f 10 H z .
PHASE ANGLE
(PE
G.)
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SIG
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V ’ - ® -4 mm
50 100 150 200 250C O R T IN G T H IC K N E S S ( U M )
0IN C R E R S IN G DEFOCUS
11B 1 2 5 r
“DIILT)m
izorm
120
ouP 11!
UJ J0 n o zc
UJ(J) 10E1 (L
100
F i g u r e 4 . 5 a : P h o t o t h e r m a l s i g n a l v a r i a t i o n w i t h i n c r e a s i n g o p t i c a l
s p o t s i z e .
F i g u r e 4 . 5 b : P h a s e a n g l e v a r i a t i o n w i t h c o a t i n g t h i c k n e s s and
o p t i c a l s p o t s i z e . T e s t f r e q u e n c y 10 H z .
300
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PH
AS
E
AN
GLE
C
DE
G
35
/ \
-5500Q
T H I C K N E S S / um
F i g u r e ^ . 5 c : T h e o r e t i c a l p h a s e a n g l e v a r i a t i o n w i t h c o a t i n g t h i c k n e s s and o p t i c a l s p o t s i z e . O p t i c a l s p o t s i z e 1 ) 0 . ^ , 2 ) 1 , 3 ) 2 , and *+) ^mm. M o d e l l e d s a m p l e i s a LC1B c o a t i n g on 3 1 6 s t a i n l e s s s t e e l and a m o d u l a t i o n f r e q u e n c y o f 10 H z . ( N o t e no a c c o u n t h a s b e e n t a k e n o f
s i g n a l a v e r a g i n g b y t h e I R d e t e c t o r o v e r t h e d e t e c t i o n a r e a . )
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SIG
NA
L
7- 1
LASER POWER / w a t t
F i g u r e * + . 6 : S i g n a l a m p l i t u d e and p h a s e a n g l e v a r i a t i o n w i t h l a s e r
p o w e r u s i n g t h e e l l i p s o i d a l m i r r o r c o l l e c t o r .
PHASE ANGLE
CDEG
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1 i o _
- f + + ■
MCJ1
0111avy
UJCO<XfL
9 0- 3 0 3 0
S A M P L E R O T A T I O N C D E G - >
F i g u r e 4 . 7 : P h a s e a n g l e v a r i a t i o n w i t h s a m p l e r o t a t i o n
g r a p h i t e and t i t a n i u m s a m p l e . I n f r a r e d d e t e c t i o n w i t h
c o 1 l e c t o r .
f o r a
mi r r o r
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PH
AS
E
AN
GLE
C
OE
G
10
50O
D I S T A N C E I N MM
F i g u r e * + . 8 : C o n s e c u t i v e 5 0 mm l i n e s t r a c e a c r o s s a 1 5 0 - 2 0 0 Hm t h i c k n e s s
s t e p on a LC1B c o a t i n g . I n c i d e n t l a s e r p o w e r i s 0 . 1 w a t t , t h e
m o d u l a t i o n f r e q u e n c y o f 10 Hz a nd i n f r a r e d d e t e c t i o n w i t h m i r r o r
co 1 l e c t o r .
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7
N>vj
r \
6LU□
U.Llw□
liiU)<IQ-
O
L A S E R POWER / W a t t
F i g u r e 4-. 9 : A p l a t o f t h e p h a s e a n g l e c h a n g e w i t h i n c i d e n t l a s e r
p o w e r f o r a 1 5 0 - 2 0 0 Hm t h i c k n e s s s t e p o n a LC1B c o a t i n g a t a
m o d u l a t i o n f r e q u e n c y o f 10 Hz and i n f r a r e d d e t e c t i o n w i t h m i r r o r
c o l l e c t o r .
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SIG
NR
L
(MV
)
3 5
S I G N R L
2 5
++ oo
1 5
P H R S E//
- 5 0 - 7 0 - 5 0 - 3 0 - 1 0 1 0 3 0 5 0 7 0 3 0R O T A T I O N A N G L E C D E G . )
3 2
3 1
3 0 A>z3 3 U
IID
8 8 Wm J
(EB7 ID Z2 00 H3 5 r inm
3 5 Adm
8 4 oV
8 3
8 2
1 3 53 5
3 01 3 4'
2 5
1 3 320
1 5
10P H R S E
1 3 01 0 2 0 3 0 4 0 5 0 5 0 7 0 8 0 3 00
D E T E C T O R A N G L E (D E C . )
F i g u r e 4 . 1 0 : P h o t o t h e r m a l s i g n a l v a r i a t i o n w i t h s a m p l e r o t a t i o n .
F i g u r e 4 . 1 1 : P h o t o t h e r m a l s i g n a l v a r i a t i o n w i t h d e t e c t o r r o t a t i o n .
PH
RS
E
RN
GL
E
CD
EG
.
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8
roCD
0LU□
U.IL
LlJ U)<I Q_
- 7 0
SA MP LE R O T A T I O N C D E G - >
J7 0
F i g u r e <=+.12a: P h a s e a n g l e v a r i a t i o n a c r o s s a t h i c k n e s s s t e p on a
LC1B c o a t i n g s a m p l e f o r v a r i o u s r o t a t i o n a n g l e s
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SIGN
AL
/ nV
20
P H R S E0
0 20DISTANCE IN MM
10
V \
VJ
20
w v / v
0
10
DISTANCE IN MM 20
20
200 DISTANCE IN MM
10
0
F i g u r e 4 . 1 P b : P h a s e a n g l e l i n e t r a c e s a c r o s s a s t e p
t h i c k n e s s c h a n g e o n a L C l t ) c o a t i n g s a m p l e a t v a r i o u s
s p e c i m e n r o t a t i o n a n g l e s .
130
PHASE ANGLE
CDEG.)
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PHRSE
RNGLE
(DEC.
2064 Hz36 Hz25 Hz10 Hz
s;t Ts'K ,h|+
280 2800 0COATING THICKNESS (/am)
F i g u r e 4 . 1 3 : P h a s e a n g l e m e a s u r e m e n t s o n f i n e < ) and
c o a r s e ( ------------ ) LC1B c o a t i n g s o n 3 1 6 s t a i n l e s s s t e e l a t m o d u l a t i o n
f r e q u e n c i e s o f a ) . 10> b ) 25» c ) 3 6 and d ) 6 4 H z .
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132
7
CD UJ□v
LlLlw□
LU<I Q_
- 3□ 2 4
S QR T. F R E Q U E N C Y C / H z 1
F i g u r e 4 . 1 * + : A p l o t o f t h e p h a s e d i f f e r e n c e w i t h s q u a r e r o o t
f r e q u e n c y b e t w e e n c o a r s e a nd f i n e LC1B c o a t i n g o f n o m i n a l
t h i c k n e s s 2 5 0 Fm.
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130
1 28
126
124
“ 3 6 H Z 122
_l 120
2 0 M MD I S TflNCE0
13010
128
POLISHED126S
/Hv 124 |
1223 6 H Z
120D I S T A N C E 25 MM0
13 0
128
126
122
120D I S T A N C E0 10 M M
130
128
126S/MV
122
120D I S T A N C E0 10 M M
F i g u r e ^ . 1 5 : P h a s e a n g l e l i n e t r a c e s on c o a r s e and f i n e LC1B
c o a t i n g b e f o r e and a f t e r p o l i s h i n g . Top f i g u r e , p h a s e on c o a r s e
s a m p l e and b o t t o m f i g u r e on f i n e c o a t i n g s a m p l e .
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PH
AS
E
CH
AN
GE
(D
EC
)30
27
21
15
30241 012
0uQ
UJ02CCru
UJincx(L
SQRT. FREQUENCY
30
27
21
1 0
15
12
3 025I S
SQRT FREQUENCY
2010
F i g u r e 4-. 1 6 : P l o t s o f t h e p h a s e d i f f e r e n c e ( m e a s u r e d r e l a t i v e t o a
f l a t g r a p h i t e s u r f a c e ) w i t h r o o t f r e q u e n c y f o r a ) a n s a n d p a p e r
r o u g h e n e d and b ) a s a w - t o o t h c u t g r a p h i t e s u r f a c e .
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SIGN
AL
/ m
V
10 4 0
PHASE
SIGNAL
UUIHI!U»IUlUllUiHU!>U»lllU)IU»IHill,>lll II,‘
2 50 DISTANCE IN MM
13X3>(Arn3>Zcnrmr \fc*mpv
20 4 0
PHASE
i—i SIGNAL
o 2 5DISTANCE IN MM
F i g u r e A . 1 6 c : S i g n a l a n d p h a s e a n g l e l i n e t r a c e a c r o s s t h e
r o u g h e n e d and s a w - t o o t h c u t g r a p h i t e r o u g h n e s s s a m p l e a t a
m o d u l a t i o n f r e q u e n c y o f 7 H z . I n c i d e n t l a s e r p o w e r i s 5 w a t t
w i t h i n f r a r e d d e t e c t i o n b y a CMT p h o t o c o n d u c t i v e d e t e c t o r and
i n f r a r e d c o l l e c t i o n b y a g e r m a n i u m l e n s .
PHASE ANGLE
CDEG.)
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PHAS
E AN
GLE
CDEG
. 6 5
□
PROPERTY BULK SURFACE
DENSITY 1940
SPECIFICHEAT 630
THERMALCONDUCTIVITY 150 113
THERMALD IFFU SIV ITY
1 2 3 x l0 E -6 L 5 4 8 x l0 E -6
THERMALEFFU SIVITY
1.35xl0E 4 2,872
PHYSICAL PROPERTY VALUES IN S I UNITS.
F i g u r e <4 . 17 : F i t t i n g o f t h e e x p e r i m e n t a l d a t a o f f i g u r e 4 . 1 6 b t o
a l a y e r o n a s u b s t r a t e t y p e s t r u c t u r e u s i n g e q u a t i o n S . 11 t o
g e n e r a t e t h e t h e o r e t i c a l p h a s e c u r v e s .
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PHA
SE
(DE
G.
25
7O
15 _
rst
ULlJ□v
LlJU)<I0.
J_______L J ; I_______I_______I
L A S E R POWER / W
- 5 2 5S A M P L E ROT- CDEG- >
F i g u r e 4 . 1 8 : P h a s e a n g l e v a r i a t i o n w i t h l a s e r p o w e r a nd s a m p l e
r o t a t i o n o n g r a p h i t e r o u g h n e s s s a m p l e s .
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i 1-------1-------1— ~i------ 1-------1------ r
A B
F i g u r e < + . 19 a : 5 0 mm p h a s e a n g l e
' s q u a r e ’ d e f e c t s a m p l e .
>v V A V V y V ^
3 p H * M w y ^
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139
0 50 nm1 J l i i I I I 1 I 1 |
0 50 nm1 i i i i i i i i i 1 ■ j
C D
F i g u r e 4 . 1 9 b : 5 0 mm p h a s e a n g l e l i n e t r a c e s on a s - s p r a y e d L.C1B
’ s q u a r e 7 d e t e c t s a m p l e .
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140
SAMPLE
DEFECTSPOSITION
25 mm
mm
5911131517
21
F i g u r e 4 . 2 0 : D e t a i l s o f 5 0 mm l i n e t r a c e l o c a t i o n on t h e s q u a r e
d e f e c t p o l i s h e d and a s - s p r a y e d LC1B c o a t i n g s a m p l e .
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POSITIONPOLISHED SURFACE AS--SPRAYED SURFACE
PHASE CHANGE (DEGREES)
PH0T0-THERMAL
A B C D A B C D123456 7
.8
.511
1.32.5 2,03.02.51.0 1.0
—
1.01.01.02.02.02.02.0
1.51.0.751.0.5
1.01.0.75.5.5
.5
.5
.51.0.5
ATTENUA1riON Ch ANGE (dB>5 mm — - — — — — — -
ULTRA 13 nn - _ -3 -2 — —SONICS 21 mm - — — 4 — —
T a b l e 4 . 1 : Summar y o f t h e p h a s e a n g l e a n d u l t r a s o n i c a t t e n u a t i o n c h a n g e a c r o s s t h e s q u a r e d e f e c t LC1B c o a t i n g s a m p l e s .
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PH
AS
E
CD
EG
.
/ \
Q
1
4
w /H Y ty v y u w/ V
1
A ". 1 II.1 ll 111 k .M il H iI I l
1 1 • i
—
□
2 5 mm L I N E T R A C E S
F i g u r e 4 - . 2 1 a : P h a s e a n g l e l i n e t r a c e s a t v a r i o u s f r e q u e n c i e s f o r
d e f e c t A i n t h e a s - s p r a y e d s a m p l e .
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PHAS
E AN
GLE
<DEG
.>
10
D 1ST ftNCE
10
4 Hzo
D I S T A N C E
10 10
8 Hzo
D I S T A N C E
10
D I S T A N C E
10
15 Hz
D 1ST A N C E
10
D 1S T A N C E
10
25 Hz
0 i i i i i i i i iD I S T A N C E
F i g u r e 4 . 2 1 b : P h a s e a n g l e l i n e t r a c e s a t v a r i o u s f r e q u e n c i e s
f o r d e f e c t B a n d L) i n t h e p o l i s h e d s a m p l e .
143
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F i g u r e * * . 2 3 : O p t i c a l m i c r o g r a p h s o f d e f e c t B i n p o l i s h e d s a m p l e .
a ) a wa y f r o m t h e d e f e c t ; 6 mm f r o m t o p e d g e o f s a m p l e , and
b ) w i t h i n t h e d e f e c t r e g i o n ; 12 mm f r o m t o p e d g e o f s a m p l e .
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145
5 d B
T
M
B
T
M
B
F i g u r e < + . 2 3 a : 5 0 mm u l t r a s o n i c a t t e n u a t i o n l i n e t r a c e s o n p o l i s h e d
LC1B ’ s q u a r e ’ d e f e c t s a m p l e . T and B a w a y f r o m t h e d e f e c t a r e a
a n d M t h r o u g h t h e m i d d l e r e g i o n o f t h e d e f e c t .
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5 d B
T
M
B
T
M
B
i g u r e ^ . 2 3 b : 5 0 mm u l t r a s o n i c a t t e n u a t i o n l i n e t r a c e s on
s - s p r a y e d LC1B ’ s q u a r e * d e f e c t s a m p l e . T a n d B a w a y f r o m t h e
e f e c t a r e a and li t h r o u g h t h e m i d d l e r e g i o n o f t h e d e f e c t .
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SIG
NA
L
lOO
A
CDLlJ□\s
UJJGZ<
UJCO<ICL
16
M S / M S
25
M S / m s
25O
D I S T A N C E / mm D I S T A N C E / mm
Figure ^.2^a: Signal and phase angle line traces at variousfrequencies through the 5 mm circular defect in mild steel/ mildsteel diffusion bonded sample.
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SIG
NA
L
/ m
vlOO
M S / M S
16 V V SI
□ 3 0
m s / m s
3 0O
D I S T A N C E / mm D I S T A N C E / mm
F i g u r e 4 . 2 4 b : As f i g . 4 . 2 4 a b u t a c r o s s a 10 mm d i a m e t e r d e f e c t .
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PH
AS
E
DIF
F.
CD
EG
2 0
5 m m
6O
2 0
10 m m
6□
S Q R T . F R E Q U E N C Y S Q R T - F R E Q U E N C Y
F i g u r e <+ . 25 : F i t t i n g o f t h e e x p e r i m e n t a l p h a s e d i f f e r e n c e d a t a
w i t h r o o t f r e q u e n c y t o t h e t h e o r e t i c a l a i r - g a p d e f e c t p h a s e c u r v e s
u s i n g t h e o n e d i m e n s i o n a l s u r f a c e t e m p e r a t u r e e x p r e s s i o n i n t a b l e
2 . 2 .
a ) 10 mm a n d b ) 5 mm d i a m e t e r d e f e c t . S o l i d c u r v e s 1) 0 . 1 , 2 ) 1,
3 ) 10 and 4 ) 1 0 0 Hm a i r - g a p t h i c k n e s s .
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SIG
NA
L
>E
\
O
M S / S S
r 2
64
2 5
lOO
6UJ□V
LUJ□Z<UJI/)<Q.
64M S / S S
2 5D I S T A N C E / mm D I S T A N C E / mm
Figure 4.E6a: Signal and phase angle line traces at variousfrequencies through the 5 mm circular defect in mild steel/stainless steel diffusion bonded sample.
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SIG
NA
L
1 □
M S / SS
>E
\
r 3
64
3 0o
1 o o
r \
6Hi□
UJJoz<LlJin<itL
64
M S / S S
3 0O
D I S T A N C E / mm D I S T A N C E / mm
F i g u r e * t . 2 6 b : As f i g . 2 6 a b u t d e f e c t d i a m e t e r 10 mm
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50
A(JUJ□\yUJJ□z<UJw<IQ_
MS/SS
2 0O
D IS T A N C E / mm
F i g u r e 4 . 2 6 c : 2 0 mm p h a s e a n g l e l i n e t r a c e s a c r o s s a 3 mm d e f e c t
d i a m e t e r a t v a r i o u s f r e q u e n c i e s . M i l d s t e e l / s t a i n l e s s s t e e l
d i f f u s i o n b o n d e d s a m p l e .
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SIGN
AL50
r\I
ULlJ□
111Joz<UJ(/)<IQ-
20O
2 0
>E\
20O
D I S T A N C E / mm D I S T A N C E / mm
F i g u r e 4 . E 6 d : S i g n a l a n d p h a s e a n g l e l i n e t r a c e s a t v a r i o u s
f r e q u e n c i e s t h r o u g h t h e 2 mm c i r c u l a r d e f e c t i n m i l d s t e e l /
s t a i n l e s s s t e e l d i f f u s i o n b o n d e d s a m p l e .
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15
s\MS / S S
go
S Q R T . F R E Q U E N C Y
F i g u r e . 2 7 : A p h a s e d i f f e r e n c e v e r s e s r o o t f r e q u e n c y p l o t f o r
t h e 1 0 , 5 3 a nd 3 mm d i a m e t e r d e f e c t s i n m i l d s t e e l / s t a i n l e s s
s t e e l s a m p l e .
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154
2 0
s\
CD LU□\y
ILLlw□LU(/)<I fL
- 5 0
3 D
oS Q R T . F R E Q U E N C Y
F i g u r e 4 . 2 8 : A t h e o r e t i c a l p l o t of" t h e p h a s e v a r i a t i o n d u e t o
s u b s u r f a c e a i r - g a p d e f e c t 1 0 0 J4fn t h i c k and 1 mm b e l o w t h e s u r f a c e
i n b u l k m i l d s t e e l . P h a s e c u r v e s a r e p l o t t e d f o r h e a t d i f f u s i o n
i n o n e a n d t h r e e d i m e n s i o n a l . L a s e r beam d i a m e t e r 1 . 5 mm.
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onCJI
8
PHASE
S/M
SIGNAL
3DISTANCE
8
PHASE
S/MV
SIGNAL
8DISTANCE 25 HH
F i g u r e ^ . 2 9 : a ) S i g n a l an d p h a s e d i f f e r e n c e l i n e t r a c e when
c o n t a c t i s made b e t w e e n a f l a t a l u m i n i u m p l a t e a n d a m i c r o m e t e r
p i n h e a d , l e f t * a n d r i g h t * when c o n t a c t i s made i n s i d e a
p a r t i a l l y d r i l l e d s u b s u r f a c e h o l e i n a n a l u m i n i u m p l a t e . ( C o n t a c t
g e o m e t r y s h o w n i n f i g u r e 3 . 7 )
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156
THERMAL THICKNESS .
WITHCONTACT \
1 / no/ CONTACT
X (INFINITETHERMAL CONTACT
J RESISTANCE)
PHASE CHANGEWITH SAMPLECONTACT
F i g u r e * + . 3 0 : A s c h e m a t i c i l l u s t r a t i o n o f t h e p h a s e c h a n g e
a no c o n t a c t a n d c o n t a c t s i t u a t i o n .
b e t w e e n
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1 57
IR DETECTION SPOT SIZE
LASERSPOTELLIPSOIDAL
COLLECTOR
INFRAREDDETECTOR
OPTICAL FIBRE CABLE TO LASER SOURCE
SAMPLESURFACE
INFRAREDTRANSMITTINGFILTER
AND & MICROMETER TRANSLATION AND ROTATION
F i g u r e ^ . 3 1 : A s c h e m a t i c i l l u s t r a t i o n o f t h e I R d e t e c t o r , s a m p l e
a n d o p t i c a l f i b r e h e a d s e t - u p f o r m e a s u r e m e n t s t a k e n w i t h t h e
s e m i - c o n d u c t o r l a s e r .
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cnoo
>E
\
J<Z□w0)
lO
O
8
“0X>COm>z(Drm/~\omco
L A S E R POWER / W a t t
F i g u r e 4 . 3 2 : P h o t o t h e r m a l s i g n a l v a r i a t i o n w i t h l a s e r p o w e r a t a
m o d u l a t i o n f r e q u e n c y o f 10 H z . T h e t e s t s a m p l e i s 2 5 0 Fm LC1B
c o a t i n g o n s t a i n l e s s s t e e l .
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15
r\
□lli□
LlIJGZ<LlJ(/)<Xa.
61
i □
>E
\
J<Zg
61
D I S T A N C E / mm D I S T A N C E / m m
F i g u r e * + . 3 3 : P h o t o t h e r m a l s i g n a l v a r i a t i o n a s t h e o p t i c a l f i b r e
h e a d i s r e t a r d e d f r o m t h e s a m p l e s u r f a c e .
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SIG
NA
L
/mV
153
LiJJCDZ<hiCO<IQ-
13816164
D I S T A N C E / m m D I S T A N C E / m m
F i g u r e 4 . 3 4 : P h o t o t h e r m a l s i g n a l v a r i a t i o n a s t h e o p t i c a l f i b r e
h e a d i s moved t h r o u g h t h e i n f r a r e d d e t e c t i o n r e g i o n f r o m t h e r i g h t
t o l e f t , ( s e e f i g . 4 . 3 1 ) .
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SIG
NA
L
/mV
150
A
6LlI□
UJJCDz<UJ(/)<I0.
1401 42
1 □
142D I S T A N C E / m m D I S T A N C E / mm
F i g u r e ^ . 3 5 : P h o t o t h e r m a l s i g n a l v a r i a t i o n a s t h e o p t i c a l f i b r e
h e a d i s moved v e r t i c a l l y d o w n w a r d s t h r o u g h t h e i n f r a r e d d e t e c t i o n
r e g i o n .
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PH
RS
E
RN
GLE
(D
EC
)
20
RRGON ION LRSER
SC LRSER
LRSER POWER 300 mW FREQUENCY 10 Hz
o 200
D I S T R N C E I N MM
F i g u r e ^ . 3 6 a : A 2 0 0 mm p h a s e a n g l e l i n e t r a c e a c r o s s a s t e p
t h i c k n e s s LC1B c o a t i n g s a m p l e a t a f r e q u e n c y o f 10 Hz w i t h o p t i c a l
h e a t i n g b y t h e G a A l A s l a s e r d i o d e a nd a r g o n i o n l a s e r a t a l a s e r
p o w e r o f 3 0 0 mW.
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PH
RS
E
AN
GLE
C D
EG
)20
LRSER POWER 300 mW FREQUENCY 25 Hz
RRGON ION LRSERSC LRSER
2000
D I S T A N C E I N MM
F i g u r e ^ . 3 6 b : As f i g . A-. 3 6 a b u t a t a f r e q u e n c y o f 2 5 H z .
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Sign
al
/ m
V
1E3 = 5 =
TGS Infrared Detector
2 -
1E2 = 5 =
1E1
1E01E1 2 5 1E2 2 5 1E3 2
Frequency/ HzF i g u r e 4 . 3 7 a : TGS d e t e c t o r s i g n a l r e s p o n s e w i t h f r e q u e n c y .
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Phas
e An
gle
(deg
.)TGS Infrared Detector
-100
150
-200
-250
-300
-3501E3 21E2 55 21E1
Frequency/ Hz
F i g u r e 4 . 3 7 b : TGS d e t e c t o r p h a s e a n g l e r e s p o n s e w i t h f r e q u e n c y .
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Norm
alis
ed
Sign
al2
1E2
5
2
1E1
5
2
1E01E1 2 5 1E2 2 5
Frequency/ HzF i g u r e ^ . 3 8 a : N o r m a l i s e d s i g n a l v a r i a t i o n w i t h f r e q u e n c y f o r 1 ) a
0 . 2 5 mm t h i c k LC1B c o a t i n g on a 3 mm t h i c k s t a i n l e s s s t e e l
s u b s t r a t e a n d 2 ) a 10 mm t h i c k t i t a n i u m b l o c k . I n c i d e n t l a s e r
p o w e r w as 3 W a t t .
1 LC1B coating
Titanium
J J 1 J _ L L 1
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Nor
m.
Phas
e A
ngle
34 -2 Titanium
1 LC1B coating
1E1 2 5 1E2 2 5Frequency/ Hz
F i g u r e 4 . 3 8 b : N o r m a l i s e d p h a s e a n g l e v a r i a t i o n w i t h f r e q u e n c y f o r
1 ) a 0 . 2 5 mm t h i c k LC1B c o a t i n g on a 3 mm t h i c k s t a i n l e s s s t e e l
s u b s t r a t e a n d 2 ) a 10 mm t h i c k t i t a n i u m b l o c k . I n c i d e n t l a s e r
p o w e r w as 3 W a t t .
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Phas
e Er
ror
(deg
.)1
0.5 -
0 -
LC18 coating
1E1 2 5 1E2 2 5Frequency/ Hz
F i g u r e ^ . 3 9 : A p l o t o f t h e p h a s e a n g l e e r r o r w i t h f r e q u e n c y f o r
s p o t m e a s u r e m e n t s o n an LC1B c o a t i n g w i t h a n i n c i d e n t l a s e r p o w e r
o f 3 w a t t a n d a l o c k - i n i n t e g r a t i o n t i m e c o n s t a n t o f 3 s e c o n d s .
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C h a p t e r 5
D i s c u s s i o n
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CHAPTER 5 D I S C U S S I O N
5 . 1 SYSTEM PERFORMANCE
ARGON ION LASER VERSES LASER DIODE PTR SYSTEM
B o t h l a s e r s o u r c e s p r o v e d s a t i s f a c t o r y i n p r o v i d i n g
s u f f i c i e n t o p t i c a l h e a t i n g f o r p h o t o t h e r m a l NDT o f
p l a s m a s p r a y e d c o a t i n g s . F r o m t h e p r a c t i c a l e x p e r i e n c e
g a i n e d i n u s i n g b o t h t h e s e l a s e r s y s t e m s t a b l e 5 . 1
c o m p a r e s a n d c o n t r a s t s t h e i r p e r f o r m a n c e . P a r t i c u l a r
a t t e n t i o n i s g i v e n t o t h e p o r t a b i l i t y o f t h e l a s e r
s y s t e m , i t s m a i n t e n a n c e r e q u i r e m e n t s and t h e n e c e s s i t y
o f a n y a u x i l i a r y e q u i p m e n t . T h e c o m p a c t n e s s o f t h e
l a s e r d i o d e s y s t e m f a v o u r s i t s u s a g e i n a p o r t a b l e
i n s p e c t i o n s y s t e m . F u r t h e r a d v a n t a g e s o f t h i s l a s e r
s y s t e m o v e r t h e a r g o n i o n l a s e r i n c l u d e l i m i t e d
m a i n t e n a n c e c o s t s , e l i m i n a t i o n o f w a t e r c o o l i n g and
s p e c i a l p o w e r s u p p l y r e q u i r e m e n t s , l o n g e r l a s e r l i f e
and d i r e c t m o d u l a t i o n o f l a s e r beam i n t e n s i t y . T h e
m a i n t e n a n c e c o s t s o f t h i s l a s e r s y s t e m a r e lo w b e c a u s e
o n l y e l e c t r o n i c c i r c u i t s a r e r e q u i r e d t o b e m a i n t a i n e d .
T h e n e e d f o r a s p e c i a l m a i n t e n a n c e c o n t r a c t f o r t h e
l a s e r i s n o t n e c e s s a r y .
I h e m a i n d e f i c i e n c i e s o f t h e l a s e r d i o d e s y s t e m a r e
t h e i n v i s i b i l i t y o f t h e l a s e r r a d i a t i o n , i t s l i m i t e d
p o w e r r a n g e and t h e h i g h beam d i v e r g e n c e ( f o r t h e
s y s t e m p r e s e n t l y e v a l u a t e d ) . T h e a r g o n i o n l a s e r
s y s t e m d o e s n o t s u f f e r f r o m t h e s e p r o b l e m s . H o w e v e r
d u e t o i t s p h y s i c a l s i z e and c o n s t r a i n t s im p o s e d by
w a t e r c o a l i n g a t e s t s y s t e m b a s e d on t h i s l a s e r s o u r c e
w o u l d b e m o r e s u i t a b l e f o r i n s p e c t i n g c o m p o n e n t s w h i c h
c a n be b r o u g h t t o t h e l a s e r r a t h e r t h a n v i c e v e r s a . I f
169
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t h e l a s e r p o w e r r e q u i r e m e n t w as b e l o w h a l f a w a t t t h e n
a i r c o o l e d a r g o n i o n l a s e r c o u l d b e c h o s e n t o b e u s e d
i n a p o r t a b l e i n s p e c t i o n s y s t e m .
O v e r t h e f i v e y e a r s i n u s i n g t h e a r g o n i o n l a s e r
s y s t e m s e v e r a 1 p r o b 1ems r e l a t e d t o w a t e r c o o l i n g w e r e
n o t e d . S c a l e b u i l d up a r o u n d t h e l a s e r t u b e p r e s e n t s a
p o t e n t i a l l y s e r i o u s p r o b l e m . I f t h e s c a l i n g i s n o t
r e m o v e d t h e n o v e r h e a t i n g o f t h e l a s e r t u b e c a n l e a d t o
i t s f r a c t u r e . A l t h o u g h r e p l a c e m e n t s t u b e s a r e
a v a i l a b l e , t h e y a r e e x p e n s i v e , up t o £ Q , 0 0 0 . A n o t h e r
p r o b l e m w i t h t h e w a t e r c o o l i n g s y s t e m i s t h e f r e q u e n t
n e c e s s i t y o f c l e a n i n g w a t e r f i l t e r s w h i c h w o u l d make a
c o n t i n u o u s o p e r a t i o n o f t h e t e s t s y s t e m d i f f i c u l t .
B o t h t h e s e p r o b l e m s c a n b e o v e r c o m e b y u s i n g a s p e c i a l
w a t e r s u p p l y s y s t e m .
T h e l a s e r p o w e r r e q u i r e m e n t f o r i n s p e c t i n g s p r a y e d
c o a t i n g s c a n r a n g e f r o m a f e w w a t t s f o r a n u n a i d e d I R
d e t e c t o r t o a f e w h u n d r e d m i l l i w a t t s f o r a w e l l
o p t i m i s e d I R d e t e c t i o n s y s t e m . U s i n g a l o w e r l a s e r
p o w e r a l s o p r o v i d e s f u r t h e r a d v a n t a g e s f o r t h e
i n s p e c t i o n s y s t e m . A w i d e r a n g e o f a l t e r n a t i v e lo w
p o w e r e d l a s e r s o u r c e s c a n b e u s e d f o r s a m p l e h e a t i n g .
T h e l a s e r h a z a r d r i s k t o t h e o p e r a t o r and r e l a t e d
p e r s o n n e l a r e r e d u c e d . I t may a l s o b e e a s i e r f o r t h e
i n s p e c t i o n s y s t e m t o mee-t t h e l a s e r s a f e t y r e g u l a t i o n s
f o r i n d u s t r i a l u s a g e .
INFRARED DETECTOR
T h e c o n v e n i e n c e o f o p e r a t i n g t h e p y r o e l e c t r i c TGS IR
d e t e c t o r a t a m b i e n t t e m p e r a t u r e s , i n a l m o s t a n y
o r i e n t a t i o n , i t s s h o r t p h y s i c a l s i z e and h i g h
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s e n s i t i v i t y i d e a l l y s u i t e d i t s u s a g e i n t h e
pho t o t h e r m a l t e s t i ng s y s t e m . T h i s d e t e c t o r w as a 1 so
o b s e r v e d t o h a v e e x c e l l e n t low f r e q u e n c y e l e c t r o n i c
n o i s e w h i c h was an e s s e n t i a l r e q u i r e m e n t i f lo w
d i f f u s i v i t y c o a t i n g s w e r e to b e i n s p e c t e d . One s h o r t
c o m i n g o t t h e s e n s o r was i t s l o n g t e r m s t a b i l i t y . I t
was o b s e r v e d t h a t o v e r a p e r i o d o f 18 m o n t h s t h e
d e t e c t o r g r a d u a l l y b e c a m e i n s e n s i t i v e and n o i s y . I t
b e c a m e n e c e s s a r y t o r e p l a c e t h e d e t e c t o r . T h e p r o b l e m
w i t h t h e s e n s o r a p p e a r s t o b e m o i s t u r e p i c k - u p b y t h e
TGS e l e m e n t 1 .
5 . 2 A P P L I C A T I O N TO NDT OF SURFACE COATINGS
The e x p e r i m e n t s r e p o r t e d i n c h a p t e r ** d e m o n s t r a t e s
t h e c a p a b i l i t y o f p h o t o t h e r m a l m e t h o d f o r t h i c k n e s s
g a u g i n g and d e f e c t d e t e c t i o n . T a b l e 5 . 1 s u m m a r i s e s
s t u d i e s r e p o r t e d i n t h i s r e s e a r c h w o r k a n d i n t h e
p u b l i s h e d l i t e r a t u r e o f m e a s u r e m e n t s o n p l a s m a s p r a y e d
c o a t i n g s made w i t h t h e p e r i o d i c o p t i c a l h e a t i n g
ct e c h n i q u e w i t h i n f r a r e d d e t f ^ t i o n .
F o r t h i c k n e s s m e a s u r e m e n t s t h e f o l l o w i n g
r e q u i r e m e n t s a r e e s s e n t i a l .
1) A s i g n i f i c a n t th e rm a l impedance mismatch between the
c o a t i n g and t h e s u b s t r a t e .
2) The e x p e r i m e n t a l phase a n g l e n o i s e a vera ged o ve r a f i n i t e
a rea on th e t e s t sample i s l e s s than t h e r e q u i r e d
t h i c k n e s s r e s o l u t i o n .
T he f i r s t c o n d i t i o n i s n e c e s s a r y f o r t h e r m a l w a v e
i n t e r f e r e n c e e f f e c t s t o o c c u r and h e n c e m ake t h i c k n e s s
m e a s u r e m e n t s t h e o r e t i c a 1 1 y p o s s i b l e . T h e s e c o n d
1 llanuf a c t u r e s r e po r t , lvlul lard , S o u t h a m p t o n .
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c o n d i t i o n s e t s t h e m in im u m t h i c k n e s s t h a t c a n be
r e l i a b l y m e a s u r e d w i t h t h e s y s t e m . T h e t h i c k n e s s
s e n s i t i v i t y o f t h e t h e r m a l i n t e r f e r e n c e t e c h n i q u e
i m p r o v e s a s t h e m a g n i t u d e o f t h e t h e r m a l wa ve
r e f l e c t i o n c o e f f i c i e n t i n c r e a s e s . R e s u l t s p r e s e n t e d i n
t h e p r e v i o u s c h a p t e r h a v e i n d i c a t e d t h a t t h i c k n e s s
s e n s i t i v i t i e s b e t t e r t h a n 2 5 Hm/ d e g r e e a r e r e a d i l y
a t t a i n a b l e f o r LC1B c o a t i n g on s t a i n l e s s s t e e l ( s e e
f i g u r e s 4 . 3 6 ) . T h e m in im u m d e t e c t a b l e t h e r m a l wav e
r e f l e c t i o n c o e f f i c i e n t m a g n i t u d e w i t h t h e a r g o n i o n
b a s e d t e s t s y s t e m d e v e l o p e d i n t h i s w o r k w o u l d b e
a b o u t O . l j a s s u m i n g t h a t t h e p h a s e n o i s e o f t h e t e s t
s a m p l e i s l e s s t h a n 1 d e g r e e .
C o a t i n g p r o p e r t i e s t h a t l i m i t a c c u r a t e t h i c k n e s s
m e a s u r e m e n t s i n c l u d e s u r f a c e r o u g h n e s s * t h i c k n e s s
f l u c t u a t i o n s a n d c h a n g e s i n t h e s u b s u r f a c e t h e r m a l
m i c r o s t r u c t u r e r e s u l t i n g f r o m p o r o s i t y * f o r e i g n
i n c l u s i o n s e t c . P h a s e a n g l e m e a s u r e m e n t s o n f i n e and
r o u g h a s - s p r a y e d LC1B c o a t i n g s h a v e sh o w n t h a t t h e
p h a s e i s p e r t u r b e d b y t h e s u r f a c e r o u g h n e s s . T h u s
s h o w i n g t h a t c a r e m u st b e t a k e n i n u s i n g c a l i b r a t i o n
c u r v e s f o r t h i c k n e s s m e a s u r e m e n t s o n r o u g h s u r f a c e s .
A c c u r a t e t h i c k n e s s v a l u e s w i l l o n l y b e o b t a i n e d f r o m
s a m p l e o f s i m i l a r s u r f a c e r o u g h n e s s .
A v a r i e t y o f s u b s u r f a c e c o n d i t i o n s h a v e b e e n
d e t e c t e d w i t h t h i s p h o t o t h e r m a l t e c h n i q u e : p o r o s i t y *
p a r t i a l c o n t a c t b e t w e e n c o a t i n g a nd s u b s t r a t e and
c o m p l e t e l y s e p a r a t e d i n t e r f a c e s . D e f e c t s as
r e p r e s e n t e d b y t h e l a t t e r tw o e x a m p l e s h a v e a
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c h a r a c t e r i s t i c p h a s e l o c u s w i t h i n c r e a s i n g m o d u l a t i o n
f r e q u e n c y : a p h a s e a d v a n c e g o i n g t o a p h a s e l a g . T he
v i s i b i l i t y o f s u b s u r f a c e d e f e c t s was d i s c u s s e d
t h e o r e t i c a l l y i n c h a p t e r 2 . F o r t h i n l a m i n a r d e f e c t
p a r a l l e l t o t h e s u r f a c e , t h e p h a s e c o n t r a s t was
p r e d i c t e d t o b e l a r g e w h e n t h e d e f e c t i s s a n d w i c h e d i n
a h i g h t h e r m a l e f f u s i v i t y m a t e r i a l . S u b m i c r o n d e f e c t
t h i c k n e s s e s w e r e a l s o p r e d i c t e d t o b e r e a d i l y
d e t e c t a b l e . T h e v i s i b i l i t y o f d e f e c t s a t d e p t h s
g r e a t e r t h a n 1 . 5 t h e r m a l d i f f u s i o n l e n g t h o f t h e
s u r f a c e l a y e r i s p o o r f o r a l l d e f e c t t h i c k n e s s e s . I n
sum m ary t h e m a i n r e q u i s i t e s f o r d e f e c t d e t e c t i o n a r e
g i v e n b e l o w .
1) The modula t ion f requency must make the thermal d i f f u s i o n
length l a r g e r than th e d e f e c t depth .
2) Severa l f requency measurements a re made to d i s t i n g u i s h the
observed phase an g le v a r i a t i o n s from t h ick n e ss and
m i c r o s t r u c t u r e r e l a t e d changes.
3) The sample phase ang le no is e i s less than the minimum
d e f e c t th ickn ess to be sensed.
F o r d e f e c t s o f f i n i t e w i d t h s i t h a s b e e n t h e o r e t i c a l l y
shown t h a t t h e y may b e d e t e c t a b l e up t o a d e p t h e q u a l
t o i t s d i a m e t e r C 7 1 J . T h i s p r e d i c t i o n a p p e a r s t o
v a l i d f o r t h e d i s c s h a p e d d e f e c t s t e s t e d i n 4 . 3 . 2 .
5 . 3 FURTHER DEVELOPMENTS
Two i n t r i n s i c l i m i t a t i o n s o f m o d u l a t e d PTR a r e t h e
s l o w i n s p e c t i o n r a t e , t y p i c a l l y f e w s e c o n d s / p o i n t and
t h e n e c e s s i t y o f m a k i n g s e v e r a l f r e q u e n c y m e a s u r e m e n t s
t o d i f f e r e n t i a t e b e t w e e n t h i c k n e s s and d e f e c t r e l a t e d
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p h a s e c h a n g e s . As n o t e d i n s e c t i o n 1 . 3 . 1 , s u r f a c e
i n s p e c t i o n r a t e s may b e i n c r e a s e d b y e m p l o y i n g a n a r e a
w i d e l o c k - i n d e t e c t i o n t e c h n i q u e . To o v e r c o m e t h e
s e c o n d d i f f i c u l t y M a n d e l i s e t a l C B 8 ,8 9 D h a v e r e c e n t l y
sh o w n t h a t b y a p p l y i n g a f r e q u e n c y c h i r p e x c i t a t i o n f o r
p h o t o t h e r m a l h e a t i n g , b o t h t h e f r e q u e n c y and t i m e
d o m a i n r e s p o n s e o f l a y e r e d s a m p l e s c a n b e o b t a i n e d
s i m u l t a n e o u s l y i n a r e l a t i v e l y s h o r t p e r i o d o f t i m e .
O t h e r a d v a n t a g e s o f t h i s e x c i t a t i o n m e t h o d i n c l u d e :
a) co n ven t ion a l l o c k - i n s i n g l e f requency measurements
can a ls o be measured w i th the same equipment,
b) a pulsed la s e r is not r e q u i r e d to o b t a i n t r a n s i e n t
thermal propagat ion i n f o r m a t i o n , and
c) reduced sample hea t in g due to s e q u e n t ia l d e p o s i t io n
o f l a s e r energy.
T h i s a l t e r n a t i v e e x c i t a t i o n t e c h n i q u e a p p e a r s t o h a v e a
g r e a t e r p o t e n t i a l f o r f u l l q u a n t i t a t i v e m a t e r i a l s
c h a r a c t e r i s a t i o n and N D T . B o t h t h e s e c h a r a c t e r i s t i c s
a r e u r g e n t l y s o u g h t a f t e r i n f u t u r e i n s p e c t i o n s y s t e m s .
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Tab le 5 . 1 : A summary o f PTR measurements on plasma spyayed
coat i n q s .
MEASUREMENT
Coat i n g /
S u b s t ra te
System
Frequency
Hz
Th ickness
Fm
Thermal
D i f f u s i v i ty
x l 0 -tf> me / s
D efec ts REF.
Mo 15 200-610 6 . 5 24
N i A l / MS 28 15-490 4 . 4 24
A l / MS i CD O 490 I n t e r f a c e 66
A l e03 / MS 16i
0 -400 2 . 2 I n t e r f a c e 8
2 r 0 a - Y c 03 /
N ic k e l
s u p e r a l l o y
0 . 3 5 50-1000 0 . 1 90
LC1B/ SS 10 ,25 50-250
j
ru 0- I n t e r f a c e ,
P o r o s i t y
22
WC + Co/ Ti 36 50 -400 3 91
. MS M i ld S te e l
. SS S t a i n l e s s S tee l
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Table 5 . 5 : A comparsion and performance o f the gas and
semiconductor 1asers f o r sample h e a t i n q .
Argon ion la se r GaAlAs Laser Diode
Laser beam
v i s i b i 1i t y
Ves No
Laser power
range
(W at t )
0 to j 0 . 0 5 to 0 . 3
Usefu l l i f e
t ime
Up to 1500 hrs 10 ,000 hrs
S p ec ia l
requ irements
F i l t e r e d water
supply ,
water c o o l in g , and
3 phase power
supply .
None
Laser system
p o r t a b i l i t y
No Yes
Maintenance
costs
High
(Replacement tube)
Low
System c o s t /
mW8x th e Argon
ion system
Sig na l
Magnitude
3x the Laser diode
Phase angle
noise
( a t 0 . 3 Wat t )
< 0 .5 degrees < 0 . 5 degrees
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A p p e n d i x
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Append i x 1
1 THERMAL HAVE REFLECTION AND TRANSMISSION COEFFICIENTS.
Assume t h a t t h e b o u n d a r y s e p a r a t i n g tw o m e d i a < 1 * 2 )
i s t h e p J a n e x = 0 , and t h a t t h e i n c i d e n t j r e f l e c t e d and
t r a n s m i t t e d p l a n e t h e r m a l w a v e m a kes t h e a n g l e ft 4. , ft,
and f t h w i t h r e s p e c t t o t h e x - a x i s , a s shown i n f i g u r e
I . L e t t h e e x p r e s s i o n f o r t h e p l a n e t h e r m a l w a v e s ,
Tj , t ,- and T t i t h e i n c i d e n t , r e f l e c t e d a nd t r a n s m i t t e d
w a v e s b e g i v e n b y :
w h e r e A i s t h e i n i t i a l a m p l i t u d e o f t h e i n c i d e n t
t h e r m a l w a v e ; R and T a r e t h e t h e r m a l w a v e r e f l e c t i o n
and t r a n s m i s s i o n c o e f f i c i e n t a t t h e i n t e r f a c e x = 0 .
F o r t h e c o n t i n u i t y o f t e m p e r a t u r e a t t h e i n t e r f a c e
x = 0 , we h a v e :
S i n c e t h i s c o n d i t i o n m u st b e t r u e f o r a l l y p o s i t i o n ,
t h e e x p o n e n t s i n t h e a b o v e e q u a t i o n m u s t b e a l l e q u a l .
I h u s we h a v e
- a jx CQsnt~a sin /lt+ /cut
T r « ARea j x cos Clr - a jy sin £lr+/cot
- a 0x cos Clt~ a 2y sin Clt+/cut
(2) <r, y sin Cl a x y sin £1 a ^y sin Clt
( 3 ) cr1y s i n / 3 ( = cr1y s i n / } r = 0 2y s i n i 2 tf r o m w h i c h t h e l a w o f r e f l e c t i o n and r e f r a c t i o n
follows:
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(3a) Dl = Dr law of reflection(3b) cr xy sin = a 2y sin D t Snells/au;
F o r c o n t i n u i t y o f f l u x a t t h e i n t e r f a c e t h e
f o l l o w i n g e q u a t i o n i s o b t a i n e d :
( 4 ) fcjCT, cos D t - R k ! a t cos jQr - T k 2a 2cos D t
a s £2,,. =42,.. and I = ( 1 - R ) ( a t y = 0 ) , t h e t h e r m a l w ave
r e f l e c t i o n and t r a n s m i s s i o n c o e f f i c i e n t c a n b e w r i t t e n
a s :
k i o j cos £21 — A: 2 <72 cos(Ca) R-- --------- — ---------- —k i a i cos u t -+- k 2 o 2 cos ii t
c o s /3 , -b c o s i2 t CG b > T T - T ----- r Tc o s j R, + O C O S i l j
2 k 2o^cosDt(5c) T = k\0 j cos.Q£-*- fc2o 2cosDt
2 b c o s D t(Gd) T =cosDt + bcosDr
w h e r e b = k^cr^ / k :l a x . F o r n o r m a l l y i n c i d e n t t h e r m a l
w a v e s , S2i=0, t h e r e f l e c t i o n and t r a n s m i s s i o n
c o e f f i c i e n t s a t x = 0 r e d u c e t o :
„ l-b 2 b(6 ) 2? = - — and 7 = -— -1 + 6 1 + 6
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1
A p p e n d i x d
ONE DIMENSIONAL COMPLEX SURFACE TEMPERATURE DERIVATION.
1 . 1 T H I N O P T IC A L L Y ABSORBING LAYER ON A NON-ABSORBING
S E M I - I N F I N I T E SUBSTRATE.
C o n s i d e r a p l a n e p e r i o d i c o p t i c a l s o u r c e
i l l u m i n a t i n g a l a y e r e d s a m p l e w i t h i n t e n s i t y 10 a t an
a n g u l a r f r e q u e n c y w:
(1) / = [ l + Gxp(ycoO]-
I h e s u r f a c e t e m p e r a t u r e o f t h e s a m p l e c a n t h e n b e
w r i t t e n a s t h e sum o f t h r e e t e m p e r a t u r e s :
V ) T = T a+ T dc+ T acw h e r e I c. , Td c a n d r « c a r e , r e s p e c t i v e l y , t h e a m b i e n t ,
s t e a d y s t a t e and p e r i o d i c t e m p e r a t u r e o f t h e s a m p l e .
To d e r i v e t h e p e r i o d i c s u r f a c e t e m p e r a t u r e o f a t h i n
o p t i c a l l y a b s o r b i n g l a y e r o n a n o n a b s o r b i n g
s e m i —i n f i n i t e s u b s t r a t e we p r o c e e d a s f o l l o w s . L e t r ,
(2 , and n b e t h e s u r f a c e r e f l e c t i v i t y , t h e b u l k o p t i c a l
a b s o r p t i o n c o e f f i c i e n t and t h e 1 i g h t - t o - h e a t c o n v e r s i o n
e f f i c i e n c y , r e s p e c t i v e l y , o f m e d iu m 1 . Assume t h a t
h e a t f l o w i s o n e d i m e n s i o n a l a n d t h a t t h e s u r f a c e l a y e r
i s i n p e r f e c t t h e r m a l c o n t a c t w i t h t h e s u b s t r a t e .
L e t k t , C i , «i. a nd a b e t h e t h e r m a l c o n d u c t i v i t y , t h e
s p e c i f i c h e a t , t h e r m a l d i f f u s i v i t y and t h e r m a l
w a v e v e c t o r o f m a t e r i a l i , i = 0 , l and 2 , ( s e e f i g . 2 ) .
The t h e r m a l d i f f u s i o n e q u a t i o n i n e a c h o f t h e m e d i a
t a k e t h e f o r m :
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(3)d * T i( x , t ' ) _ 1 d T t{ x , t )
d x 7 a, dt
f i ( x . t )layer
* \
~ 0 la y e r 0 , 2
w h e r e H i s t h e n e t h e a t d e n s i t y p r o d u c e d a t a p o i n t x
i n t h e s a m p l e . I f l i g h t i s e x p o n e n t i a l l y a b s o r b e d i n
t h e s a m p l e ( B e e r ’ s Law ) t h e n H i s g i v e n b y :
( 4 ) R (x = - - - - - - - - - - - - - - - - -- - - - - - - -Ro[ 1 e x p (Jcu £ ) ]
S i n c e I and h e n c e I a r e h a r m o n i c i n t i m e ;
(5) T , ( x , t ) = T , ( x ) e x p ( J u } f )
t h e a b o v e t h e r m a l d i f f u s i o n e q u a t i o n s c a n b e r e w r i t t e n
a s :
l a y e r 0
- } 2 T 0 ( x , c o ) f ' j c u )( 6 a ) - - - - - - i>— — ' - | T 0 ( x , w ) - 0 x > 0
J x a V a „ J
d2T t( x , a > ) ( j a > \ _ t f ( x , a > )
l a y e r 1
(6b) ----- ---------i - i— r,(x.tB)-’ -----i - L < x < 0d x 2 V “ i 1 * ,
l a y e r d
, , . y 2 T j ( x . t o ) ( j u j(6 c ) .............. ....... ....... ... T . , ( x . u . ' ) - 0 x < - L
J x 2 V J
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I he e q u a t i o n s 6 a - 6 c a r e c o u p l e d v i a t h e b o u n d a r y
c o n d i t i o n s o f t e m p e r a t u r e a n d h e a t f l u x c o n t i n u i t y a t
a l l t h e i n t e r f a c e s :
(7?.) T t\ u j , boundary ) = T } { to , boundary )
a;*, b o u n d a r y ) T A t o , b o u n d a r y J(7b) k t d - “ k j d --------------------------d x d x
I h e t i m e d e p e n d a n t s o l u t i o n s t o e q u a t i o n 6 f o r t h e
p e r i o d i c t e m p e r a t u r e d i s t r i b u t i o n i n t h e s a m p l e a r e
g i v e n b y t h e e q u a t i o n s :
l a y e r 0
(8a) T 0(x,o))--C1exp(-cr0.v)
layer 1(8 b ) T i ( x , c o ) - C 2e x p ( c r l x ) + C 3e x p ( - c r I x )
(1 - r )/t,exp(ff tx) 2 k l { a i - p i )
1 a y e r c!
( 8 c ) T 2 ( x ,co) - C 4 c x p ( a 2 x )
I h e q u a n t i t y o f i n t e r e s t i s t h e f u n c t i o n f o r t h e
t e m p e r a t u r e f i e l d a t t h e s u r f a c e o f m ed iu m 1» f i ( w , O ) .
T h i s c a n b e d e t e r m i n e d by e v a l u a t i o n t h e c o e f f i c i e n t C.a
s u b j e c t t o t h e b o u n d a r y c o n d i t i o n s o f e q u a t i o n 7 , w h i c h
y i e l d t h e f o l l o w i n g m a t r i x e q u a t i o n :
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(9)
1 - 11
0 X "
0 X ' 1
-bX
0
0
- y
- x - b . r- 1
" c r - Ec 2 b<,r i £
C 3 EB
L C 4_ _ r i E B _
(9a) o r r , 4 ] [ C ] = [ £ ]
and
( 10)k i Cf i
k (-1 & t- li- 1,2
( 1 1 ) X ” e x p j ^ i Z i ) and K - exp(cf2I1)
( 12)
The s o l u t i o n o f t h e m a t r i x e q u a t i o n 9 i s
( 1 3 )
f r o m w h i c h t h e p e r i o d i c s u r f a c e t e m p e r a t u r e , 1 . , ^ ,
f o l l o w s on e v a l u a t i n g t h e c o e f f i c i e n t C.t 1 :
( 1 4 ) T -(1 -r)r?£/0
2 kf f { l - r0re-2aL)
+ Te/? + o’ /? -c r
1 t h e s u f f i x 1 r e f e r r i n g t o t h e s u r f a c e l a y e r m a t e r i a l p r o p e r t i e s h a s b e e n r e l a x e d .
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w h e r e P i s t h e t h e r m a l w a v e r e f l e c t i o n c o e f f i c i e n t a t
t h e l a y e r / s u b s t r a t e i n t e r f a c e , P= ( 1 -be*,. ) / ( l + b a i ) and
r’e t h e r e f l e c t i o n c o e f f i c i e n t a t t h e l a y e r / a i r
i n t e r f a c e , r<> = u n i t y f o r s o l i d - a i r i n t e r f a c e . F o r an
o p t i c a l l y o p a q u e s u r f a c e l a y e r , ft x L .1 > > 1 , e q u a t i o n 14
r e d u c e s t o :
( 1 - r)/(15) Tac =2 k a
1 + f e ' 2 " 1
1 - T e - 2 a L
1 > 2 THERMAL CONTACT R E S IS T A N C E .
T h e a b o v e s o l u t i o n f o r t h e p e r i o d i c s u r f a c e
t e m p e r a t u r e a p p l i e s t o a t h i n o p t i c a l l y a b s o r b i n g
l a y e r i n p e r f e c t t h e r m a l c o n t a c t w i t h a n o n a b s o r b i n g
t h e r m a l l y t h i c k s u b s t r a t e . I f t h e l a y e r / s u b s t r a t e
i n t e r f a c e i s p a r t i a l l y b o n d e d t h e n t h e i n t e r f a c e w i l l
p r e s e n t a t h e r m a l r e s i s t a n c e t o h e a t f l o w . T h e
p e r i o d i c s u r f a c e t e m p e r a t u r e m u s t now b e o b t a i n e d b y
i n t r o d u c i n g a ’ t h e r m a l c o n t a c t r e s i s t a n c e * t e r m , R , t o
t h e t e m p e r a t u r e c o n t i n u i t y b o u n d a r y c o n d i t i o n o f
e q u a t i o n 7 a :
(16) T l ( - L l . w ) = T 2( - L l , a j ) * R % 2i T ^ L “ CU'>Z x
T h e s o l u t i o n f o r t a k e s t h e same f o r m a s e q u a t i o n 14
b u t w i t h T r e p l a c e d w i t h :
1 - b 1 + Rk 2 On( 1 7 ) r = 1 b { + Rk 2 (J
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h e n c e m a k i n g t h e l a y e r / s u b s t r a t e t h e r m a l w ave
r e f l e c t i o n c o e f f i c i e n t b o t h c o m p l e x and f r e q u e n c y
d e p e n d a n t .
1 . 3 A I R GAP DEFECT.
I f t h e l a y e r / s u b s t r a t e i n t e r f a c e i s l o c a l l y
s e p a r a t e d s u c h t h a t an a i r g a p i s s a n d w i c h e d b e t w e e n
t h e l a y e r a n d t h e s u b s t r a t e , t h e n t h e p e r i o d i c s u r f a c e
t e m p e r a t u r e c a n be o b t a i n e d b y s o l v i n g t h e h e a t
d i f f u s i o n e q u a t i o n w i t h p e r i o d i c b o u n d a r y c o n d i t i o n s o f
t e m p e r a t u r e a nd f l u x c o n t i n u i t y a t t h e a i r / l a y e r
, l a y e r / a i r and a i r / s u b s t r a t e i n t e r f a c e s , s e e f i g u r e
3 . T h e s o l u t i o n f o r t h e s u r f a c e t e m p e r a t u r e r e q u i r e s
t h e s i m u l t a n e o u s s o l u t i o n o f s i x e q u a t i o n s w h i c h on
s o l v i n g g i v e s f o r t h e s u r f a c e t e m p e r a t u r e :
w h e r e r i s d e f i n e d a s :
(1 8 )T a c 2 k l a l
_ „ - 2 ar i + I 2e(19 ) r
i + r l r 2e~2,’ zL:‘
1 - b i 1 - b 2
( 2 0 ) r ‘ = r r r 7 a n d =
T h i s r e p r e s e n t a t i o n f o r I mc i s i d e n t i c a l i n f o r m t o t h e
s u r f a c e t e m p e r a t u r e e x p r e s s i o n f o r a n o p t i c a l l y o p a q u e
1 8 4
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l a y e r o n a s e m i - i n f i n i t e s u b s t r a t e , s e e e q u a t i o n 1 5 .
A l s o , a s w i t h t h e t h e r m a l c o n t a c t r e s i s t a n c e m o d e l , a
c o m p l e x and f r e q u e n c y d e p e n d a n t t h e r m a l w a v e r e f l e c t i o n
c o e f f i c i e n t i s o b t a i n e d f o r t h e i n t e r f a c e d e f e c t .
1 STEADY STATE TEMPERATURE:
OPAQUE S E M I - I N F I N I T E LA Y ER .
T h e s t e a d y s t a t e , T d ^ , t e m p e r a t u r e r i s e o f t h e
s a m p l e c a n a l s o b e o b t a i n e d i n a s i m i l a r m a n n e r a s t h a t
f o r a n a b s o r b i n g l a y e r o n a t r a n s p a r e n t s u b s t r a t e b y
p u t t i n g w=0 i n e q u a t i o n 6 a n d t h e n s o l v i n g t h e t i m e
i n d e p e n d e n t h e a t d i f f u s i o n e q u a t i o n s u s i n g t h e b o u n d a r y
c o n d i t i o n s o f t e m p e r a t u r e an d f l u x c o n t i n u i t y . T h e
s o l u t i o n f o r t h e s t e a d y s t a t e t e m p e r a t u r e i s t h e n g i v e n
b y t h e e x p r e s s i o n :
F o r an o p a q u e i n s u l a t o r on a c o n d u c t i n g s u b s t r a t e t h i s
e q u a t i o n s i m p l i f i e s t o :
(21)
(22)
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Append i x 3
1 E F F E C T I V E THERMAL C O N D U C T I V I T Y OF A GAS TRAPPED
BETWEEN NARROWLY SPACED PARALLEL PL A T E S .
T h e r e a r e two d i s t i n c t modes o f g a s h e a t c o n d u c t i o n ;
t h e m o l e c u l a r h e a t t r a n s f e r and c o n t i n u u m h e a t
t r a n s f e r . I n t h e m o l e c u l a r r e g i m e , c o l l i s i o n s o c c u r
b e t w e e n g a s m o l e c u l e s much l e s s f r e q u e n t l y t h e n b e t w e e n
t h e g a s m o l e c u l e s and t h e ' h o t ’ o r ’ c o l d ’ s u r f a c e s .
I n t h i s r e g i m e m o l e c u l a r h e a t t r a n s f e r i s d i r e c t l y
p r o p o r t i o n a l t o t h e s y s t e m p r e s s u r e and i s a l s o
i n f l u e n c e d b y t h e a c c o m m o d a t i o n c o e f f i c i e n t , oc, w h i c h
c a n b e d e f i n e d a s t h e e n e r g y e x c h a n g e d b e t w e e n a
m o l e c u l e a n d a s u r f a c e w i t h r e s p e c t t o t h e maximum
e n e r g y e x c h a n g e p o s s i b l e .
I n t h e c o n t i n u u m r e g i m e h e a t c o n d u c t i o n i s
r e l a t i v e l y i n d e p e n d e n t o f p r e s s u r e a n d a l s o h a s t h e
maximum t h e r m a l c o n d u c t i v i t y . T h e b a s i c e q u a t i o n f o r
t h e t h e r m a l c o n d u c t i v i t y o f a g a s i s 4 :
(1) K„ = €TjCu
e = ( 9 6 - 5 ) / 4
77 = p v \ / 2
C 0= R J M { y - 1)
w h e r e
€ i s a c o n s t a n t ,
n i s t he v i s c o s i t y c o e f f i c i e n t ,
Cs, i s t he s p e c i f i c h e a t .
7 i s t he s p e c i f i c h e a t r a t i o ,
9 i s t he d e n s i t y ,
v i s t he mean speed,
1 N . V . l ' s e d e r b e r g . T h e r m a l c o n d u c t i v i t y o f g a s e s and l i q u i d s . ( M . I . T . P r e s s , 1 9 6 b ) C h a p . I V .
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X is the mean f r e e p a th ,
R0 is the u n i v e r s a l gas c o n s t a n t , and
M i s the molecu lar mass.
By s u b s t i t u t i o n ,
(2) K ff= s p C v vk/2.D e f i n i n g t h e mean f r e e p a t h X a s ;
(3) k =( j _ \
L u J1
I-1
w h e r e Xp i s t h e p a r t i c l e t o p a r t i c l e p a t h l e n g t h ( =
k T / T 2 cr P ) , k i s t h e B o l t z m a n n c o n s t a n t , a i s t h e
c o l l i s i o n c r o s s - s e c t i o n , a n d L t h e s y s t e m
c h a r a c t e r i s t i c d i m e n s i o n s ( v o l u m e / a r e a ) .
By s u b s t i t u t i o n ,
e p C 0v(4) K — —
3 2 ( 1/ A p + 1 /L)T h i s e q u a t i o n a l l o w s c a l c u l a t i o n o f t h e g a s t h e r m a l
c o n d u c t i v i t y o v e r t h e r a n g e f r o m m o l e c u l a r t r a n s f e r
r e g i m e t o c o n t i n u u m . E q u a t i o n a s s u m e s a n
a c c o m m o d a t i o n c o e f f i c i e n t o f 1 f o r a l l t h e s u r f a c e s .
I n g e n e r a l a l i e s i n t h e r a n g e 0 t o 1 . To a c c o u n t
f o r t h i s c o e f f i c i e n t , t h e f a c t o r F i s i n t r o d u c e d a s
f o 1 l o w s :
(5)^ epCav
3 2(1 /kp+F/L)
F r e p r e s e n t s a a c c o m m o d a t i o n f a c t o r r e s e m b l i n g t h e
e m i s s i v i t y f a c t o r i n r a d i a t i v e h e a t t r a n s f e r . F o r
p a r a l l e l p l a t e s o f e q u a l s i z e , F i s g i v e n b y
(6) c- 1 1 ,F = — + -------- 1a i a 2
2 H.M. S t r o n g etal. J. App 1 . Phys. 3_1_ p<43 (1960)
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F ro m e q u a t i o n ^ o r 5 i t c a n b e s e e n t h a t f o r l a r g e
s e p a r a t i o n , L» t h e t h e r m a l c o n d u c t i v i t y a p p r o a c h e s
t h a t o f t h e b u l k v a l u e . When g a s i s t r a p p e d b e t w e e n
s u r f a c e s w i t h s e p a r a t i o n a p p r o a c h i n g t h e mean f r e e p a t h
, t h e n t h e t h e r m a l c o n d u c t i v i t y o f t h e g a s c a n b e
r e d u c e d s i g n i f i c a n t l y . F o r e x a m p l e f o r L = 0 . l H m > and
oc =a = 0 . 5 , t h e g a s t h e r m a l c o n d u c t i v i t y i s r e d u c e d b y
£5*/. f r o m i t s b u l k v a l u e :
188
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REFLECTED THERMAL WAVE
TRANSMITTED THERMAL WAVE
MEDIUM 1
INCIDENTTHERMALWAVE
MEDIUM 2X=0 .
F i g u r e I s R e f l e c t i o n a n d r e f r a c t i o n o f p l a n e t h e r m a l
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AIR
CDATINGC 1 K1 ? !
C KSUBSTRATE 2 2
F i g u r e E : M o d e l l e d c o a t i n g / s u b s t r a t e s y s t e m .
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191
CDATING
* , AIR-GAP
3 SUBSTRATE
F ig u re 3: a) A i r gap and b)
CDATING THERMAL CONTACT RESISTANCE < R'>
SUBSTRATE
thermal co n ta c t r e s i s t a n c e i n t e r f a c e d e f e c t s .
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R e f e r e n c e s
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REFERENCES
1 Proc. 11th I n t . Conf . Thermal Spraying ( IT S C ) .
8 - 12th S ep t . 1986. M o n t r e a l , Canada.
2 Eds, 1. Kvernes, W.J.G. Bunk and J .G . Wurm
Proc. Advanced M a t e r i a l Research and Development f o r Transp ort
Ceramic Coat in gs f o r Heat Engines ." 2 6 - 2 8 t h Nov. , S t rasb o rg ,
France. (198b)
ISBN 2 - 8 6 8 8 3 - 0 2 ^ - 2
3 Ed, E. Lang
"Coat ings f o r high temperature a p p l i c a t i o n s . "
Appl . S c i . Pub. ( l l .K ) , ISBN 0 - 8 5 3 3 ^ - 2 2 1 - 0 (1983)
** Anon
"Sprayed c o a t i n g s . " , Chapter 10.
From: Wear r e s i s t a n t su r face s in E n g in ee r in g .
HMSO P u b l i c a t i o n s . ISBN 0 -1 1 5 1 3 8 2 6 -9
5 Ed, E.A . Ash
"Scanned Image Microscopy" .
Academic P ress , England (1980)
6 G. Busse
"Photothermal t ran sm iss io n prob ing o f a m e t a l . "
I n f r a r e d Phys. 20 p419-^22 (1980 )
7 M. Luukka la , A. Letho , J . J a a r in e n and M. Jokien
"Photothermal imaging and thermal s u r f a c e waves as a NDT too l
f o r c o a t i n g s . "
IEEE U l t r a s o n i c symp. p591-59^ (1982)
8 D.P. Almond, P.M. P a t e l , H. R e i t e r
" P o t e n t i a l v a lu e of photothermal imaging f o r the t e s t i n g of
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9 M. Egee, R. D a r t o i s , J. Marx and C. B iss ie ux
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10 A.C. Tam and B. S u l l i v a n
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11 P. C ie l o
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17 D.L . Ba lageas, A.A. Deom and D.M. Boscher.
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18 K. Kobayasi and T. Kumada
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20 A. Letho , M .J oke in , J . j a a r i n e n , T.T iusanen and M. lu ukka la
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22 D.P. Almond, P.M. P a t e l , I . M . Pickup and H. R e i t e r
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23 G. Busse and K .F . Renk
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24 P.M. P a t e l and D.P . Almond
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25 F. G i t z h o f e r , C. M a r t i n and P. Fauchais
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26 J.M. M i lne and W.N. Reynolds
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27 P. C ie l o * X. Maldague, A.A. Deom and R. Lewak
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28 T .S . D u r ra n i * F. L o t t i , K. Boyle, R. Abdel -Aal and A. H a l l
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33 J. Marx, C. D r o u l l e , M. Egee, E. Van S c h e l , F . P o t l e r and G.
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34 P . - E . Nordal and S.O. Kanstad
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37 J . T . Luxon and D.E. Parker
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39 J . L . Beaudoin, E. Merienne, R. Danjoux and M. Egee.
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57 C.A. B ennet ,J r and R.R. P a t t y
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62 M. Beyfuss, R. T i l g n e r and J . Baumann
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63 R.C. P ro g e lh o f , J . L . Thorne and R.R. Ruetsch
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66 P.M. P a t e l , D.P. Almond and H. R e i t e r
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77 EG&G Instrum ents L t d , Doncast le House, B r a c k n e l l , B e rk s h i re ,
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85 S p e c t ra -P h y s ic s L t d , Boundary way, Hemel Hempstead, H e r t s ,
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VO D.P. Almond, P.M. P a te l and H. R e i t e r
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91 J. M o r r i s , P.M. P a t e l , D.P. Almond and H. R e i t e r
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