I n t e r f e r e n c j a p r o m i e n i o w a n i a
Z a s t o s o w a n i a
M e t r o l o g i a
N a n o t e c h n o l o g i e
C z u j n i k i s z c z e g l n i e [w i a t Bo w o d o w e
E l e m e n t y f o t o n i c z n e
W y j a [n i a n i e :
g e n e r a c j i m o d w w l a s e r z e
p r o p a g a c j i m o d w w [w i a t Bo w o d a c h
G e n e r a c j a f e m t o s e k u n d o w y c h i m p u l s w
I n t e r f e r e n c j a p r o m i e n i o w a n i a
D w a p u n k t o w e zr d Ba
A 1
D w i e f a l e z p u n k t w A n , n = 1 , 2
r 1
P
V 1 = V 0 1 e x p ( i t )
V 2 = V 0 2 e x p ( i t )
r 2
V 0 n a m p l i t u d a z e s p o l o n a
A 2
u w z g l d n i a j c a p o c z t k o w f a z n
V 0 n = V 0 n e x p ( i n )
P o l e w p u n k c i e P p o p r z e j [c i u d r g r n
V P ( t ) = V 1 e x p ( i k r 1 ) + V 2 e x p ( i k r 2 ) = [ V 0 1 e x p ( i k r 1 ) + V 0 2 e x p ( i k r 2 ) ] e x p ( i t )
"
I P = V P ( t ) V P ( t )
I n t e n s y w n o [ !
" "
I P = V 0 1 V 0 1 + V 0 2 V 0 2 +
" "
+ V 0 1 V 0 2 e x p [ i k ( r 1 - r 2 ) ] + V 0 1 V 0 2 e x p [ - i k ( r 1 - r 2 ) ]
I n t e r f e r e n c j a p r o m i e n i o w a n i a c d
" "
I P = V 0 1 V 0 1 + V 0 2 V 0 2 +
" "
+ V 0 1 V 0 2 e x p [ i k ( r 1 - r 2 ) ] + V 0 1 V 0 2 e x p [ - i k ( r 1 - r 2 ) ]
"
V 0 1 V 0 1 = I 0 1
I 0 n j e s t i n t e n s y w n o [c i p r o m i e n i o w a n i a w p u n k c i e P
" p o c h o d z c e g o o d p u n k t u A n n = 1 , 2
V 0 2 V 0 2 = I 0 2
"
= 1 - 2
V 0 1 V 0 2 = V 0 1 V 0 2 e x p [ i ( 1 - 2 ) ] = I 0 1 I 0 2 e x p ( i )
"
" "
V 0 1 V 0 2 = ( V 0 1 V 0 2 ) = I 0 1 I 0 2 e x p ( - i )
I P = I 0 1 + I 0 2 + I 0 1 I 0 2 [ e x p ( i x ) + e x p ( - i x ) ]
w i c
x = k ( r 1 - r 2 ) +
g d z i e
e x p ( i x ) + e x p ( - i x ) = 2 c o s x
I P = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s x
g d y |
I n t e r f e r e n c j a p r o m i e n i o w a n i a c d
A 1
r 1
P
r 2
A 2
i o s t a t e c z n i e w y n i k i n t e r f e r e n c j i d l a 2 p u n k t o w y c h zr d e B
I P = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s [ k ( r 1 - r 2 ) + ]
= 1 - 2 r |n i c a f a z p o c z t k o w y c h o b y d w u i n t e r f e r u j c y c h f a l
F a l e m o n o c h r o m a t y c z n e e m i t o w a n e p r z e z 2 a t o m y
P r z y p a d k o w e i n i e z a l e |n e e m i s j e f o t o n w d l a o b u zr d e B
F a z y p o c z t k o w e 1 ( t ) i 2 ( t ) s p r z y p a d k o w y m i
i s z y b k o z m i e n n y m i f u n k c j a m i c z a s u t
R |n i c a f a z ( t ) j e s t t a k s a m f u n k c j , a w i c
I P ( t ) = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s [ k ( r 1 - r 2 ) + ( t ) ]
R e j e s t r u j e m y [r e d n i w a r t o [ w c z a s i e t z n a c z n i e d Bu |s z y m o d
o k r e s u p r z y p a d k o w y c h z m i a n
1
I P =
P
+"I ( t ) d t = I 1 + I 2 g d y | u [r e d n i e n i e c o s d a j e w a r t o [ z e r o w
t
t
W o p t y c z n y m p a [m i e i n t e r f e r e n c j i p r o m i e n i o w a n i a z d w c h
n i e z a l e |n y c h zr d e B n i e m o |n a z a r e j e s t r o w a
F a l e s n i e k o h e r e n t n e ( n i e s p j n e )
F a l a m o n o c h r o m a t y c z n a e m i t o w a n a
p r z e z p u n k t o w e zr d Bo
A 1
z w i e r c i a d Bo
A 0 zr d Bo p i e r w o t n e
A 1 i A 2 zr d Ba w t r n e
A 1 P = r 1 A 2 P = r 2
A 0 a" A 2 P
d z i e l n i k
T e r a z r |n i c a f a z p o c z t k o w y c h = 0
D l a r |n y c h p o Bo |e D p u n k t w P s t a c j o n a r n y r o z k Ba d i n t e n s y w n o [c i
I P = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s [ k ( r 1 - r 2 ) ]
F a l a m o n o c h r o m a t y c z n a
e m i t o w a n a p r z e z p u n k t o w e zr d Bo c d
D Bu g o [ f a l i w o [r o d k u o w s p Bc z y n n i k u z a Ba m a n i a n
v p r d k o [ f a l i T o k r e s
= v T
O z n a c z a j c p r z e z 0 d Bu g o [ f a l i w p r |n i , w t e d y
c T 0 o r a z k = 2 2 n
=
= =
0
n n
n r
O z n a c z e n i e m = r z d i n t e r f e r e n c j i
r = r 1 - r 2
0
R w n a n i e i n t e r f e r e n c y j n e
# #
n r
# #
I P = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s #2 = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s ( 2 m )
0 #
# #
I l o c z y n n r j e s t d r o g o p t y c z n , a w i c n r - r |n i c d r g o p t y c z n y c h
F a l a m o n o c h r o m a t y c z n a
e m i t o w a n a p r z e z p u n k t o w e zr d Bo c d
P r |e k j a s n y
I P m a x = I 0 1 + I 0 2 + 2 I 0 1 I 0 2
0
g d y c o s = 1 ! n r = 2 K l u b m = 0 , 1 , 2 , . .
2
I P m i n = I 0 1 + I 0 2 - 2 I 0 1 I 0 2
P r |e k c i e m n y
0
g d y c o s = - 1 !
n r = ( 2 K + 1 ) l u b m = 0 . 5 , 1 . 5 , 2 . 5 . .
2
I P m a x - I P m i n
I 0 1 = I 0 2 = I 0
K o n t r a s t C = m a k s y m a l n y C = 1 g d y
I P m a x + I P m i n
I P m i n = 0 I P m a x = 4 I 0
i w t e d y
I P = 4 I 0 c o s 2 ( m )
I n t e r f e r e n c j a f a l e m i t o w a n y c h p r z e z a t o m
A t o m n i e p r o m i e n i u j e [w i a t Be m
A 1 x
r 1
m o n o c h r o m a t y c z n y m
P
W p Ba s z c z y zn i e d l a r |n y c h
r 1 = r 2
r 2
d Bu g o [c i f a l , a w i c i k o Bo w e j
l i c z b y f a l o w e j k , r o z k Ba d
A 2
b d z i e r |n y , g d y |
I P ( k ) = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s ( k r )
2
1 I P 2 > 1
T y l k o w p u n k c i e P d l a r = 0
m a m y p r |e k j a s n y d l a
k a |d e g o
i n t e r f e r e n c j a . e x e
x
r = 0
O b r a z d l a 2 d Bu g o [c i f a l
I n t e r f e r e n c j a w [w i e t l e b i a By m
x
0
I n t e r f e r e n c j a f a l e m i t o w a n y c h p r z e z zr d Bo p u n k t o w e
yr d Bo p r o m i e n i u j e w p r z e d z i a l e " ( 1 , 2 ) i k " ( k 1 , k 2 )
A 1 x
r 1
I P ( k ) = I 0 1 + I 0 2 + 2 I 0 1 I 0 2 c o s ( k r )
P
r 1 = r 2
r 2
O d b i o r n i k r e j e s t r u j e s u m
i n t e n s y w n o [c i d l a k a |d e g o k
A 2
I P C =
P
+"I ( k ) d k
k
W p u n k c i e r = 0 ) !
I P C = m a x
W r a z z e w z r o s t e m o d l e g Bo [c i o d p u n k t u , d l a k t r e g o r 1 = r 2 ! r o [n i e r
o s c y l u j w a r t o [c i c o s ( k r ) m i d z y + 1 a - 1 r |n i e d l a r |n y c h k
K o n t r a s t p r |k w z m n i e j s z a s i
I s t n i e j e g r a n i c z n a o d l e g Bo [ x g p o z a k t r k o n t r a s t z a n i k n i e
I n t e r f e r e n c j a f a l e m i t o w a n y c h p r z e z a t o m p r z y k Ba d
2
N i e c h l i n i a s p e k t r a l n a m a p o s t a
#
k - k 0 #
# #
I k = I 0 e x p #-
# #
#
k
# #
# #
# #
I k
I 0
O d b i o r n i k r e j e s t r u j e s u m
i n t e n s y w n o [c i d l a k a |d e g o k
I P C =
P
+"I ( k ) d k
k
D l a r w n y c h i n t e n s y w n o [c i
k 0
k
i n t e r f e r u j c y c h f a l I 0 1 = I 0 2 = 0 . 5 I 0
k
o t r z y m a m y d l a j e d n e j d Bu g o [c i f a l i
I P ( k ) = I 0 + I 0 c o s ( k r )
A d l a c a Be g o w i d m a p o r o z w i z a n i u c a Bk i
2
] c o s ( k 0 r ) }
I P C =
P
+"I ( k ) d k = I 0 C { 1 + e x p [ - ( 0 . 5 k r )
k
I 0 C i n t e n s y w n o [ zr d Ba p i e r w o t n e g o ( c a Be g o w i d m a )
W y n i k i n t e r f e r e n c j i d l a d w c h w a r t o [c i k
2 r g
I P C / I 0 C
2
k = 0 . 0 2
1
0
0
r
2 r g
P r o m i e n i o w a n i e
I P C / I 0 C
q u a s i k o h e r e n t n e
2
k = 0 . 0 4
P r o m i e n i o w a n i e
1
n i e k o h e r e n t n e
0
0
r
P r o m i e n i o w a n i e k o h e r e n t n e
I n t e r f e r e n c j a f a l e m i t o w a n y c h p r z e z a t o m p r z y k Ba d
W r a z z e w z r o s t e m k m a l e j e
o b s z a r p r |k w z w y s o k i m k o n t r a s t e m
W a r u n e k w y s o k i e g o k o n t r a s t u
C e" 0 . 9 p r o m i e n i o w a n i e q u a s i k o h e r e n t n e
0 . 6 5 2
r g = H"
k 1 0
A b y u z y s k a p r |k i p r z y d u |e j r |n i c y d r g t r z e b a s t o s o w a
zr d Ba q u a s i m o n o c h r o m a t y c z n e
P r z e Bo m o w a r o l a l a s e r w
I n t e r f e r e n c j a p r o m i e n i o d b i t y c h o d
d w c h p o w i e r z c h n i
2
h
R w n a n i e c i e m n e g o p r |k a d l a m a By c h
k t w l u b d u |y c h p r o m i e n i R
2 h = ( K + 0 . 5 ) K = 0 , 1 , 2 , . .
R
h
P r |k i ( I s a a c a )
O b r a z p r |k w
N e w t o n a ( 1 6 4 2 - 1 7 2 7 )
I n t e r f e r o m e t r y
p o w i e r z c h n i a
s p r a w d z a n a
s p r a w d z i a n
O b
P r o g r a m a u t o m a t y c z n i e
w y z n a c z a k s z t a Bt p o w i e r z c h n i
s p r a w d z a n e j z d o k Ba d n o [c i
r z d u / 5 0
d z i e l n i k
l a s e r
k a m e r a
C C D
I n t e r f e r o m e t r ( H y p o l i t e a ) F i z e a u ( c z y t a j f i z o ) ( 1 8 1 9 - 1 8 9 6 )
I n t e r f e r o m e t r y
E l e m e n t
b a d a n y
k a m e r a
C C D
L a s e r z
u k Ba d e m
o p t y c z n y m
K a n a B
o d n i e s i e n i a
I n t e r f e r o m e t r ( L ) M a c h a - ( L ) Z e h n d e r a
P r z y k Ba d y
W p By w k o n w e k c j i p o w i e t r z a
K o n w e k c j a p o w i e t r z a w
p Bo m i e n i u [w i e c y
S t r u g a p o w i e t r z a
P r |k i N e w t o n a i p By t k a
w [w i e t l e b i a By m !
P By t k a o z m i e n n e j
g r u b o [c i
M u c h a n a
w o d z i e
L i t e r a t u r a u z u p e Bn i a j c a
J . R . M e y e r - A r e n d t : W s t p d o o p t y k i . P W N , W a r s z a w a 1 9 7 7 ,
p a r a g r a f y 2 . 2 2 . 5
E . H e c h t , A . Z a j a c : O p t i c s . A d d i s o n - W e s l e y P u b l . C o . , R e a d i n g M a s s .
1 9 7 4 , r o z d z i a B 9
B . E . A . S a l e h , M . C . T e i c h : F u n d a m e n t a l s o f P h o t o n i c s , J o h n W i l e y &
S o n s , N e w Y o r k 1 9 9 1 , p a r a g r a f 2 . 5
R . J zw i c k i : O p t y k a i n s t r u m e n t a l n a . W N T , W a r s z a w a 1 9 7 0 , p a r a g r a f 3 . 2 .
F r a g m e n t y k s i |k i , F u n d a c j a W s p i e r a n i a R o z w o j u i W d r a |a n i a T e c h n i k
O p t y c z n y c h
J . P e t y k i e w i c z : O p t y k a f a l o w a . P W N , W a r s z a w a 1 9 8 6 , r o z d z i a B 3
M . B o r n , E . W o l f : P r i n c i p l e s o f O p t i c s . P e r g a m o n P r e s s , O x f o r d 1 9 8 0 ,
r o z d z i a B V I I
L i t e r a t u r a p o d s t a w o w a p o z i o m w y |s z y n a u k o w a
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