Biomedical Engineering Reference
In-Depth Information
The Jones vector for an incident beam is deined as
¨
ª
E
E
¸
x
E
¹
(4.14)
©
in
º
y
The emerging beam is then obtained from
EJ
J
J
J
J
E
(4.15)
out
P
(/)
Q
2
QR
(
'
,
Q
/)
4
M
(,)
BR
QR
(
'
,/) ()
Q
4
P
0
in
1
1
¨
0
¸
©
©
©
¹
¹
¹
¥
§ ¦
E
(4.16)
B
µ
·
out
R
'
R
E
sin
(cos(
2
)sin(
)
i
sin
2
))
x
1
2
ª
º
The emerging beam components are deined with
a
a
¨
E
E
¸
x
E
¹
(4.17)
©
out
ª
º
y
And its intensity using
*
*
I
aa aa
EEEE
(4.18)
out
x
x
y
y
B
¥
§ ¦ µ
22
¨ ª
2
2
1
2
¸ º
I
E
sin
cos (
2
R
)sin
'
sin (
2
R
)
(4.19)
·
out
x
2
The maximum observed intensity in the emerging beam occurs
when B
=
Q if G 1 = Q / 2 or
R = Q / 2.
2 (4.20)
Relying on this, we measure the maximum I G 0 M ex/ 2 and minimum
I G 0 M ex green light intensities from stacked quarter-wave plates placed
within the polariscope and oriented with R
I
E
outMAX
x
= 0 and we normalize
the observed green light intensity I G as follows to compensate for
external noise (Fig. 4.7):
I
I
M
GGex
Gex
0
I
(4.21)
GN
I
I
M
M
/
2
G
0
ex
¨
¸
¥
§ ¦
µ
·
¥
§ ¦
µ
·
Re
Q
MQ
M
2
2
2
2
R
ex
R
I GN
sin
cos (
2
)sin
sin (
2
)
¹ ¹
(4.22)
© ©
M
2
ª
ºº
G
G
In this coniguration, we expect M G to be as close as possible to
M ex in order to reduce the inluence of stress direction in magnitude
measurements. For models of vasculature, R is the direction of the
projection of T
in the polarizer plane, it is desirable to quantify
its contribution into the stress magnitude measurements. For
2
 
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