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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