Respect for Tissue Representation Using Photoelastic Stress Analysis for Endovascular Surgery Simulation - Microsurgery: Advances, Simulations, and Applications - page 131

Using Jones calculus, the components of the polariscope can be
deined as follows [5]:

•

Polarizer

¨

10
00

¸
º ¹

J P () (4.7)

ª ©

0

•

Analyzer

¨

00
01

¸
º ¹

J P (/) (4.8)

ª ©

Q 2

The total phase shift between the ield components for quarter-
wave retarder is represented by

QM
M

ex
G

' 1 (4.9)

2

For this study, we selected wavelength retarders of M ex = 560 nm
wavelength to study the retardation of the observed beam that has a
wavelength M G . The matrix corresponding to a quarter-wave retarder
rotated π /4 is

¨ ' ' ¸

1 1

cos i sin

©
©
©
©

¹
¹
¹
¹

2 2

J (4.10) ' Q

QR (, /) 4

' '

1

1 1

i sin cos

ª

2 2

º

And corresponding to a quarter-wave retarder rotated - π /4 is

' '

¨ ¸

1 1

cos i sin

©
©
©
©

¹
¹
¹
¹

2 2

J (4.11)

QR (, ' Q /) 4

' '

1

1 1

i sin cos

ª

2 2

º

The matrix corresponding to the blood vessel phantom is then
represented by

¨ B B B ¸

R R

cos i sin cos 2 i sin sin 2

©
©
©
©

¹
¹
¹
¹

2 2 2

J (4.12)

M (,) BR

B B B

i sin sin 2

R

cos i sin cos R 2

ª

2 2 2

º

where R is the stress direction and

B is the retardation in radians and
Re in nanometers. For green light study,

2Re
G

Q
M

B

(4.13)