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In-Depth Information
S
z
=
S
z
R
(
)
=
S
zy
−
cos
sin
S
yy
S
τ
=
R
(
−
)
S
τ
R
(
)
=
sin
2
cos
−
sin
cos
cos
2
−
sin
S
z
=
S
z
R
(
)
=
S
zy
−
sin
cos
S
yy
S
τ
=
R
(
−
)
S
τ
R
(
)
=
sin
2
cos
−
sin
,
(4
cos
cos
2
−
sin
.
90)
where [
R
(
)] is the rotation matrix
cos
sin
[
R
(
)]
=
.
−
sin
cos
Represent the total effect of both prisms as a sum of their partial effects:
H
z
H
A
z
H
A
z
H
A
H
A
H
A
=
+
,
τ
=
τ
+
τ
.
(4
.
91)
Substituting (4.84), (4.85) into (4.91), we get
τ
=
S
z
H
N
τ
+
S
z
H
N
τ
=
S
z
+
S
z
H
N
[
S
z
]
H
N
τ
(4
.
92)
τ
=
S
τ
H
N
τ
+
S
τ
H
N
τ
=
S
τ
+
S
τ
H
N
[
S
τ
]
H
N
τ
,
whence
=
S
z
+
S
z
[
S
z
]
(4
.
93)
=
S
τ
+
S
τ
.
[
S
τ
]
Thus, we decompose the measured matrices [S
z
]
,
[S
τ
] reflecting both the prisms
into the partial matrices
S
z
,
S
τ
and
S
z
,
S
τ
reflecting each prism separately.
There exist linear relations between components of the measured and partial
matrices. According to (4.90) and (4.93),
S
zy
sin
−
S
zy
sin
S
zx
=−
(4
.
94)
S
zy
cos
+
S
zy
cos
S
zy
=
and
