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Astronomical Applications Department, U.S. Naval Observatory - Beam Comp Example (Page 13)

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Astronomical Applications Department, U.S. Naval Observatory - Beam Comp Example
In this section we decompose the OPD into a Zernike series. First, read the Zernike routines,
then set the compression factor to 10, the distance to the detector to 20 cm, and normalize the
radius (as required by Zernike expansion routine). Now R will be the input beam radius.
>
read`d:/optics/AESOP/zseries.p`:
The OPD then looks like this:
OPD for Zernike Series Input
>
opd := collect( subs( rho=R*rho, OPD ),
[Delta,psi,cos(phi),rho,d], simplify );
opd


:=


+
1
1024
C2
(
)
-
+
280 359 C R11 d
f14
1
1024
(
)
-
+ +
+ +
878 C3 C 359 C4 14 405 C2 R11
f13 C
11


-
-
7
128
C2
(
)
- +
10 11 C R9 d
f
12
1
128
(
)
+ -
-
+
77 C4 7 2 C 189 C3 90 C2 R9
f
11
C
9
+


+
3
32
C2
(
)
-
9 C 10 R7 d
f10
1
32
(
)
+ -
+
30 C 3 64 C2 27 C3 R7
f9
7
+


-
-
1
8
C2
(
)
- +
10 7 C R5 d
f
8
1
16
(
)
+
-
+
14 C3 16 C 36 C2 3 R5
f
7
5
+


+
1
2
C2
(
)
-
C
2 R3 d
f6
1
4
(
)
+
-
+
1 2 C3 6 C2 2 C R3
f5
3
+

( )
cos
3

+


+
7
2048
C2
(
)
-
13 C 19 R11 d
f
14
1
2048
(
)
-
-
+
+ +
289 C3 5 C 91 C4 14 198 C2 R11
f
13
C
11


-
-
5
512
C2
(
)
- +
17 11 C R9 d
f12
1
1024
(
)
-
+
+
-
28 349 C3 230 C2 110 C4 13 C R9
f11 C
9
+


+
5
64
C2
(
)
-
3 C 5 R7 d
f
10
1
64
(
)
+ -
+
15 C3 3 47 C2 28 C R7
f
9
7
+


-
-
1
16
C2
(
)
- +
13 7 C R5 d
f8
1
64
(
)
+ +
-
50 C 9 28 C3 90 C2 R5
f7
5
+


+
1
8
C2
(
)
- +
11 5 C R3 d
f
6
1
8
(
)
-
+ +
+
17 C2 3 8 C 5 C3 R3
f
5
3
+

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