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Astronomical Applications Department, U.S. Naval Observatory - Beam Comp Example (Page 19)

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Astronomical Applications Department, U.S. Naval Observatory - Beam Comp Example


-
+
-
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-
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1
1024
R11
11
f10
1
256
R9
9
f8
1
64
R7
7
f6
1
16
R5
5
f4
1
4
R3
3
f2
2 R
( )
cos
+
>
cost(");
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433 additions 3710 multiplications 187 divisions 13 functions
Now calculate the Zernike series coefficients:
Zernike Series Calculation
>
verbosity := 1: time0 := time():
>
ZernikeSeries( opd, 12, [Delta,psi,R,d] );
ZernikeSeries[65]: (disk averaged OPD)
ZernikeSeries[65]: calculating the coefficients [0, 0]...
ZernikeSeries[103]: A[0, 0]:


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17
8192
C2 d
f14
1
57344
- -
119 C2 14 174 C
f13
R12



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-
19
3072
C2 d
f12
1
3072
- -
+
3 25 C 19 C2
f11
R10


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9
512
C2 d
f10
1
2560
-
-
45 C2 48 C 10
f9
R8
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+


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-
3
64
C2 d
f8
1
256
- -
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4 11 C 12 C2
f7
R6


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11
96
C2 d
f6
1
96
-
-
11 C2 8 C 6
f5
R4
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+


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-
1
4
C2 d
f4
1
8
- +
-
2 2 C2 C
f3
R2
1
2
C2 d
f2
1
2
- +
2 C2
f
+
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2

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9
2048
C2 d
f13
1
14336
- -
63 C2 2 93 C
f12
R12


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-
41
3072
C2 d
f11
1
3072
- -
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2 55 C 41 C2
f10
R10
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5
128
C2 d
f9
1
640
-
-
25 C2 28 C 2
f8
R8


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-
7
64
C2 d
f7
1
64
- -
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1 7 C 7 C2
f6
R6
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7
24
C2 d
f5
1
24
-
-
7 C2 6 C 2
f4
R4


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-
3
4
C2 d
f3
1
4
- +
-
2 3 C2 2 C
f2
R2
4 2 C2
+
+
- +
2
C2 d
f
+



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19
8192
C2 d
f12
1
57344
-
+
133 C2 198 C 8
f11
R12

+


-
-
11
1536
C2 d
f10
1
6144
+ -
44 C2 3 60 C
f9
R10


+
11
512
C2 d
f8
1
2560
-
+ +
64 C 4 55 C2
f7
R8
+
+

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