Astronomical Applications Department, U.S. Naval Observatory Beam Comp Example Page 10
+
1
8
C2
(
)
-
20 C 19 d
f3
1
24
-
+
+
+
141 C2 60 C3 72 C 1
f2
3
+
-
+
-
-
-
C2
(
)
- +
7 4 C d
f
11 C2 4 C 4 C3
1
3
+
( )
cos
3
+
+
31
1024
C2 d
f12
1
2048
+ -
62 C2 4 91 C
f11
12
-
-
5
64
C2 d
f10
1
512
+ -
40 C2 3 53 C
f9
10
+
+
3
16
C2 d
f8
1
64
(
)
-
12 C 1 (
)
-
C
1
f7
8
-
-
13
32
C2 d
f6
1
32
+
-
1 13 C2 12 C
f5
6
+
+
+
3
4
C2 d
f4
1
4
C
(
)
- +
2 3 C
f3
4
-
-
C2 d
f2
1
2
- +
1 2 C2
f
2
+
+
( )
cos
2
+
9
8192
C2 d
f12
1
8192
C
(
)
-
9 C 16
f11
12
-
-
1
256
C2 d
f10
1
1024
C
(
)
- +
7 4 C
f9
10
+
+
+
7
512
C2 d
f8
1
512
C
(
)
- +
12 7 C
f7
8
-
-
3
64
C2 d
f6
1
64
C
(
)
-
3 C 5
f5
6
+
+
+
5
32
C2 d
f4
1
32
C
(
)
- +
8 5 C
f3
4
-
-
1
2
C2 d
f2
1
4
-
+
2 C2 4 C 1
f
2
2 C2 d
+
+
+
2 f (
)
-
C
1 (
)
+
C
1
+
2
-
+
-
+
-
+
1
1024
11
f10
1
256
9
f8
1
64
7
f6
1
16
5
f4
1
4
3
f2
2
( )
cos
+
>
cost(OPD);
+
+
+
433 additions 2565 multiplications 187 divisions 13 functions
The Aperture-Averaged OPD
The OPD averaged over an annular aperture of inner and outer radii a and b is:
>
OPD_avg;
1
2
C2
f2
1
4
C2
(
)
+
a2 b2
f4
11
96
C2
(
)
-
+
b2 a b a2
(
)
+ +
a b b2 a2
f6
-
+
3
64
C
2
(
)
+
a
2
b
2
(
)
+
b
4
a
4
f8
9
512
C
2
%4 %3
f10
-
+
