+
1
12
C2
(
)
- +
17 16 C d
f3
1
144
-
+
+
-
444 C2 216 C 192 C3 7
f2
R3
+
3
-
+
-
+
-
5
14336
R11
f10
1
672
R9
f8
1
160
R7
f6
1
40
R5
f4
1
12
R3
f2
+
(
)
-
3
3
2
( )
cos
Notice that it is linear in both
and
. Let's see what angle compensates for a translation,
to first order in angle.
>
collect( expansion( ZernikeTerm(3,1,c), psi, 1, ON ), [psi,Delta], factor
);
1
860160
R3
( )
cos
(
)
- +
2 3
2
1863680 f9 C2 16128 R4 f5 C 680320 R6 f3 C4
+
-
(
1597440 R6 f3 C3 23040 R6 f3 C 213750 R8 C3 d 2053632 R2 f7 C2
+
-
-
-
1322496 R4 f5 C2 1185408 R4 f5 C4 2757888 R4 f5 C3 75264 R2 f7 C
+
+
-
-
334350 R8 f C4 4800 R8 f C 775650 R8 f C3 334350 R8 C4 d 718080 R6 f3 C2
+
+
-
+
-
2472960 f
8
C
3
d
1433600 f
8
C
4
d
4171776 R
2
f
7
C
3
1645056 R
2
f
7
C
4
-
+
+
-
321750 R8 f C2 1433600 f9 C4 2096640 R2 f6 C3 d 4121600 f9 C3 232960 f9 C
+
+
+
-
+
4875 R8 f 1185408 R4 f4 C4 d 1645056 R2 f6 C4 d 1161216 R4 f4 C3 d
-
+
-
-
528000 R6 f2 C3 d 680320 R6 f2 C4 d 20800 R6 f3
+
-
+
)
2
f13 C
(
)
1
215040
-
R3
( )
cos
(
)
- +
2 3
2
(
)
-
+
-
+
+
320 R6 f2 75 R8 5376 R2 f6 17920 f8 1344 R4 f4
f10
+
1
860160
R3
( )
cos
(
)
- +
2 3
2
394240 f9 C2 40320 R4 f5 C 183040 R6 f3 C4
+
-
(
474560 R6 f3 C3 8000 R6 f3 C 82950 R8 C3 d 526848 R2 f7 C2 392448 R4 f5 C2
+
+
-
-
+
298368 R4 f5 C4 768768 R4 f5 C3 96768 R2 f7 C 94425 R8 f C4 525 R8 f C
+
-
-
+
-
240900 R8 f C3 94425 R8 C4 d 246400 R6 f3 C2 609280 f8 C3 d 286720 f8 C4 d
-
+
-
-
+
1064448 R2 f7 C3 376320 R2 f7 C4 120825 R8 f C2 286720 f9 C4
+
-
+
+
602112 R
2
f
6
C
3
d
931840 f
9
C
3
161280 f
9
C
5250 R
8
f
298368 R
4
f
4
C
4
d
+
-
+
+
+
376320 R2 f6 C4 d 376320 R4 f4 C3 d 188800 R6 f2 C3 d 183040 R6 f2 C4 d
-
-
+
-
22400 R
6
f
3
-
)
3
f
14
C
(
)
1
215040
-
