ZernikeSeries[9053]: calculating the coefficients [12, 4]...
ZernikeSeries[9209]: calculating the coefficients [12, 6]...
ZernikeSeries[9358]: calculating the coefficients [12, 8]...
ZernikeSeries[9509]: calculating the coefficients [12, 10]...
ZernikeSeries[9662]: calculating the coefficients [12, 12]...
>
cost(S);
+
+
+
1605 additions 11173 multiplications 690 divisions 17 functions
>
cost(opd);
+
+
+
433 additions 3710 multiplications 187 divisions 13 functions
>
save OPD, OPD_avg, opd, S, c, `d:/optics/AESOP/BeamCompExample.eqs`;
Sanity Check
The series expansion of the wavefront is stored in S, and the series coefficients are stored in
the table, c. As a quick check, let's make sure S is identical to the OPD:
>
factor( expand(S-opd) );
0
Elimination of Coma, Due to a Mirror Displacement, by a Compensating
Mirror Rotation
We can use the function ZernikeTerm() to access the individual components. For
example, the coma term is
>
ZernikeTerm(3,1,c);
+
5
57344
C2
(
)
-
+
1106 1259 C d
f14
5
57344
-
-
+ +
1259 C4 3212 C3 7 C 70 1611 C2
f13 C
R11
-
-
1
1344
C2
(
)
-
+
295 286 C d
f12
1
2688
-
+
-
+
770 C2 1483 C3 572 C4 25 C 70
f11 C
R9
+
+
1
320
C2
(
)
-
+
140 111 C d
f10
1
320
+ +
-
146 C 15 111 C3 286 C2
f9
R7
+
-
-
7
80
C2
(
)
- +
8 5 C d
f8
1
80
+
-
+
35 C3 49 C 99 C2 9
f7
R5
+
+
1
24
C2
(
)
- +
17 8 C d
f6
1
48
(
)
+
4 C 1 (
)
-
+
4 C2 14 C 9
f5
R3
+
3
+
+
15
28672
C2
(
)
-
743 C 475 d
f13
5
57344
-
+
+
+
-
10342 C3 4458 C4 4290 C2 64 C 65
f12 C
R11
