Topcon KR-1W - Page 110

108
DISPLAYING THE MEASUREMENT RESULT
(REFERENCE) WAVEFRONT AND ZERNIKE COEFFICIENTS
Zernike coefficients, meaning and classification are shown below.
Table. 1: Zernike Terms Up to 6
th
Order
Z
n
m
Coefficient n m Z Meaning/Classification
Z
2
-2
C
2-2
2 -2 r
2
sin2 2
nd
order Astigmatism
Z
2
0
C
2-0
2 0 2r
2
- 1 Defocus
Z
2
2
C
22
2 2 r
2
cos2 2
nd
order Astigmatism
Z
3
-3
C
3-3
3 -3 r
3
sin3 3
rd
Trifoil
Z
3
-1
C
3-1
3 -1 (3r
3
- 2r) sin Coma Y
Z
3
1
C
31
3 1 (3r
3
- 2r) cos Coma X
Z
3
3
C
33
3 3 r
3
cos3 3
rd
Trifoil
Z
4
-4
C
4-4
4 -4 r
4
sin4
Z
4
-2
C
4-2
4 -2 (4r
4
- 3r
2
) sin2 4
th
Order Astigmatism
Z
4
0
C
40
4 0 6r
4
- 6r
2
+ 1 Spherical aberration
Z
4
2
C
42
4 2 (4r
4
- 3r
2
) cos2 4
th
Order Astigmatism
Z
4
4
C
44
4 4 r
4
cos4
Z
5
-5
C
5-5
5 -5 r
5
sin5
Z
5
-3
C
5-3
5 -3 (5r
5
- 4r
3
) sin3 5
th
Order Trifoil
Z
5
-1
C
5-1
5 -1 (10r
5
- 12r
3
+ 3r) sin 5
th
Order Coma Y
Z
5
1
C
51
5 1 (10r
5
- 12r
3
+ 3r) cos 5
th
Order Coma X
Z
5
3
C
53
5 3 (5r
5
- 4r
3
) cos3 5
th
Order Trifoil
Z
5
5
C
55
5 5 r
5
cos5
Z
6
-6
C
6-6
6 -6 r
6
sin6
Z
6
-4
C
6-4
6 -4 (6r
6
- 5r
4
) sin4
Z
6
-2
C
6-2
6 -2 (15r
6
- 20r
4
+ 6r
2
) sin2 6
th
Order Astigmatism
Z
6
0
C
60
6 0 20r
6
- 30r
4
+ 12r
2
- 1 6
th
Order Spherical aberration
Z
6
2
C
62
6 2 (15r
6
- 20r
4
+ 6r
2
) cos2 6
th
Order Astigmatism
Z
6
4
C
64
6 4 (6r
6
- 5r
4
) cos4
Z
6
6
C
66
6 6 r
6
cos6