92
DISPLAYING THE MEASUREMENT RESULT
(REFERENCE) WAVEFRONT AND ZERNIKE COEFFICIENTS
Zernike coefficients, meaning and classification are shown below.
Z
n
m
Coefficient
n
m
Z
Meaning/Classification
Z
2
-2
C
2-2
2
-2
r
2
sin2
ϕ
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
ϕ
2
nd
order Astigmatism
Z
3
-3
C
3-3
3
-3
r
3
sin3
ϕ
3
rd
Trifoil
Z
3
-1
C
3-1
3
-1
(3r
3
- 2r) sin
ϕ
Coma Y
Z
3
1
C
31
3
1
(3r
3
- 2r) cos
ϕ
Coma X
Z
3
3
C
33
3
3
r
3
cos3
ϕ
3
rd
Trifoil
Z
4
-4
C
4-4
4
-4
r
4
sin4
ϕ
Z
4
-2
C
4-2
4
-2
(4r
4
- 3r
2
) sin2
ϕ
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
ϕ
4
th
Order Astigmatism
Z
4
4
C
44
4
4
r
4
cos4
ϕ
Z
5
-5
C
5-5
5
-5
r
5
sin5
ϕ
Z
5
-3
C
5-3
5
-3
(5r
5
- 4r
3
) sin3
ϕ
5
th
Order Trifoil
Z
5
-1
C
5-1
5
-1
(10r
5
- 12r
3
+ 3r) sin
ϕ
5
th
Order Coma Y
Z
5
1
C
51
5
1
(10r
5
- 12r
3
+ 3r) cos
ϕ
5
th
Order Coma X
Z
5
3
C
53
5
3
(5r
5
- 4r
3
) cos3
ϕ
5
th
Order Trifoil
Z
5
5
C
55
5
5
r
5
cos5
ϕ
Z
6
-6
C
6-6
6
-6
r
6
sin6
ϕ
Z
6
-4
C
6-4
6
-4
(6r
6
- 5r
4
) sin4
ϕ
Z
6
-2
C
6-2
6
-2
(15r
6
- 20r
4
+ 6r
2
) sin2
ϕ
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
ϕ
6
th
Order Astigmatism
Z
6
4
C
64
6
4
(6r
6
- 5r
4
) cos4
ϕ
Z
6
6
C
66
6
6
r
6
cos6
ϕ
Table. 1: Zernike Terms Up to 6
th
Order
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