THORLABS WFS20-14AR, Руководство по эксплуатации

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Wavefront Sensor
The following tables give the Zernike polynomials in Polar (Radial) and Cartesian coordinates of
order 0 to 4 according to the
ANSI Standard Z80.28-210 .
Mode Order Frequency Norm Zernike Polynomial, Polar
1 0 0 1
1
2 1 -1 2
ρ*sin(θ)
3 1 +1 2
ρ*cos(θ)
4 2 -2
ρ
2
*sin(2θ)
5 2 0 2ρ
2
-1
6 2 +2
ρ
2
*cos(2θ)
7 3 -3 ρ
3
*sin(3θ)
8 3 -1
3ρ
3
*sin(θ)-2ρ*sin(θ)
9 3 +1 3ρ
3
*cos(θ)-2ρ*cos(θ)
10 3 +3
ρ
3
*cos(3θ)
11 4 -4
ρ
4
*sin(4θ)
12 4 -2
4ρ
4
*sin(2θ)-3ρ
2
*sin(2θ)
13 4 0
6ρ
4
- 6ρ
2
+1
14 4 +2 4ρ
4
*cos(2θ)-3ρ
2
*cos(2θ)
15 4 +4
ρ
4
*cos(4θ)
Mode Order Frequency Name Norm Zernike Polynomial, Cartesian
1 0 0 Piston 1
1
2 1 -1 Tip Y 2 y
3 1 +1 Tilt X 2
x
4 2 -2 Astigmatism ± 45°
2xy
5 2 0 Defocus 2x
2
+ 2y
2
-1
6 2 +2 Astigmatism 0° / 90°
x
2
- y
2
7 3 -3 Trefoil Y 3x
2
y -y
3
8 3 -1 Coma X
3x
2
y + 3y
3
- 2y
9 3 +1 Coma Y 3x
3
+ 3xy
2
- 2x
10 3 +3 Trefoil x
x
3
- 3xy
2
11 4 -4 Tetrafoil Y
4x
3
y - 4xy
3
12 4 -2 Sec. Astig. Y
8x
3
y + 8xy
3
- 6xy
13 4 0 Spher. Aberr. 3
6x
4
+ 12x
2
y
2
+ 6y
4
- 6x
2
- 6y
2
+1
14 4 +2 Sec. Astig. X 4x
4
- 4y
4
- 3x
2
+ 3y
2
15 4 +4 Tetrafoil X
x
4
- 6x
2
y
2
+ y
4