Die ersten 15 Zernike-Polynome

j $n$ $m$ Name Formel Bild
1 0 0 Piston $Z_1 = 1$ Z1
2 1 1 Tip $Z_2 = 2r \cos \theta$ Z2
3 1 1 Tilt $Z_3 = 2r \sin \theta$ Z3
4 2 0 Defokus $Z_4 = \sqrt{3} (2r^2 -1)$ Z4
5 2 2 Astigmatismus $Z_5 = \sqrt{6}r^2 \sin 2 \theta$ Z5
6 2 2 Astigmatismus $Z_6 = \sqrt{6}r^2 \cos 2 \theta$ Z6
7 3 1 Koma $Z_7 = \sqrt{8} (3r^3-2r) \sin \theta$ Z7
8 3 1 Koma $Z_8 = \sqrt{8} (3r^3-2r) \cos \theta$ Z8
9 3 3 Trefoil $Z_9 = \sqrt{8} 3r^3 \sin 3 \theta $ Z9
10 3 3 Trefoil $Z_{10} = \sqrt{8} 3r^3 \cos 3 \theta$ Z10
11 4 0 Sphärische
Aberration		 $Z_{11}=\sqrt{5} (6r^4 -6r^2 +1)$ Z11
12 4 2 Astigmatismus
5ter Ordnung		 $Z_{12} = \sqrt{10}( 10r^4 -3r^3) \cos 2\theta$ Z12
13 4 2 Astigmatismus
5ter Ordnung		 $Z_{13} = \sqrt{10}( 10r^4 -3r^3) \sin 2\theta$ Z13
14 4 4 Ashtray $Z_{14} = \sqrt{10}r^4 \cos 4\theta$ Z14
15 4 4 Ashtray $Z_{15} = \sqrt{10}r^4 \sin 4\theta$ Z15