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Pervye 15 polinomov Zernike

j Nazvanie Formula Izobrazhenie

1 0 0 Porshen'

2 1 1 Naklon $Z_2 = 2r \cos \theta$

3 1 1 Naklon $Z_3 = 2r \sin \theta$

4 2 0 Rasfokusirovka $Z_4 = \sqrt{3} (2r^2 -1)$

5 2 2 Astigmatizm $Z_5 = \sqrt{6}r^2 \sin 2 \theta$

6 2 2 Astigmatizm $Z_6 = \sqrt{6}r^2 \cos 2 \theta$

7 3 1 Koma $Z_7 = \sqrt{8} (3r^3-2r) \sin \theta$

8 3 1 Koma $Z_8 = \sqrt{8} (3r^3-2r) \cos \theta$

9 3 3 Trilistnik $Z_9 = \sqrt{8} 3r^3 \sin 3 \theta$

10 3 3 Trilistnik $Z_{10} = \sqrt{8} 3r^3 \cos 3 \theta$ Z10

11 4 0 Sfericheskii $Z_{11}=\sqrt{5} (6r^4 -6r^2 +1)$ Z11

12 4 2 Astigm. 5-go por. $Z_{12} = \sqrt{10}( 10r^4 -3r^3) \cos 2\theta$ Z12

13 4 2 Astigm. 5-go por. $Z_{13} = \sqrt{10}( 10r^4 -3r^3) \sin 2\theta$ Z13

14 4 2 Pepel'nica $Z_{14} = \sqrt{10}r^4 \cos 4\theta$ Z14

15 4 2 Pepel'nica $Z_{15} = \sqrt{10}r^4 \sin 4\theta$ Z15

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Astrometriya - Astronomicheskie instrumenty - Astronomicheskoe obrazovanie - Astrofizika - Istoriya astronomii - Kosmonavtika, issledovanie kosmosa - Lyubitel'skaya astronomiya - Planety i Solnechnaya sistema - Solnce

j			Nazvanie	Formula	Izobrazhenie
1	0	0	Porshen'
2	1	1	Naklon	$Z_2 = 2r \cos \theta$
3	1	1	Naklon	$Z_3 = 2r \sin \theta$
4	2	0	Rasfokusirovka	$Z_4 = \sqrt{3} (2r^2 -1)$
5	2	2	Astigmatizm	$Z_5 = \sqrt{6}r^2 \sin 2 \theta$
6	2	2	Astigmatizm	$Z_6 = \sqrt{6}r^2 \cos 2 \theta$
7	3	1	Koma	$Z_7 = \sqrt{8} (3r^3-2r) \sin \theta$
8	3	1	Koma	$Z_8 = \sqrt{8} (3r^3-2r) \cos \theta$
9	3	3	Trilistnik	$Z_9 = \sqrt{8} 3r^3 \sin 3 \theta$
10	3	3	Trilistnik	$Z_{10} = \sqrt{8} 3r^3 \cos 3 \theta$
11	4	0	Sfericheskii	$Z_{11}=\sqrt{5} (6r^4 -6r^2 +1)$
12	4	2	Astigm. 5-go por.	$Z_{12} = \sqrt{10}( 10r^4 -3r^3) \cos 2\theta$
13	4	2	Astigm. 5-go por.	$Z_{13} = \sqrt{10}( 10r^4 -3r^3) \sin 2\theta$
14	4	2	Pepel'nica	$Z_{14} = \sqrt{10}r^4 \cos 4\theta$
15	4	2	Pepel'nica	$Z_{15} = \sqrt{10}r^4 \sin 4\theta$