Open Access
Table A.1
Low-order Zernike circle polynomials and their correspondent name in aberrations.
| n | 𝓁 | Polynomial  |
Name |
|---|---|---|---|
| 0 | 0 | 1 | Piston |
| 1 | –1 | ϱ sin ϑ | y-tilt |
| 1 | 1 | ϱ COS ϑ | x-tilt |
| 2 | –2 | ϱ2 sin 2ϑ | 45° primary astigmatism |
| 2 | 0 | (2ϱ2 – 1) | Defocus |
| 2 | 2 | ϱ2 COS 2ϑ | 0° primary astigmatism |
| 3 | –3 | ϱ3 sin 3ϑ | |
| 3 | –1 | (3ϱ3 – 2ϱ) sin ϑ | Primary y-coma |
| 3 | 1 | (3ϱ3 – 2ϱ) COS ϑ | Primary x-coma |
| 3 | 3 | ϱ3 COS 3ϑ | |
| 4 | –4 | ϱ4 COS 4ϑ | |
| 4 | –2 | (4ϱ4–3ρ2)sin 2ϑ | 45° secondary astigmatism |
| 4 | 0 | (6ϱ4 – 6ϱ2 + 1) | Primary spherical |
| 4 | 2 | (4ϱ4 – 3ϱ2)cos 2ϑ | 0° secondary astigmatism |
| 4 | 4 | ϱ4 COS 4ϑ | |
| 5 | –5 | ϱ5 sin 5ϑ | |
| 5 | –3 | (5ϱ5 – 4ϱ3) sin 3ϑ | |
| 5 | -1 | (10ϱ5 – 12ϱ3 + 3ϱ)sin ϱ | Secondary y-coma |
| 5 | 1 | (10ϱ5 – 12ϱ3 + 3ϱ)cos ϱ | Secondary x-coma |
| 5 | 3 | (5ϱ5 – 4ϱ3) cos 3ϑ | |
| 5 | 5 | ϱ5 COS 5ϑ |
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