Seidel aberrations

Definition

Consider an optical system that is rotationally symmetric about its axis. Let $h$ be the normalised height of the object point above the axis. Let $(\rho, \theta)$ be normalised polar coordinates in the exit pupil, with $\theta$ measured from the direction of $h$. By the symmetry, the wave aberration $W$ is a function of $h^2$, $\rho^2$ and $h \rho \cos\theta$, and it has an expansion $$W = \sum W_{klm} \, h^k \rho^l \cos^m \theta .$$ The terms of total degree $k + l = 4$ are the primary or Seidel aberrations:

1. spherical aberration $W_{040} \rho^4$;
2. coma $W_{131} h \rho^3 \cos\theta$;
3. astigmatism $W_{222} h^2 \rho^2 \cos^2\theta$;
4. field curvature $W_{220} h^2 \rho^2$;
5. distortion $W_{311} h^3 \rho \cos\theta$.