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A Ritchey–Chrétien telescope has hyperbolic primary and secondary mirrors chosen to cancel third-order spherical aberration and coma. It retains astigmatism and field curvature; wide-field instruments may require additional correction.

An underfocus setting that balances objective-lens spherical aberration against defocus to provide a broad first phase-contrast band for a weak phase object. A common approximate convention is $\Delta f_S\simeq -1.2\sqrt{C_S\lambda }$ for positive $C_S$; numerical optimization conventions differ slightly.

A Schmidt camera combines a spherical primary mirror with a thin aspheric corrector at the mirror’s centre of curvature. The corrector compensates spherical aberration; the symmetric stop location gives a wide useful field. The native focal surface is curved and lies inside the instrument.

The five Seidel aberrations of a rotationally symmetric optical system are spherical aberration, coma, astigmatism, field curvature, and optical distortion.

The unnormalized rotationally symmetric mode is $Z_4^0(\rho )=6{\rho }^4-6{\rho }^2+1$. It describes balanced primary spherical aberration. The lower-degree terms make it orthogonal to constant piston and quadratic defocus under the disk area measure: direct integration gives ${\int }_0^1{Z}_4^0\rho d\rho =0$ and ${\int }_0^1{Z}_4^0(2{\rho }^2-1)\rho d\rho =0$.