Spherical aberration

This phenomenon commonly affects lenses and curved mirrors, as these components are often shaped in a spherical manner for ease of manufacturing.

The effect of spherical aberration was first identified in the 11th century by Ibn al-Haytham who discussed it in his work Kitāb al-Manāẓir.

Lens systems with aberration correction are usually designed by numerical ray tracing.

Because of spherical aberration, telescopes with focal ratio less than f/10 are usually made with non-spherical mirrors or with correcting lenses.

[2] In 2018, Rafael G. González-Acuña and Héctor A. Chaparro-Romo, graduate students at the National Autonomous University of Mexico and the Monterrey Institute of Technology and Higher Education in Mexico, found a closed formula for a lens surface that eliminates spherical aberration.

Many ways to estimate the diameter of the focused spot due to spherical aberration are based on ray optics.

Therefore, the results can be wrong due to interference effects arisen from the wave nature of light.

A rather simple formalism based on ray optics, which holds for thin lenses only, is the Coddington notation.

On top is a depiction of a perfect lens without spherical aberration: all incoming rays are focused in the focal point .
The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration: The different rays do not meet after the lens in one focal point. The further the rays are from the optical axis , the closer to the lens they intersect the optical axis (positive spherical aberration).
(Drawing is exaggerated.)
Spherical aberration of collimated light incident on a concave spherical mirror .
Longitudinal sections through a focused beam with negative (top row), zero (middle row), and positive spherical aberration (bottom row). The lens is to the left.
A point source as imaged by a system with negative (top row), zero (middle row), and positive spherical aberration (bottom row). The middle column shows the focused image, columns to the left show defocusing toward the inside, and columns to the right show defocusing toward the outside.