Spherical aberration

Lore & Background

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. A spherical lens has an aplanatic point only at a lateral distance from the optical axis that equals the radius of the spherical surface divided by the index of refraction of the lens material. Spherical aberration makes the focus of telescopes and other instruments less than ideal, an important effect because spherical shapes are much easier to produce than aspherical ones.

Reader's Guide

Spherical aberration is a fundamental concern in optical design, as it limits the sharpness of images formed by lenses and mirrors with spherical surfaces. Its significance stems from the trade-off between manufacturing ease and optical performance: spherical surfaces are simpler and cheaper to produce, but they introduce focusing errors that become pronounced at short focal ratios, or 'fast' lenses. Correction methods include using combinations of convex and concave lenses, aspheric lenses, or aplanatic lenses, often designed through numerical ray tracing. For small telescopes with focal ratios shorter than f/10, spherical aberration prevents sharp focusing of light from distant point sources, necessitating non-spherical mirrors or correcting lenses. The effect is proportional to the fourth power of the diameter and inversely proportional to the third power of the focal length, making it especially critical in compact, high-aperture systems.

Did You Know?

• Spherical aberration was first identified in the 11th century by Ibn al-Haytham in his work Kitāb al-Manāẓir.
• A spherical lens has an aplanatic point only at a lateral distance from the optical axis equal to the radius divided by the refractive index.
• The effect is proportional to the fourth power of the diameter and inversely proportional to the third power of the focal length.