# Spherical aberration

Spherical aberration is a defect in spherical mirrors and some lenses and eyepieces that causes parallel rays of light incident on the element at different distances from the optical axis to focus at different points along the axis. This deviation reduces the quality of images produced by optical systems.

There is no place where all the rays come to a single focus and produce a sharp image. Spherical aberration can be reduced by narrowing the lens so that rays do not pass through the edges, and by combining lenses to compensate for the defects in each type of lens.

It occurs in optical systems with rotational symmetry (spherical mirrors, simple lenses, etc.) and is due to the fact that, if the system is divided into many circular zones, cones of light rays emerge from them, converging at different points on the optical axis, which, if the object is placed at infinity, coincide with as many foci of the system. Of these, the focus for the rays coming from the zone closest to the axis (paraxial zone) is called the paraxial focus, and that for the zone farthest from the axis (marginal zone) is called the marginal focus.

The set of rays coming from the optical system encloses a rotationally rugged surface called the caustic. If the marginal focus is closer to the system than the paraxial focus, the system is said to be undercorrected, otherwise it is said to be overcorrected. The distance between these two focal points, called the stick, is a measure of spherical aberration (longitudinal aberration or aperture aberration, since it depends on the aperture diameter of the system). Then, if the beam leaving the optical system is cut by a screen perpendicular to the axis, a circle is observed on the screen whose radius is minimum for an intermediate position between the two foci. The radius of this circle (circle of least confusion) is a measure of the so-called transverse spherical aberration.

Spherical aberration, which is present in virtually all optical systems except plane and parabolic mirrors, can be partially corrected in spherical mirrors by interposing in the path of the rays a plano-convex lens (Schmidt foil), which tends to compensate for the aberration of the mirror itself. To minimize the effects of spherical aberration, the optical system affected by it can always be properly diaphragmed. A system in which spherical aberration has been corrected is called aplanatic.

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