Spherical aberration
Encyclopedia
Not be confused with barrel distortion
Barrel distortion
In geometric optics and cathode ray tube displays, distortion is a deviation from rectilinear projection, a projection in which straight lines in a scene remain straight in an image...

, in which the image appears to be warped onto a sphere.

Spherical aberration is an optical effect observed in an optical device (lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

, mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

, etc.) that occurs due to the increased refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

of light rays when they strike a lens or a reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

of light rays when they strike a mirror near its edge, in comparison with those that strike nearer the centre. It signifies a deviation of the device from the norm, i.e., it results in an imperfection of the produced image.

A sphere lens has an aplanatic point (i.e., no spherical aberration) only at a radius that equals the radius of the sphere divided by the index of refraction of the lens material. A typical value of refractive index for crown glass is 1.5, (See list) which indicates that only about 43% of the area (67% of diameter) of a spherical lens is useful. It is often considered to be an imperfection of telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

s and other instruments which makes their focusing
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...

less than ideal due to the spherical
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

shape of lenses and mirrors. This is an important effect, because spherical shapes are much easier to produce than the perfect aspherical profile and so most lenses have spherical shapes. So great is the difference in cost of manufacture that for most mass-produced lens systems, the cost of design and multiple spherical elements is often less than simpler designs that include aspheric lenses.

"Positive" spherical aberration means peripheral rays are bent too much. "Negative" spherical aberration means peripheral rays are not bent enough.

The effect is proportional to the fourth power of the diameter and inversely proportional to the third power of the focal length, so it is much more pronounced at short focal ratios, i.e., "fast" lenses.

For small telescopes using spherical mirrors with focal ratios shorter than f/10, light from a distant point source (such as a star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

) is not all focused at the same point. Particularly, light striking the inner part of the mirror focuses farther from the mirror than light striking the outer part. As a result the image cannot be focused as sharply as if the aberration were not present. Because of spherical aberration, telescopes shorter than f/10 are usually made with non-spherical mirrors or with correcting lenses.

In lens systems, the effect can be minimized using special combinations of convex and concave lenses, as well as using aspheric lens
Aspheric lens
An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens....

es.

For simple designs one can sometimes calculate parameters that minimize spherical aberration. For example, in a design consisting of a single lens with spherical surfaces and a given object distance o, image distance i, and refractive index n, one can minimize spherical aberration by adjusting the radii of curvature and of the front and back surfaces of the lens such that .

• Aspheric lens
Aspheric lens
An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens....

• Aberration in optical systems
Aberration in optical systems
Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge...

• Cartesian oval
Cartesian oval
In geometry, a Cartesian oval, named after René Descartes, is determined as follows. Let and be fixed points in the plane, and let and denote the Euclidean distances from these points to a third variable point . Let and be arbitrary real numbers. Then the Cartesian oval is the locus of...

• Hubble Space Telescope
Hubble Space Telescope
The Hubble Space Telescope is a space telescope that was carried into orbit by a Space Shuttle in 1990 and remains in operation. A 2.4 meter aperture telescope in low Earth orbit, Hubble's four main instruments observe in the near ultraviolet, visible, and near infrared...

• Maksutov telescope
Maksutov telescope
The Maksutov is a catadioptric telescope design that combines a spherical mirror with a weakly negative meniscus lens in a design that takes advantage of all the surfaces being nearly "spherically symmetrical". The negative lens is usually full diameter and placed at the entrance pupil of the...

• Parabolic reflector
Parabolic reflector
A parabolic reflector is a reflective device used to collect or project energy such as light, sound, or radio waves. Its shape is that of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis...

• Ritchey-Chrétien telescope
Ritchey-Chrétien telescope
A Ritchey–Chrétien telescope is a specialized Cassegrain telescope designed to eliminate coma, thus providing a large field of view compared to a more conventional configuration. An RCT has a hyperbolic primary and a hyperbolic secondary mirror. It was invented in the early 1910s by American...

• Schmidt corrector plate
Schmidt corrector plate
A Schmidt corrector plate is an aspheric lens which is designed to correct the spherical aberration in the spherical primary mirror it is combined with. It was invented by Bernhard Schmidt in 1931, although it may have been independently invented by Finnish astronomer Yrjö Väisälä in 1924...

• Soft focus
Soft focus
In photography, soft focus is a lens flaw, in which the lens forms images that are blurred due to spherical aberration. A soft focus lens deliberately introduces spherical aberration in order to give the appearance of blurring the image while retaining sharp edges; it is not the same as an...