Editing Lens (section)

== Aberrations ==
{{Optical aberration}}
{{Main|Optical aberration}}

Lenses do not form perfect images, and always introduce some degree of distortion or ''aberration'' that makes the image an imperfect replica of the object. Careful design of the lens system for a particular application minimizes the aberration. Several types of aberration affect image quality, including spherical aberration, coma, and chromatic aberration.

=== Spherical aberration ===
{{Main|Spherical aberration}}

''Spherical aberration'' occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be [[Fabrication and testing of optical components|ground and polished]], and so are often used. Spherical aberration causes beams parallel to, but laterally distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Spherical aberration can be minimised with normal lens shapes by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

[[File:lens5.svg|frameless]]

=== Coma ===
{{Main|Coma (optics)}}

''Coma'', or ''comatic aberration'', derives its name from the [[comet]]-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis {{mvar|θ}}. Rays that pass through the centre of a lens of focal length {{mvar|f}} are focused at a point with distance {{math|''f'' [[Tangent function|tan]] ''θ''}} from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a ''comatic circle'' (see each circle of the image in the below figure). The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called ''bestform'' lenses.

[[File:lens-coma.svg|frameless]]

=== Chromatic aberration ===
{{Main|Chromatic aberration}}

''Chromatic aberration'' is caused by the [[dispersion (optics)|dispersion]] of the lens material—the variation of its [[refractive index]], {{mvar|n}}, with the wavelength of light. Since, from [[#Lensmaker's equation|the formulae above]], {{mvar|f}} is dependent upon {{mvar|n}}, it follows that light of different wavelengths is focused to different positions. Chromatic aberration of a lens is seen as fringes of colour around the image. It can be minimised by using an [[Achromatic lens|achromatic doublet]] (or ''achromat'') in which two materials with differing dispersion are bonded together to form a single lens. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. The use of achromats was an important step in the development of the optical microscope. An [[apochromat]] is a lens or lens system with even better chromatic aberration correction, combined with improved spherical aberration correction. Apochromats are much more expensive than achromats.

Different lens materials may also be used to minimise chromatic aberration, such as specialised coatings or lenses made from the crystal [[fluorite]]. This naturally occurring substance has the highest known [[Abbe number]], indicating that the material has low dispersion.

[[File:Chromatic aberration lens diagram.svg|frameless]]
[[File:Lens6b-en.svg|frameless]]

=== Other types of aberration ===
Other kinds of aberration include ''[[field curvature]]'', [[Distortion (optics)|''barrel ''and ''pincushion distortion'']], and ''[[Astigmatism (optical systems)|astigmatism]]''.

=== Aperture diffraction ===
Even if a lens is designed to minimize or eliminate the aberrations described above, the image quality is still limited by the [[diffraction]] of light passing through the lens' finite [[aperture]]. A [[diffraction-limited]] lens is one in which aberrations have been reduced to the point where the image quality is primarily limited by diffraction under the design conditions.