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| {{refimprove|date=August 2006}}
| | Name: Lindsay Brentnall<br>My age: 25<br>Country: Brazil<br>Home town: Cuiaba <br>Post code: 78075-610<br>Street: Via Principal 1 638<br><br>My weblog; [http://hemorrhoidtreatmentfix.com/hemorrhoid-symptoms symptoms of hemorrhoids] |
| {{Optical aberration}}
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| :''Not to be confused with [[barrel distortion]], in which the image appears to be warped onto a sphere.'' | |
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| '''Spherical aberration''' is an optical effect observed in an [[optical device]] ([[lens (optics)|lens]], [[mirror]], etc.) that occurs due to the increased [[refraction]] of light rays when they strike a lens or a [[Reflection (physics)|reflection]] 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.
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| [[image:Spherical aberration 2.svg|thumb|center|300px|On top is a depiction of a perfect lens without spherical aberration: all incoming rays are focused in the [[Focus (optics)|focal point]].<br/><br/>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).<br/><br/>(Drawing is exaggerated.)]]
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| [[Image:Caustic of a circle 2.svg|thumb|right|150px|Spherical aberration of [[collimated light]] incident on a concave [[spherical mirror]].]]
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| A spherical lens has an [[Optical aberration#Aberration of elements, i.e. smallest objects at right angles to the axis|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 of refractive indices|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]]s and other instruments which makes their [[Focus (optics)|focusing]] less than ideal due to the [[sphere|spherical]] shape of lenses and mirrors. This is an important effect, because spherical shapes are much easier to produce than aspherical ones. In many cases, it is cheaper to use multiple spherical elements to compensate for spherical aberration than it is to use a single aspheric lens.
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| "Positive" spherical aberration means peripheral rays are bent too much. "Negative" spherical aberration means peripheral rays are not bent enough.
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| 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 ratio]]s, i.e., "fast" lenses.
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| [[image:spherical-aberration-slice.jpg|thumb|center|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.]]
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| In lens systems, the effect can be minimized using special combinations of [[Lens (optics)#Types of simple lenses|convex]] and [[Lens (optics)#Types of simple lenses|concave lenses]], as well as using [[aspheric lens]]es.
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| 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 <math>R_1</math> and <math>R_2</math> of the front and back surfaces of the lens such that
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| :<math>\frac{R_1+R_2}{R_1-R_2}=\frac{2 \left( n^2-1 \right)}{n+2}\left( \frac{i+o}{i-o}\right)</math> . | |
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| {{-}}
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| [[image:spherical-aberration-disk.jpg|thumb|300 px|center|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 shows defocusing toward the inside, and columns to the right show defocusing toward the outside.]]
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| For small telescopes using spherical mirrors with [[focal ratio]]s shorter than f/10, light from a distant point source (such as a [[star]]) 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.
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| ==See also==
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| *[[Aspheric lens]]
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| *[[Aberration in optical systems]]
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| *[[Cartesian oval]]
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| *[[Hubble Space Telescope]]
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| *[[Maksutov telescope]]
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| *[[Parabolic reflector]]
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| *[[Ritchey-Chrétien telescope]]
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| *[[Schmidt corrector plate]]
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| *[[Soft focus]]
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| ==External links==
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| * ''[http://toothwalker.org/optics/spherical.html Spherical aberration]'' at ''vanwalree.com'', PA van Walree, viewed 28 January 2007.
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| * http://www.telescope-optics.net/spherical1.htm
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| [[Category:Optics]]
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| [[Category:Geometrical optics]]
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| [[de:Abbildungsfehler#Sphärische Aberration]]
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Name: Lindsay Brentnall
My age: 25
Country: Brazil
Home town: Cuiaba
Post code: 78075-610
Street: Via Principal 1 638
My weblog; symptoms of hemorrhoids