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| [[File:Pfeilhöhe.svg|thumb|right|upright|An aspheric biconvex lens.]]
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| An '''aspheric lens''' or '''asphere''' is a [[lens (optics)|lens]] whose surface profiles are not portions of a [[sphere]] or [[Cylinder (geometry)|cylinder]]. In [[photography]], a lens assembly that includes an aspheric element is often called an '''aspherical lens'''.
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| The asphere's more complex surface profile can reduce or eliminate [[spherical aberration]] and also reduce other [[Aberration in optical systems|optical aberrations]] compared to a [[simple lens]]. A single aspheric lens can often replace a much more complex multi-lens system. The resulting device is smaller and lighter, and sometimes cheaper than the multi-lens design.<ref name=looklens>{{cite web |url=http://www.looklens.com/camera-lens-tips/what-do-aspheric-or-aspherical-mean-3.html |title=What do "aspheric" or "aspherical" mean? |publisher=Fuzhou Looklens Optics |accessdate=June 15, 2012}}</ref> Aspheric elements are used in the design of multi-element [[wide-angle lens|wide-angle]] and fast [[normal lens]]es to reduce aberrations. They are also used in combination with reflective elements ([[catadioptric system]]s) such as the aspherical [[Schmidt corrector plate]] used in the [[Schmidt camera]]s and the [[Schmidt-Cassegrain telescope]]s. Small molded aspheres are often used for [[collimated light|collimating]] [[diode laser]]s.
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| Aspheric lenses are also sometimes used for [[eyeglasses]]. These are typically designed to give a thinner lens, and also distort the viewer's eyes less as seen by other people, producing better aesthetic appearance.<ref name=opticampus>{{Cite web|url=http://www.opticampus.com/cecourse.php?url=lens_design/&OPTICAMP=f1e4252df70c63961503c46d0c8d8b60#asphericity |title=Ophthalmic Lens Design |first=Darryl |last=Meister |work=OptiCampus.com}}</ref> Aspheric eyeglass lenses typically do not provide better vision than standard "best form" lenses, but rather allow a thinner, flatter lens to be made without compromising the optical performance.<ref name=opticampus/>
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| ==Surface profile==
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| While in principle aspheric surfaces can take a wide variety of forms, aspheric lenses are often designed with surfaces of the form
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| :<math>z(r)=\frac{r^2}{R\left (1+\sqrt{1-(1+\kappa)\frac{r^2}{R^2}}\right )}+\alpha_1 r^2+\alpha_2 r^4+\alpha_3 r^6+\cdots ,</math> <ref name=Pruss>{{Cite journal|title=Testing aspheres |journal =Optics & Photonics News |date=April 2008 |volume=19 |issue=4 |page=26 |first=Christof |last=Pruss |coauthors=et al.|bibcode = 2008OptPN..19...26H |doi = 10.1364/OPN.19.4.000026 }}</ref>
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| where the [[optic axis]] is presumed to lie in the '''z''' direction, and <math>z(r)</math> is the ''sag''—the z-component of the [[Displacement (vector)|displacement]] of the surface from the [[Vertex (optics)|vertex]], at distance <math>r</math> from the axis. The coefficients <math>\alpha_i</math> describe the deviation of the surface from the [[axial symmetry|axially symmetric]] [[quadric surface]] specified by <math>R</math> and <math>\kappa</math>.
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| If the coefficients <math>\alpha_i</math> are all zero, then <math>R</math> is the ''radius of curvature'' and <math>\kappa</math> is the [[conic constant]], as measured at the vertex (where <math>r=0</math>). In this case, the surface has the form of a [[conic section]] rotated about the optic axis, with form determined by <math>\kappa</math>:
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| :{| class="wikitable"
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| ! <math>\kappa</math> !! Conic section
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| | <math>\kappa < -1</math> || [[hyperbola]]
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| | <math>\kappa = -1</math> || [[parabola]]
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| | <math>-1 < \kappa < 0</math> || [[ellipse]] (surface is a [[prolate spheroid]])
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| | <math>\kappa = 0</math> || [[sphere]]
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| | <math>\kappa > 0</math> || ellipse (surface is an [[oblate spheroid]])
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| |}
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| ==Manufacture==
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| [[File:Schema lame de Schmidt.svg|thumb|Cross section of the [[Schmidt corrector plate]], a common aspheric lens]]
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| Small glass or plastic aspheric lenses can be made by molding, which allows cheap mass production. Due to their low cost and good performance, molded aspheres are commonly used in inexpensive consumer [[camera]]s, camera phones, and CD players.<ref name=looklens/> They are also commonly used for [[laser diode]] collimation, and for coupling light into and out of [[optical fiber]]s.
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| Larger aspheres are made by [[Fabrication and testing of optical components|grinding and polishing]]. Lenses produced by these techniques are used in [[telescope]]s, [[projection TV]]s, [[missile guidance system]]s, and scientific research instruments. They can be made by point-contact contouring to roughly the right form<ref name=OPN>{{Cite journal|title=Surface finishing of complex optics |first=Aric B. |last=Shorey |coauthors=Golini, Don; Kordonski, William |journal=Optics and Photonics News |publisher=Optical Society of America |volume=18 |issue=10 |date = October 2007|pages=14–16}}</ref> which is then polished to its final shape. In other designs, such as the Schmidt systems, the aspheric corrector plate can be made by using a vacuum to distort an optically parallel plate into a curve which is then polished "flat" on one side. Aspheric surfaces can also be made by polishing with a small tool with a compliant surface that conforms to the optic, although precise control of the surface form and quality is difficult, and the results may change as the tool wears.
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| Single-point [[diamond turning]] is an alternate process, in which a computer-controlled [[Lathe (tool)|lathe]] uses a diamond tip to directly cut the desired profile into a piece of glass or another optical material. Diamond turning is slow and has limitations in the materials on which it can be used, and the surface accuracy and smoothness that can be achieved.<ref name=OPN/> It is particularly useful for [[infrared]] optics.
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| Several "finishing" methods can be used to improve the precision and surface quality of the polished surface. These include [[ion beam|ion-beam]] finishing, abrasive water [[Jet (fluid)|jet]]s, and [[magnetorheological finishing]], in which a magnetically guided fluid jet is used to remove material from the surface.<ref name=OPN/>
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| Another method for producing aspheric lenses is by depositing optical resin onto a spherical lens to form a composite lens of aspherical shape. Plasma ablation has also been proposed.
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| [[File:Dualrotatingfloatingaxis.gif|thumb|300px|[[Lapping]] tool on a spindle below the lens, and mounting tool on a second spindle (swung out) uses [[Pitch (resin)|pitch]] to hold the lens shown with its concave side down]]
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| The non-spherical curvature of an aspheric lens can also be created by blending from a spherical into an aspherical curvature by grinding the curvatures off-axis. Dual rotating axis grinding can be used for high index glass that isn't easily spin molded, as the [[CR-39]] resin lens is. Techniques such as [[laser ablation]] can also be used to modify the curvature of a lens, but the polish quality of the resulting surfaces is not as good as those achieved with [[lapidary]] techniques.
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| Standards for the dispensing of prescription eyeglass lenses discourage the use of curvatures that deviate from definite focal lengths. Multiple focal lengths are accepted in the form of [[bifocals]], [[trifocals]], vari-focals, and cylindrical components for [[Astigmatism (eye)|astigmatism]].
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| ==Ophthalmic uses==
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| [[File:OpticTest.gif|thumb|Concave aspheres fitted in a [[Glasses|spectacle]] frame. The lenses' "minus" powers [[Magnification|minify]] the test pattern and bring it into better focus at the center of the lenses. Reflections from the non-aspheric anterior surfaces are also visible.]]
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| Like other [[corrective lens|lenses for vision correction]], aspheric lenses can be categorized as convex or concave.
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| Convex aspheric curvatures are used in many [[presbyopia|presbyopic]] [[Progressive lens|vari-focal lens]]es to increase the [[optical power]] over part of the lens, aiding in near-pointed tasks such as reading. The reading portion is an aspheric "progressive add". Also, in [[aphakia]] or extreme [[hyperopia]], high plus power aspheric lenses can be prescribed, but this practice is becoming obsolete, replaced by surgical implants of [[intra-ocular lens]]es. Many convex types of lens have been approved by governing agencies regulating prescriptions.
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| Concave aspheres are used for the correction of high [[myopia]]. They are not commercially available from optical dispensaries, but rather must be specially ordered with instructions from the fitting practitioner, much like how a prosthetic is customized for an individual.
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| The range of lens powers available to dispensing opticians for filling prescriptions, even in an aspheric form, is limited practically by the size of the image formed on the [[retina]]. High minus lenses cause an image so small that shape and form aren't discernible, generally at about -15 [[diopters]], while high plus lenses cause a tunnel of imagery so large that objects appear to pop in and out of a reduced field of view, generally at about +15 diopters.
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| In prescriptions for both [[hyperopia|farsightedness]] and [[myopia|nearsightedness]], the lens curve flattens toward the edge of the glass,<ref>{{Cite book|url=http://books.google.com/?id=Zl45vQkISCwC&pg=PA173&dq=dispensing+for+aphakia#PPA178,M1 |title=Ophthalmic Lenses and Dispensing |first=Mo |last=Jalie |publisher=Elsevier Health Sciences |year=2003 |isbn=0-7506-5526-7 |page=178}}</ref> except for progressive reading adds for [[presbyopia]], where seamless vari-focal portions change toward a progressively more plus [[diopter]]. High minus aspheres for myopes do not necessarily need progressive add portions, because the design of the lens curvature already progresses toward a less-minus/more-plus dioptric power from the center of the lens to the edge. High plus aspheres for hyperopes progress toward less-plus at the periphery. The aspheric curvature on high plus lenses are ground on the anterior side of the lens, whereas the aspheric curvature of high minus lenses are ground onto the posterior side of the lens. Progressive add reading portions for plus lenses are also ground onto the anterior surface of the lens. The blended curvature of aspheres reduces [[scotoma]], a ringed blind spot.
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| ===Non-optical advantages===
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| {{Unreferenced section|date=September 2011}}
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| High minus lenses, especially finished in a plastic resin lens, have dangerously curved edges that do not bevel off sufficiently to protect the eye from injury. Serious injury to the eye is often seen from blunt trauma, when the edge of a thick lens has been mounted in a poorly fitted frame.
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| Bi-concave lens design is different from the usual "best form" curvatures ordered in low power thin lens prescriptions, but by splitting the curvature in thirds or so, a thinner high minus lens is developed, although costing more, and more difficult to dispense.
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| ==History==
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| [[File:aspheric navitar elgeet.jpg|right|The Elgeet Golden Navitar 16mm Aspheric Wide Angle Lens shot and Advertisement from the 1950s.]]
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| In 984, [[Ibn Sahl]] first discovered the law of [[refraction]], usually called [[Snell's law]],<ref>K. B. Wolf, "Geometry and dynamics in refracting systems", ''European Journal of Physics'' '''16''', p. 14–20, 1995.</ref><ref name=rashed90>R. Rashed, "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses", ''[[Isis (journal)|Isis]]'' '''81''', p. 464–491, 1990.</ref>{{Verify source|date=September 2010}} which he used to work out the shapes of anaclastic lenses that focus light with no geometric aberrations.
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| Early attempts at making aspheric lenses to correct spherical aberration were made by [[René Descartes]] in the 1620s, and by [[Constantijn Huygens]] in the 1630s; the cross-section of the shape devised by Descartes for this purpose is known as a [[Cartesian oval]]. The [[Visby lenses]] found in Viking treasures on the island of [[Gotland]] dating from the 10th or 11th century are also aspheric, but exhibit a wide variety of image qualities, ranging from similar to modern aspherics in one case to worse than spheric lenses in others.<ref name=schmidt>{{cite journal | last = Schmidt | first = Olaf | authorlink = | coauthors = Karl-Heinz Wilms, Bernd Lingelbach | title = The Visby Lenses | journal = Optometry & Vision Science | volume = 76 | issue = 9 | pages = 624–630 | publisher = | location = | date = September 1999 | url = http://www.kleinesdorfinschleswigholstein.de/buerger/oschmi/visby/visbye.htm| issn = | doi = | id = | accessdate = }}</ref> The origin of the lenses is unknown, as is their purpose (they may have been made as jewelry rather than for imaging).<ref name=schmidt />
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| [[Francis Smethwick]] ground the first high-quality aspheric lenses and presented them to the [[Royal Society]] on February 27, [[Old Style and New Style dates|1667/8]].<ref name=Smethwick>{{Cite journal| year = 1668 ([[Old Style and New Style dates|NS]]) | title = An Account of the Invention of Grinding Optick and Burning-Glasses, of a Figure not-Spherical, produced before the Royal Society | journal = Philosophical Transactions of the Royal Society | volume = 3 | pages = 631–2 | url = http://archive.org/details/philtrans05653941 | format = PDF | accessdate=April 4, 2012 |doi=10.1098/rstl.1668.0005| issue = 33–44}}</ref> A telescope containing three aspheric elements was judged by those present "to exceed [a common, but very good telescope] in goodness, by taking in a greater Angle and representing the Objects more exactly in their respective proportions, and enduring a greater Aperture, free from Colours."<ref name=Smethwick /> Aspheric [[reading glasses|reading]] and [[burning glass]]es also outdid their spherical equivalents.<ref name=Smethwick />
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| [[Moritz von Rohr]] is usually credited with the design of the first aspheric lenses for eyeglasses. He invented the eyeglass lens designs that became the Zeiss Punktal lenses.
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| The world's first commercial, mass-produced aspheric lens element was manufactured by Elgeet for use in the Golden [[Navitar]] 12 mm {{f/|1.2}} wide angle lens for use on 16 mm movie cameras in 1956. This lens received a great deal of industry acclaim during its day. The aspheric elements were created by the use of a membrane polishing technique.{{Citation needed|date=September 2011}}
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| ==Testing of aspheric lens systems==
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| The optical quality of a lens system can be tested in an optics or physics laboratory using bench apertures, optic tubes, lenses, and a source. Refractive and reflective optical properties can be tabulated as a function of wavelength, to approximate system performances; tolerances and errors can also be evaluated. In addition to focal integrity, aspheric lens systems can be tested for aberrations before being deployed.
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| ==See also==
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| *[[Hyperbola]]
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| *[[Parabola]]
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| *[[Radius of curvature (optics)]]
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| ==References==
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| <references/>
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| {{DEFAULTSORT:Aspheric Lens}}
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| [[Category:Lenses]]
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