Aspheric lens
An aspheric lens or asphere is a 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...

 whose surface profiles are not portions of a 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...

 or cylinder
Cylinder (geometry)
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...

. In photography
Photography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...

, a lens assembly that includes an aspheric element is often called an aspherical lens.

The asphere's more complex surface profile can reduce or eliminate spherical aberration
Spherical aberration
thumb|right|Spherical aberration. A perfect lens focuses all incoming rays to a point on the [[Optical axis|optic axis]]. A real lens with spherical surfaces suffers from spherical aberration: it focuses rays more tightly if they enter it far from the optic axis than if they enter closer to the...

 and also reduce other optical aberrations
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...

 compared to a simple lens
Simple lens
In optics, a simple lens or singlet lens is a lens consisting of a single simple element. Typical examples include a magnifying glass or a lens in a pair of simple reading glasses....

. A single aspheric lens can often replace a much more complex multi-lens system. The resulting device is smaller and lighter, and possibly cheaper than the multi-lens design. Aspheric elements are used in the design of multi-element wide-angle
Wide-angle lens
From a design perspective, a wide angle lens is one that projects a substantially larger image circle than would be typical for a standard design lens of the same focal length; this enables either large tilt & shift movements with a view camera, or lenses with wide fields of view.More informally,...

 and fast normal lens
Normal lens
In photography and cinematography a normal lens, also called a standard lens, is a lens that reproduces perspective that generally looks "natural" to a human observer under normal viewing conditions, as compared with lenses with longer or shorter focal lengths which produce an expanded or...

es to reduce aberrations. They are also used in combination with reflective elements (catadioptric systems) such as the aspherical 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...

 used in the Schmidt camera
Schmidt camera
A Schmidt camera, also referred to as the Schmidt telescope, is a catadioptric astrophotographic telescope designed to provide wide fields of view with limited aberrations. Other similar designs are the Wright Camera and Lurie-Houghton telescope....

s and the Schmidt-Cassegrain telescope
Schmidt-Cassegrain telescope
The Schmidt–Cassegrain is a catadioptric telescope that combines a cassegrain reflector's optical path with a Schmidt corrector plate to make a compact astronomical instrument that uses simple spherical surfaces.-Invention and design:...


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. 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.

Surface profile

While in principle aspheric surfaces can take a wide variety of forms, aspheric lenses are often designed with surfaces of the form
where the optic axis is presumed to lie in the z direction, and is the sag—the z-component of the displacement
Displacement (vector)
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P...

 of the surface from the vertex, at distance from the axis. The coefficients describe the deviation of the surface from the axially symmetric
Axial symmetry
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis . For example, a baseball bat or a tea saucer looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially...

 quadric surface specified by and .

If the coefficients are all zero, then is the radius of curvature and is the conic constant
Conic constant
In geometry, the conic constant is a quantity describing conic sections, and is represented by the letter K...

, as measured at the vertex (where ). In this case, the surface has the form of a conic section
Conic section
In mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...

 rotated about the optic axis, with form determined by :
Conic section
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...

In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

 (surface is a prolate spheroid
Prolate spheroid
A prolate spheroid is a spheroid in which the polar axis is greater than the equatorial diameter. Prolate spheroids stand in contrast to oblate spheroids...

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...

ellipse (surface is an oblate spheroid)


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
A camera is a device that records and stores images. These images may be still photographs or moving images such as videos or movies. The term camera comes from the camera obscura , an early mechanism for projecting images...

s, camera phones, and CD players. They are also commonly used for laser diode
Laser diode
The laser diode is a laser where the active medium is a semiconductor similar to that found in a light-emitting diode. The most common type of laser diode is formed from a p-n junction and powered by injected electric current...

 collimation, and for coupling light into and out of optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...


Larger aspheres are made by grinding and polishing. Lenses produced by these techniques are used in 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, projection TVs, missile guidance systems, and scientific research instruments. They can be made by point-contact contouring to roughly the right form 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.

Single-point diamond turning
Diamond turning
Diamond turning is a process of mechanical machining of precision elements using lathes or derivative machine tools equipped with natural or synthetic diamond-tipped tool bits...

 is an alternate process, in which a computer-controlled 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. It is particularly useful for infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...


Several "finishing" methods can be used to improve the precision and surface quality of the polished surface. These include ion-beam
Ion beam
An ion beam is a type of charged particle beam consisting of ions. Ion beams have many uses in electronics manufacturing and other industries. A variety of ion beam sources exist, some derived from the mercury vapor thrusters developed by NASA in the 1960s.-Ion beam etching or sputtering:One type...

 finishing, abrasive water jet
Jet (fluid)
A jet is an efflux of fluid that is projected into a surrounding medium, usually from some kind of a nozzle, aperture or orifice. Jets can travel long distances without dissipating...

s, and magnetorheological finishing
Magnetorheological Finishing
Magnetorheological finishing is a precision surface finishing technology. Optical surfaces are polished in a computer-controlled magnetorheological finishing slurry. Unlike conventional rigid lap polishing, the MR fluid's shape and stiffness can be magnetically manipulated and controlled in real...

, in which a magnetically guided fluid jet is used to remove material from the surface.

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.

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
CR-39, or allyl diglycol carbonate , is a plastic polymer commonly used in the manufacture of eyeglass lenses. The abbreviation stands for “Columbia Resin #39,” because it was the 39th formula of a thermosetting plastic developed by the Columbia Resins project in 1940.The first commercial use of...

 resin lens is. Techniques such as laser ablation
Laser ablation
Laser ablation is the process of removing material from a solid surface by irradiating it with a laser beam. At low laser flux, the material is heated by the absorbed laser energy and evaporates or sublimates. At high laser flux, the material is typically converted to a plasma...

 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
A lapidary is an artist or artisan who forms stone, mineral, gemstones, and other suitably durable materials into decorative items such as engraved gems, including cameos, or cabochons, and faceted designs...


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
Bifocals are eyeglasses with two distinct optical powers. Bifocals are most commonly prescribed to people with presbyopia who also require a correction for myopia, hyperopia, and/or astigmatism.-History:...

, trifocals, vari-focals, and cylindrical components for astigmatism
Astigmatism (eye)
Astigmatism is an optical defect in which vision is blurred due to the inability of the optics of the eye to focus a point object into a sharp focused image on the retina. This may be due to an irregular or toric curvature of the cornea or lens. There are two types of astigmatism: regular and...


Ophthalmic uses

Like other lenses for vision correction
Corrective lens
A corrective lens is a lens worn in front of the eye, mainly used to treat myopia, hyperopia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye...

, aspheric lenses can be categorized as convex or concave.

Convex aspheric curvatures are used in many presbyopic
Presbyopia is a condition where the eye exhibits a progressively diminished ability to focus on near objects with age. Presbyopia’s exact mechanisms are not known with certainty; the research evidence most strongly supports a loss of elasticity of the crystalline lens, although changes in the...

 vari-focal lenses to increase the optical power
Optical power
Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of 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
Aphakia is the absence of the lens of the eye, due to surgical removal, a perforating wound or ulcer, or congenital anomaly. It causes a loss of accommodation, hyperopia, and a deep anterior chamber. Complications include detachment of the vitreous or retina, and glaucoma.Aphakic people are...

 or extreme hyperopia
Hyperopia, also known as farsightedness, longsightedness or hypermetropia, is a defect of vision caused by an imperfection in the eye , causing difficulty focusing on near objects, and in extreme cases causing a sufferer to be unable to focus on objects at any distance...

, high plus power aspheric lenses can be prescribed, but this practice is becoming obsolete, replaced by surgical implants of intra-ocular lenses. Many convex types of lens have been approved by governing agencies regulating prescriptions.

Concave aspheres are used for the correction of high myopia
Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...

. 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.

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
The vertebrate retina is a light-sensitive tissue lining the inner surface of the eye. The optics of the eye create an image of the visual world on the retina, which serves much the same function as the film in a camera. Light striking the retina initiates a cascade of chemical and electrical...

. 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.

In prescriptions for both farsightedness
Hyperopia, also known as farsightedness, longsightedness or hypermetropia, is a defect of vision caused by an imperfection in the eye , causing difficulty focusing on near objects, and in extreme cases causing a sufferer to be unable to focus on objects at any distance...

 and nearsightedness
Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...

, the lens curve flattens toward the edge of the glass, except for progressive reading adds for presbyopia
Presbyopia is a condition where the eye exhibits a progressively diminished ability to focus on near objects with age. Presbyopia’s exact mechanisms are not known with certainty; the research evidence most strongly supports a loss of elasticity of the crystalline lens, although changes in the...

, 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 scotoma is an area of partial alteration in one's field of vision consisting of a partially diminished or entirely degenerated visual acuity which is surrounded by a field of normal - or relatively well-preserved - vision.Every normal mammalian eye has a scotoma in its field of vision, usually...

, a ringed blind spot
Blind spot
Blind spot may refer to:In ophthalmology:*Scotoma, an obscuration of the visual field*Optic disc, also known as the anatomical blind spot, the specific region of the retina where the optic nerve and blood vessels pass through to connect to the back of the eye*Blind spot , also known as the...


Non-optical advantages

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.
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.


In 984
Year 984 was a leap year starting on Tuesday of the Julian calendar.- Asia :* Emperor Kazan succeeds Emperor En'yū on the throne of Japan....

, Ibn Sahl
Ibn Sahl
This article is about the physicist. For the physician, see Ali ibn Sahl Rabban al-Tabari. For the poet, see Ibn Sahl of Sevilla.Ibn Sahl was a Muslim Persian mathematician, physicist and optics engineer of the Islamic Golden Age associated with the Abbasid court of Baghdad...

 first discovered the law of 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...

, usually called Snell's law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

, which he used to work out the shapes of anaclastic lenses that focus light with no geometric aberrations.

Early attempts at making aspheric lenses to correct spherical aberration were made by René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

 in the 1620s, and by Constantijn Huygens
Constantijn Huygens
Constantijn Huygens , was a Dutch Golden Age poet and composer. He was secretary to two Princes of Orange: Frederick Henry and William II, and the father of the scientist Christiaan Huygens.-Biography:...

 in the 1630s; the cross-section of the shape devised by Descartes for this purpose is known as a 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...

. The Visby lenses
Visby lenses
The Visby lenses are a collection of lens-shaped manufactured objects made of rock crystal found in several Viking graves on the island of Gotland, Sweden, dating from the 11th or 12th century...

 produced by Vikings on the island of Gotland
Gotland is a county, province, municipality and diocese of Sweden; it is Sweden's largest island and the largest island in the Baltic Sea. At 3,140 square kilometers in area, the region makes up less than one percent of Sweden's total land area...

 in the 10th or 11th century are also aspheric, but there is no evidence that the science behind the technique was known, they were 'simply' produced by craftsmen working from experience of what worked.

Francis Smethwick ground the first high-quality aspheric lenses and presented them to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

 on February 27, 1667/8
Old Style and New Style dates
Old Style and New Style are used in English language historical studies either to indicate that the start of the Julian year has been adjusted to start on 1 January even though documents written at the time use a different start of year ; or to indicate that a date conforms to the Julian...

. A telescope containing three aspheric elements was judged superior to a "common, yet very good" telescope used for comparison, and aspheric reading and burning glasses also outdid their spherical equivalents.

Moritz von Rohr
Moritz von Rohr
Moritz von Rohr was an optical scientist at Carl Zeiss in Jena.A street in Jena is named after him: Moritz-von-Rohr-Straße, near Carl-Zeiss-Promenade and Otto-Schott-Straße, reminders of the proud optical heritage of the city.-Life:...

 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.

The world's first commercial, mass produced aspheric lens element was manufactured by Elgeet for use in the Golden Navitar
Founded1973 TypePrivateHeadquartersRochester, New YorkKey PeopleCo-President:Jeremy Goldstein,Co-President: Julian GoldsteinIndustrySemiconductor, Biotechnology, Homeland Security, Food & Beverage, Metrology, Simulation, Presentation Products...

12mm f1.2 wide angle lens for use on 16mm 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.

Testing of aspheric lens systems

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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