![Pfeilhöhe](https://upload.wikimedia.org/wikipedia/commons/4/43/Pfeilh%C3%B6he.svg)
An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a
lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
whose surface profiles are not portions of a
sphere
A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
or
cylinder
A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
A cylinder may also be defined as an infin ...
. In
photography
Photography is the art, application, and practice of creating durable images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film. It is employed ...
, 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
In optics, spherical aberration (SA) is a type of optical aberration, aberration found in optical systems that have elements with spherical surfaces. Lens (optics), Lenses and curved mirrors are prime examples, because this shape is easier to man ...
and also reduce other
optical aberrations
In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with th ...
such as
astigmatism
Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at nig ...
, compared to a
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.
Simple lenses are prone to aberrations, especially chromatic aberr ...
. 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.
Aspheric elements are used in the design of multi-element
wide-angle and fast
normal lens
In photography and cinematography, a normal lens is a lens that reproduces a field of view that appears "natural" to a human observer. In contrast, depth compression and expansion with shorter or longer focal lengths introduces noticeable, and som ...
es to reduce aberrations. They are also used in combination with reflective elements (
catadioptric system
A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, he ...
s) such as the aspherical
Schmidt corrector plate
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. The design was invented by Bernhard Schmidt in 1930.
Some notable e ...
used in the
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. The design was invented by Bernhard Schmidt in 1930.
Some notable exa ...
s and the
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
The A ...
s. Small molded aspheres are often used for
collimating
A collimated beam of light or other electromagnetic radiation has parallel ray (optics), rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no beam divergence, divergence, would not disperse with di ...
diode laser
The laser diode chip removed and placed on the eye of a needle for scale
A laser diode (LD, also injection laser diode or ILD, or diode laser) is a semiconductor device similar to a light-emitting diode in which a diode pumped directly with e ...
s.
Aspheric lenses are also sometimes used for
eyeglasses
Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples or ...
. Aspheric eyeglass lenses allow for crisper vision than standard "best form" lenses, mostly when looking in other directions than the lens optical center. Moreover, the reduction of the magnification effect of a lens may help with prescriptions that have different powers in the 2 eyes (
anisometropia
Anisometropia refers to a condition when two eyes have unequal refractive power. Generally, a difference in power of one diopter (1D) or more is the accepted threshold to label the condition anisometropia. Patients can tolerate 3 D of anisometro ...
). Not related to the optical quality, they may give a thinner lens, and also distort the viewer's eyes less as seen by other people, producing better aesthetic appearance.
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
An optical axis is a line along which there is some degree of rotational symmetry in an optics, optical system such as a camera lens, microscope or telescopic sight.
The optical axis is an imaginary line that defines the path along which light ...
is presumed to lie in the z direction, and
is the ''sag''—the z-component of the
displacement
Displacement may refer to:
Physical sciences
Mathematics and Physics
*Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
of the surface from the
vertex
Vertex, vertices or vertexes may refer to:
Science and technology Mathematics and computer science
*Vertex (geometry), a point where two or more curves, lines, or edges meet
*Vertex (computer graphics), a data structure that describes the position ...
, at distance
from the axis. The coefficients
describe the deviation of the surface from the
axially symmetric
In geometry, circular symmetry is a type of continuous symmetry for a Plane (geometry), planar object that can be rotational symmetry, rotated by any arbitrary angle and map onto itself.
Rotational circular symmetry is isomorphic with the circl ...
quadric surface specified by
and
.
If the coefficients
are all zero, then
is the ''radius of curvature'' and
is the
conic constant, as measured at the vertex (where
). In this case, the surface has the form of a
conic section
In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a specia ...
rotated about the optic axis, with form determined by
:
:
The above equation suffers from strong correlation between the coefficients of the first term and the polynomial terms. This leads to strong divergences when it comes to fitting the equation to an aspheric surface. Therefore, different equations using "Q-polynomials" where coefficients are orthogonal to each other are an alternative that is sometimes used.
Manufacture
![Schema lame de Schmidt](https://upload.wikimedia.org/wikipedia/commons/b/b2/Schema_lame_de_Schmidt.svg)
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 an Optics, optical instrument that can capture an image. Most cameras can capture 2D images, with some more advanced models being able to capture 3D images. At a basic level, most cameras consist of sealed boxes (the camera body), ...
s, camera phones, and CD players.
[ They are also commonly used for ]laser diode
file:Laser diode chip.jpg, The laser diode chip removed and placed on the eye of a needle for scale
A laser diode (LD, also injection laser diode or ILD, or diode laser) is a semiconductor device similar to a light-emitting diode in which a di ...
collimation, and for coupling light into and out of optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
s.
Larger aspheres are made by grinding and polishing. Lenses produced by these techniques are used in telescope
A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
s, projection TV
Rear-projection television (RPTV) is a type of large-screen television display technology. Until approximately 2006, most of the relatively affordable consumer large screen TVs up to used rear-projection technology. A variation is a video projec ...
s, 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 is turning using a cutting tool with a diamond tip. It is a process of mechanical machining of precision elements using lathes or derivative machine tools (e.g., turn-mills, rotary transfers) equipped with natural or synthetic d ...
is an alternate process, in which a computer-controlled lathe
A lathe () is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, and turning, with tools that are applied to the workpiece to c ...
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 (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
optics.
Several "finishing" methods can be used to improve the precision and surface quality of the polished surface. These include ion-beam finishing, abrasive water jets, and magnetorheological finishing
Magnetorheological finishing (MRF) is a precision surface finishing technology. Optical surfaces are polished in a computer-controlled magnetorheological (MR) finishing slurry. Unlike conventional rigid lap polishing, the MR fluid's shape and sti ...
, 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
Poly(allyl diglycol carbonate) (PADC) is a plastic commonly used in the manufacture of eyeglass lenses alongside the material PMMA (polymethyl methacrylate). The monomer is allyl diglycol carbonate (ADC). The term CR-39 technically refers to the ...
resin lens is. Techniques such as laser ablation
Laser ablation or photoablation (also called laser blasting) is the process of removing material from a solid (or occasionally liquid) surface by irradiating it with a laser beam. At low laser flux, the material is heated by the absorbed laser ...
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
Lapidary (from the Latin ) is the practice of shaping stone, minerals, or gemstones into decorative items such as cabochons, engraved gems (including cameos), and faceted designs. A person who practices lapidary is known as a lapidarist. A la ...
techniques.
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 commonly prescribed to people with presbyopia who also require a correction for myopia, hyperopia, and/or astigmatism.
History
Benjamin Franklin is generally credited with t ...
, trifocals, vari-focals, and cylindrical components for astigmatism
Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at nig ...
.
Metrology
Measurement technology plays a decisive role in the manufacturing of aspherical lenses. Depending on the manufacturing process and processing status, various measurement tasks are distinguished:
* form of asphere
* surface form deviation
* slope error
* centre thickness
* roughness
A distinction is made between tactile, i.e. touching, and non-contact measurement methods. The decision as to which method is used depends on accuracy but also on manufacturing state.
Tactile measurement
Tactile measurement is mainly used between two grinding operations to control the shape of the asphere and to adjust the following operation. A profile gauge probe is used to measure a section across the lens surface. The rotation symmetry of the lenses means that the combination of several of these profiles provides a sufficiently precise knowledge of the shape of the lens. Any damage to the lens surface caused by the probe tip would be removed in subsequent steps.
Non-contact measurement
Interferometers are used when measuring sensitive or polished surfaces. By superimposing a reference beam with the beam reflected from the surface to be measured, error maps, known as interferograms, are created which represent a full-field deviation of the surface shape.
Computer-generated hologram (CGH)
Computer-generated holograms (CGHs) represent a method for the interferometric determination of the deviation of the lens from the nominal geometry. These generate an aspherical wavefront in the target shape and thus enable the determination of deviations of the lens from the target shape in an interference image. CGHs must be manufactured specifically for each test item and are therefore only economical for series production.
Interferometric measurement
Another possibility is the interferometric measurement of aspheres in subareas, with minimal deviations to the best-fit sphere, and subsequent combination of the submeasurements to a full-surface interferogram. These are very flexible in comparison to CGHs and are also suitable for the production of prototypes and small series.
Ophthalmic uses
Like other lenses for vision correction, aspheric lenses can be categorized as convex or concave.
Convex aspheric curvatures are used in many presbyopic
Presbyopia is physiological insufficiency of accommodation associated with the aging of the eye that results in progressively worsening ability to focus clearly on close objects. Also known as age-related farsightedness (or age-related long si ...
vari-focal lenses to increase the optical power
In optics, optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens (optics), lens, mirror, or other optical system converges or diverges light. It is equal to the Mu ...
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, such as in cataract surgery, a perforating wound or ulcer, or congenital anomaly. It causes a loss of accommodation, high degree of farsightedness (hyperopia), and a deep a ...
or extreme hyperopia
Far-sightedness, also known as long-sightedness, hypermetropia, or hyperopia, is a condition of the eye where distant objects are seen clearly but near objects appear blurred. This blurred effect is due to incoming light being focused behind, i ...
, 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
Near-sightedness, also known as myopia and short-sightedness, is an eye disease where light focuses in front of, instead of on, the retina. As a result, distant objects appear blurry while close objects appear normal. Other symptoms may include ...
. 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 retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye of most vertebrates and some molluscs. The optics of the eye create a focused two-dimensional image of the visual world on the retina, which then ...
. High minus lenses cause an image so small that shape and form aren't discernible, generally at about −15 diopters
A dioptre (British spelling) or diopter (American spelling) is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dioptre = 1 m−1. It is normally used to express the optical power of a lens or cu ...
, 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
Far-sightedness, also known as long-sightedness, hypermetropia, or hyperopia, is a condition of the eye where distant objects are seen clearly but near objects appear blurred. This blurred effect is due to incoming light being focused behind, i ...
and nearsightedness
Near-sightedness, also known as myopia and short-sightedness, is an eye disease where light focuses in front of, instead of on, the retina. As a result, distant objects appear blurry while close objects appear normal. Other symptoms may include ...
, the lens curve flattens toward the edge of the glass, except for progressive reading adds for presbyopia
Presbyopia is physiological insufficiency of accommodation associated with the aging of the eye that results in progressively worsening ability to focus clearly on close objects. Also known as age-related farsightedness (or age-related long si ...
, where seamless vari-focal portions change toward a progressively more plus diopter
A dioptre (British spelling) or diopter (American spelling) is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dioptre = 1 m−1. It is normally used to express the optical power of a lens or cur ...
. 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 the field of vision consisting of a partially diminished or entirely degenerated visual acuity that is surrounded by a field of normal – or relatively well-preserved – vision.
Every normal mam ...
, a ringed blind spot.
Camera lenses
Aspheric elements are often used in camera lenses. This is often indicated by the abbreviation ASPH in the names of such products.
History
In 984, Ibn Sahl first discovered the law of refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, usually called Snell's law
Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
, 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 ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
in the 1620s, and by Christiaan Huygens
Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...
in the 1670s; the cross-section of the shape devised by Descartes for this purpose is known as a Cartesian oval
In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These curves are named after French mathematician René Descartes, who used them in optics.
Def ...
. The Visby lenses
One of the Visby lenses in a silver setting
The Visby lenses are a collection of lens-shaped manufactured objects made of rock crystal (quartz) found in several Viking graves on the island of Gotland, Sweden, and dating from the 11th or 12th cen ...
found in Viking treasures on the island of Gotland
Gotland (, ; ''Gutland'' in Gutnish), also historically spelled Gottland or Gothland (), is Sweden's largest island. It is also a province, county, municipality, and diocese. The province includes the islands of Fårö and Gotska Sandön to the ...
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. The origin of the lenses is unknown, as is their purpose (they may have been made as jewelry rather than for imaging).
Francis Smethwick ground the first high-quality aspheric lenses and presented them to the Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
on February 27, 1667/8. A telescope containing three aspheric elements was judged by those present "to exceed common, but very good telescopein 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." Aspheric reading
Reading is the process of taking in the sense or meaning of Letter (alphabet), letters, symbols, etc., especially by Visual perception, sight or Somatosensory system, touch.
For educators and researchers, reading is a multifaceted process invo ...
and burning glass
A burning glass or burning lens is a large convex lens that can concentrate the sun's rays onto a small area, heating up the area and thus resulting in ignition of the exposed surface. Burning mirrors achieve a similar effect by using reflecting s ...
es also outdid their spherical equivalents.
Moritz von Rohr
Moritz von Rohr (4 April 1868 – 20 June 1940) was an optical scientist at Carl Zeiss in Jena, Germany.
A street in Jena is named after him: Moritz-von-Rohr-Straße, near Carl-Zeiss-Promenade and Otto-Schott-Straße.
Life
Moritz von Ro ...
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 12 mm normal lens for use on 16 mm movie cameras in 1956. (See Image sensor format
In digital photography, the image sensor format is the shape and size of the image sensor.
The image sensor format of a digital camera determines the angle of view of a particular lens when used with a particular sensor. Because the image se ...
.) 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.
The first 35 mm camera lens
A camera lens (also known as photographic lens or photographic objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capab ...
with an aspheric lens element was the Fisheye-Nikkor 10 mm OP introduced in 1968.
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.
The use of interferometers has become a standard method of testing optical surfaces. Typical interferometer testing is done for flat and spherical optical elements. The use of a null corrector in the test can remove the aspheric component of the surface and allow testing using a flat or spherical reference.
In nature
Trilobites
Trilobites (; meaning "three lobes") are extinct marine arthropods that form the class Trilobita. Trilobites form one of the earliest-known groups of arthropods. The first appearance of trilobites in the fossil record defines the base of the At ...
, one of the earliest types of animal with sophisticated eyes, had lenses with two aspheric elements.
See also
*Hyperbola
In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, cal ...
*Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
One descript ...
*Precision glass moulding
Precision glass moulding is a replicative process that allows the production of high precision optical components from glass without grinding and polishing. The process is also known as ultra-precision glass pressing. It is used to manufacture p ...
*Radius of curvature (optics)
Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. The vertex of the lens s ...
References
External links
*
{{DEFAULTSORT:Aspheric Lens
Lenses