An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere
or cylinder. In photography, 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 and also reduce other optical aberrations
such as astigmatism, 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. Aspheric elements are used in the design of
multi-element wide-angle and fast normal lenses to reduce aberrations. They are also used
in combination with reflective elements such as the aspherical Schmidt corrector plate
used in the Schmidt cameras and the Schmidt-Cassegrain telescopes. Small molded aspheres are often
used for collimating diode lasers. Aspheric lenses are also sometimes used for
eyeglasses. 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. 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 is presumed to lie in the z direction, and is the sag—the z-component
of the displacement of the surface from the vertex, at distance from the axis. The coefficients
describe the deviation of the surface from the axially symmetric 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. In this case, the
surface has the form of a conic section rotated about the optic axis, with form determined
by :
Unfortunately, the above equation suffers among others 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
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 cameras, camera phones, and CD players. They are also commonly
used for laser diode collimation, and for coupling light into and out of optical fibers.
Larger aspheres are made by grinding and polishing. Lenses produced by these techniques are used
in telescopes, 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 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 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, 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
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. 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. 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 vari-focal lenses 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 lenses. Many convex types of lens have been approved
by governing agencies regulating prescriptions. 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. 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. In prescriptions for both farsightedness and
nearsightedness, the lens curve flattens toward the edge of the glass, 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.
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.
History
In 984, Ibn Sahl first discovered the law of refraction, usually called Snell's law,
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 in the 1620s, and by Christiaan
Huygens in the 1670s; 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. The origin of the lenses is unknown, as is their purpose.
Francis Smethwick ground the first high-quality aspheric lenses and presented them to the
Royal Society on February 27, 1667/8. 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." Aspheric reading and burning glasses
also outdid their spherical equivalents. 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. 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 normal 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. 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.
See also Hyperbola
Parabola Radius of curvature
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