Corrective lens
A corrective lens is a lens worn on or before the eye, used to treat myopia, hyperopia, astigmatism, and presbyopia. The most common types of corrective lenses are eyeglass lenses and contact lenses. Intraocular lenses are also beginning to become common. Myopia (near sightedness) requires biconcave or diverging lenses, whereas hyperopia (far sightedness) requires biconvex or converging lenses.
Corrective lenses are usually prescribed by an optometrist. The prescription consists of the necessary corrections for refraction errors in each eye, individually for distance vision and near vision, for a total of four possible correction specifications. Each specification can include a spherical correction in diopters for near/far sightedness and/or presbyopia, a cylindrical correction in diopters combined with the cylinder axis in degrees, correcting for any cylindrical deformation of the eye (i.e., astigmatism). Infrequently, prism and base values may also be specified to correct for a muscular imbalance and/or errors in eye orientation.
In some cases, mild farsightedness can be treated with simple magnifying lenses or commodity reading glasses that can be purchased without a prescription. However, an optometrist may need to prescribe a correction for both eyes or each eye, individually, allowing lenses to be custom ground to the patient's specific needs. Usually, the amount of correction necessary for both eyes is similar, although in rare cases the prescriptions can differ by a wide margin.
Patients with presbyopia or other disorders of accommodation often benefit from bifocals, or lenses with separate sections ground to different prescriptions for different circumstances. Typically a person with myopia would have one section of a prescription lens that has a certain diverging power while another section of the lens would have a lower diverging power for close-up work.  Similarly a person with hyperopia would have one section of the lens with a certain converging power and another section with a greater power for close-up work.

# Eyeglass lenses

# Lens types
- Single vision  has the same optical correction over the entire area of the lens.
- Bifocal  the upper part of the lens is generally used for distance vision, while the lower part is used for near vision.  A segment line separates the two.
- Trifocal  similar to bifocals, except that the two bifocal areas are separated by a third middle area with no correction, used for intermediate distance vision. This lens type has two segment lines, dividing the three different correcting segments.
- Progressive or varifocal  provide a smooth transition in a bifocal or trifocal lens, eliminating characteristic segment lines.

# Lens shapes
Although corrective lenses can be produced in many different shapes, the most common single vision shapes are convex-concave and plano-concave for the treatment of myopia, and biconvex for the treatment of presbyopia. The difference in curvature between the front and rear surface leads to the corrective power of the lens.
Bifocals and trifocals result in more complex lens shapes that are a combination of the common shapes. Progressive lenses, which eliminate the line in bi/tri-focals, further dull the ability to categorize the shape.
Optically, base curves in the best spherical form, for a particular prescription, result in the best characteristics across the entire surface of the lens. Cosmetically, a more plano outer surface, especially for convex-concave lenses, may be desired, despite a reduction in optical quality at points distant from the optical center of the lens.

# Refractive index
In the UK and the US, the refractive index is generally specified with respect to the yellow He-d Fraunhofer line, commonly abbreviated as nd. Lens materials are classified by their refractive index, as follows:
- Normal index - 1.48  nd < 1.54
- Mid-index - 1.54  nd < 1.64
- High-index - 1.64  nd < 1.74
- Very high index - 1.74  nd
Despite this classification, nd values that are 1.60 are often, especially for marketing purposes, referred to as high-index. Likewise, Trivex and other borderline normal/mid-index materials, are often referred to as mid-index.
Increased index advantages:
- Thinner lenses for cosmetics.
- In highly myopic cases high index can minimize edge thickness. This reduces light entering into the edge of the lens, reducing an additional source of internal reflections.
Increased index disadvantages:
- Poorer Abbe number.
- Poorer light transmission and reflection on lens, according to the Fresnel Reflection equation, increasing importance of Anti-reflective coating.
- Theoretically, manufacturing defects have more impact on optical quality.
- Theoretically, off-axis optical quality degrades (oblique astigmatic error). This degradation should not be perceptible in practice.

# Optical quality

## Abbe number
Of all of the properties of a particular lens material, the one that most closely relates to its optical performance is its dispersion, which is specified by the Abbe number. Lower Abbe numbers result in the presence of chromatic aberration (i.e., color fringes above/below or to the left/right of a high contrast object), especially in larger lens sizes and stronger prescriptions (4D or greater). Generally, lower Abbe numbers are a property of mid and higher index lenses that cannot be avoided, regardless of the material used. The Abbe number for a material at a particular refractive index formulation is usually specified as its Abbe value.
In practice, ABBEs effect on chromatic aberration can be roughly estimated to change 1:1, meaning a change from 30 to 32 ABBE will not have a practically noticeable benefit, but a change from 30-47 could be beneficial for users with strong prescriptions that move their eyes and look off-axis of optical center of the lens. Note that some users do not sense color fringing directly but will just describe 'off-axis blurriness'.
Abbe values even as high as that of  (Vd45) produce chromatic aberrations which can be perceptible to a user in lenses larger than 40mm in diameter and especially in strengths that are in excess of 4D. At 8D even glass (Vd58) produces chromatic aberration that can be noticed by a user.  Chromatic aberration is independent of the lens being of spherical, aspheric, or atoric design.
The eyes ABBE number is independent of the importance of the corrective lenss ABBE, since the human eye:
- Moves to keep the visual axis close to its achromatic axis, which is completely free of dispersion (i.e. to see the dispersion one would have to concentrate on points in the periphery of vision, where visual clarity is quite poor)
- Is very insensitive, especially to color, in the periphery (i.e., at retinal points distant from the achromatic axis and thus not falling on the fovea, where the cone cells responsible for color vision are concentrated (See: Anatomy and Physiology of the Retina))
In contrast, the eye moves to look through various parts of a corrective lens as it shifts its gaze, some of which can be as much as several centimeters off of the optical center. Thus, despite the eye's ABBE properties, the corrective lens's ABBE value cannot be dismissed. People who are sensitive to the effects of chromatic aberrations, have stronger prescriptions, often look off the lenss optical center, or prefer larger corrective lens sizes may be impacted by chromatic aberration. To minimize chromatic aberration, a doctor or wearer can:
- Try to use the smallest vertical lens size that is comfortable. Generally, chromatic aberrations are more noticeable as the pupil moves vertically below the optical center of the lens (e.g., reading or looking at the ground while standing or walking). Keep in mind that a smaller vertical lens size will result in a greater amount of vertical head movement, especially while performing activities that involve short and intermediate distance viewing, which could lead to an increase in neck strain, especially in occupations involving a large vertical field of view.
- Restrict the choice of lens material to the highest ABBE value at acceptable thickness. The oldest most basic commonly used lens materials also happen to have the best optical characteristics at the expense of corrective lens thickness (i.e. cosmetics). Newer materials have focused on improved cosmetics and increased impact safety, at the expense of optical quality. All lenses sold in USA pass the FDA ball-drop impact test, and depending on needed index these seem to currently have best in class ABBE vs Index (Nd): Glass (2x weight of plastics) or CR-39 (2mm vs 1.5mm thickness typical on newer materials) 58 @ 1.5, Sola Spectralite (47@1.53), Sola Finalite (43@1.6), and Hoya Eyry (36 @ 1.7). For impact resistance safety glass is offered at a variety of indexes at high ABBE, but is still 2x the weight of plastics. Polycarbonate (Vd=30-32) has very poor ABBE, but is tried and true. Trivex (Vd=43 @ 1.53), is also heavily marketed as an impact resistant alternative to Polycarbonate, for individuals who dont need polycarbonates index. Trivex is also one of the lightest material available.

## Power error (-D corrections for myopia)
Power error is the change in the optical power of a lens as the eye looks through various points on the area of the lens. Generally, it is least present at the optic center and gets progressively worse as one looks towards the edges of the lens. The actual amount of power error is highly dependent on the strength of the prescription as well as whether a best spherical form of lens or an optically optimal aspherical form was used in the manufacture of the lens. Generally, best spherical form lenses attempt to keep the ocular curve between four and seven diopters.

## Lens induced oblique astigmatism (+D corrections for presbyopia)
As the eye shifts its gaze from looking through the optical center of the corrective lens, the lens induced astigmatism value increases. In a spherical lens, especially one with a strong correction whose base curve is not in the best spherical form, such increases can significantly impact the clarity of vision in the periphery.

## Minimizing power error and lens induced astigmatism
As corrective power increases, even optimally designed lenses will have distortion that can be noticed by a user. This particularly affects individuals that use the off-axis areas of their lenses for visually demanding tasks. For individuals sensitive to lens errors, the best way to eliminate lens induced aberrations is to use contact lenses. Contacts eliminate all these aberrations since the lens then moves with the eye.
Barring contacts, a good lens designer doesnt have many parameters which can be traded off to improve vision. Index has little effect on error. Note that, chromatic aberration is often perceived as blurry vision in the lens periphery giving the impression of power error, although this is actually due to color shifting. Chromatic aberration can be improved by using a material with improved ABBE. The best way to combat lens induced power error is to limit the choice of corrective lens to one that is in the best spherical form. A lens designer determines the best-form spherical curve using the Oswalt curve on the Tscherning ellipse. This design gives the best achievable optical quality and least sensitivity to lens fitting. A flatter base-curve is sometime selected for cosmetic reasons. Aspheric or atoric design can reduce errors induced by using a suboptimal flatter base-curve.  They cannot surpass the optical quality of a spherical best-form lens, but can reduce the error induced by using a flatter than optimal base curve. The improvement due to flattening is most evident for strong farsighted lenses. High myopes (-6D) may see a slight cosmetic benefit with larger lenses. Mild prescriptions will have no perceptible benefit (-2D). Even at high prescriptions some high myope prescriptions with small lenses may not see any difference, since some aspheric lenses have a spherically designed center area for improve vision and fit.
In practice, labs tend to produce pre-finished and finished lenses in groups of narrow power ranges to reduce inventory. Lens powers that fall into the range of the prescriptions of each group share a constant base curve. For example, corrections from -4.00D to -4.50D may be grouped and forced to share the same base curve characteristics, but the spherical form is only best for a -4.25D prescription. In this case the error will be imperceptible to the human eye. However, some manufacturers may further cost-reduce inventory and group over a larger range which will result in perceptible error for some users in the range who also use the off-axis area of their lens. Additionally some manufacturers may verge toward a slightly flatter curve. Although if only a slight bias toward plano is introduced it may be negligible cosmetically and optically. These optical degradations due to base-curve grouping also apply to aspherics since their shapes are intentionally flattened and then asphericized to minimize error for the average base curve in the grouping.

# Cosmetics & Weight

## Reducing lens thickness
Note that the greatest cosmetic improvement on lens thickness (and weight) is had from choosing a frame which holds physically small lenses. The curves on the front and back of a lens are ideally formed with the specific radius of a sphere. This radius is set by the lens designer based on the prescription and cosmetic consideration. Selecting a smaller lens will mean less of this sphere surface is represented by the lens surface, meaning the lens will have a thinner edge (myopia) or center (hyperopia).
Index can improve the lens thinness, but at a point no more improvement will be realized.  For example, if an index and lens size is selected with center to edge thickness difference of 1mm then changing index can only improve thickness by a fraction of this. This is also true with aspheric design lenses.
The lens minimum thickness can also be varied. The FDA ball drop test sets the minimum thickness of materials. Glass or CR-39 requires 2.0mm, but some newer materials only require 1.5mm or even 1.0mm minimum thickness.

## Weight
Material density typically increases as lens thickness is reduced by increasing index.  There is also a minimum lens thickness required to support the lens shape. These factors results in a thinner lens which is not lighter than the original. There are lens materials with lower density at higher index which can result in a truly lighter index. These materials can be found a material property table. Reducing frame lens size will give the most noticeable improvement in weight for a given material.

## Minification & Magnification
Aspheric/atoric design can reduce minification and magnification of the eye for observers at some angles.

# Lens materials

## Optical crown glass (B270)
- Refractive index (nd): 1.52288
- Abbe value (Vd): 58.5
- Density: 2.55 g/cm3 (the heaviest corrective lens material in common use, today)
- UV cutoff: 320 nm
Glass lenses have become less common in recent years due to the danger of shattering and their relatively high weight compared to CR-39 plastic lenses. They still remain in use for specialised circumstances, for example in extremely high prescriptions (currently, glass lenses can be manufactured up to a refractive index of 1.9) and in certain occupations where the hard surface of glass offers more protection from sparks or shards of material. If the highest Abbe value is desired, the only choices for common lens optical material are optical crown glass and CR-39.
Higher quality optical-grade glass materials exist (e.g., Borosilicate crown glasses such as BK7 (nd=1.51680 / Vd=64.17 / D=2.51 g/cm3), which is commonly used in telescopes and binoculars, and fluorite crown glasses such as Schott N-FK51A (nd=1.48656 / Vd=84.47 / D=3.675 g/cm3), which is 16.2 times the price of a comparable amount of BK7, and are commonly used in high-end camera lenses). However, one would be very hard pressed to find a laboratory that would be willing to acquire or shape custom eyeglass lenses, considering that the order would most likely consist of just two different lenses, out of these materials. Generally, Vd values above 60 are of dubious value, except in combinations of extreme prescriptions, large lens sizes, a high wearer sensitivity to dispersion, and occupations that involve work with high contrast elements (e.g., reading dark print on very bright white paper, construction involving contrast of building elements against a cloudy white sky, a workplace with recessed can or other concentrated small area lighting, etc. ..).

## Plastic (CR-39TM)
- Refractive index (nd): 1.498 (standard)
- Abbe value (Vd): 59.3
- Density: 1.31 g/cm3
- UV cutoff: 355 nm
Plastic lenses are currently the most commonly prescribed lens, due to their relative safety, low cost, ease of production, and outstanding optical quality. The main drawbacks are the ease by which a lens can be scratched, and the limitations and costs of producing higher index lenses.

## TrivexTM
- Refractive index (nd): 1.532
- Abbe value (Vd): 43 - 45 (depending on licensing manufacturer)
- Density: 1.1 g/cm3 (the lightest corrective lens material in common use)
- UV cutoff: 380 nm
TrivexTM is a relative newcomer that possesses the UV blocking properties and shatter resistance of polycarbonate while at the same time offering far superior optical quality (i.e., higher Abbe value) and a slightly lower density.  Its lower refractive index of 1.532 vs. polycarbonate's 1.586, however, may result in slightly thicker lenses. Along with polycarbonate and the various high-index plastics, Trivex is a lab favorite for use in rimless frames, due to the ease with which it can be drilled as well as its resistance to cracking around the drill holes. One other advantage that Trivex has over polycarbonate is that it can be easily tinted, if desired.

## Polycarbonate
- Refractive index (nd): 1.586
- Abbe value (Vd): 30
- Density: 1.2 g/cm3
- UV cutoff: 385 nm
Lighter weight than normal plastic.  Less tendency to irritate your nose or leave red marks on your nose where the glasses touch your nose.  Polycarb blocks UV rays, is shatter resistant and is used in sports glasses and glasses for children and teenagers.  Polycarb is soft and will scratch easily.  Because of that, scratch coating is typically done after generation of the prescription and polishing of the lens. Standard polycarbonate with an Abbe value of 30 is one of the worst materials optically, if chromatic aberration intolerance is of concern. Along with Trivex and the high-index plastics, polycarbonate is an excellent choice for rimless eyeglasses.

## High-index plastics (polyurethanes)
- Refractive index (nd): 1.640 - 1.740
- Abbe value (Vd): 42 - 32 (higher indexes generally result in lower Abbe values)
- Density: 1.3 - 1.5 (g/cm3)
- UV cutoff: 380 nm - 400 nm
High-index plastics allow for thinner lenses. The lenses may not be lighter, however, due to the increase in density vs. mid- and normal index materials. Despite being popular with customers, due their thinner appearance, high-index lenses also suffer from a much higher level of chromatic aberrations due to their lower Abbe value. For people with strong prescriptions, the significant reduction in thickness may warrant the reduction in optical quality. Aside from thinness of the lens, another advantage of high-index plastics is their strength and shatter resistance, although not as shatter resistant as polycarbonate. This makes them another excellent choice for rimless eyeglasses.

## Ophthalmic material property tables
Reflected light calculated using Fresnel Reflection Equation for normal waves against air on two interfaces. This is reflection w/o AR coating.
Compilations of manufacturer material data can be found at opticampus,  firstvisionmedia, and eyecarecontacts. Additional information on branding can be found at eyetopics.
Indices of refraction for a range of materials can be found in the List of indices of refraction.

# Lens coatings

## Anti-reflective
Anti-reflective coatings help to make the eye behind the lens more visible. They also help lessen back reflections of the white of the eye as well as bright objects behind the eyeglasses wearer (e.g., windows, lamps). Such reduction of back reflections increases the apparent contrast of surroundings. At night, anti-reflective coatings help to reduce headlight glare from oncoming cars, street lamps and heavily lit or neon signs.
One problem with anti-reflective coatings is that historically they have been very easy to scratch. Newer coatings, such as Crizal AlizeTM with its 5.0 rating and Hoya's Super HiVisionTM with its 10.9 rating on the COLTS Bayer Abrasion Test (glass averages 12-14), try to address this problem by combining scratch resistance with the anti-reflective coating. They also offer a measure of dirt and smudge resistance, due to their hydrophobic properties (110 water drop contact angle for Super HiVisionTM and 112 for Crizal AlizeTM).

## Ultraviolet protection
A UV coating is used to reduce the transmission of light in the ultraviolet spectrum. UV-B radiation increases the likelihood of cataracts, while long term exposure to UV-A radiation can damage the retina. DNA damage from UV light is cumulative and irreversible. Some materials, such as Trivex and Polycarbonate naturally block most UV light and do not benefit from the application of a UV coating.

## Scratch resistance
Highly recommended, especially for polycarbonate and softer materials, to make lenses last longer.  This is done automatically by many labs for polycarbonate and high index lenses.

# Confusing corrective lens industry terminology
Several terms in the ophthalmic industry have multiple meanings. Several terms are confusing and misleading for consumers and even many people who work in the industry.

## Spheric vs Aspheric, Atoric, etc
Most all lens manufacturer's claim that "aspherics improve vision over spheric", but this statement could be misleading to individuals who dont know there is a tacit qualifying statement "when compared to a spheric flattened away from best-form for cosmetic reasons". This qualification is necessary since best-form spherics are always better than aspherics for an ophthalmic lens application. Aspherics for corrective lenses are only used to attempt to improve the degradation caused by deviating from best-form sphere resulting from making a flatter lens for cosmetic reasons.  The same applies for Atoric and Bi-Asphierc.
Some eye care practitioners and literature in the industry notice that aspheric designs are used in cameras, binoculars. They (falsely) conclude that aspherics/atorics are a sign of good optics in eyewear. Cameras and telescopes use multiple lens elements and have different design criteria.  Ophthalmic lens only contain 1 lens element and the best-form spheric lens gives the best vision. In cases, where best-form is not used, such as cosmetic flattening, thinning or wrap-around sunglasses, an aspheric design can only attempt to reduce the amount of increased optical distortions induced by not using the best-form lens.

## Optical Aberrations of the eye lens vs corrective lens
Optical terms are used to describe error in the eyes lens and the corrective lens. This can cause confusion, since astigmatism or ABBE has drastically different impact on vision depending on which lens has the error.

## Astigmatism disambiguation
Astigmatism of the eye:  People subscribed a sphere and a cylinder prescription have astigmatism of the eye and can be given a toric lens to correct it.
Astigmatism of the corrective lens: This phenomenon is called Lens induced Oblique Astigmatism Error (OAE) or power error (see subheading) and induced when the eye looks through the ophthalmic lens at a point oblique to the optical center (OC). This may become especially evident beyond -6D.
Example: A patient with astigmatism (or no astigmatism) of the eye and a high prescription may notice astigmatism of the lens (OAE) when looking through the corner of their glasses.

## Aspheric and atoric disambiguation
An ophthalmic "aspheric lens" specifically refers to a subclass of aspheric lens. Designs referring to flatter curves are trading off optical quality for cosmetic appearance. An aspheric lens attempts to correct the error induced by flattening the lens by using a non-spheric lens shape. Typically the design focuses on reducing the error (OAE) across the horizontal and vertical lens axis edges. This can be primarily beneficial to farsites, which have a thick lens center.
An Atoric lens design refers to a lens with more complex aspheric lens design.  An Atoric lens design can address error over more corners of the lens, not just the horizontal and vertical axis.
A toric (two words, not atoric) lens is a lens designed to compensate for the patients with astigmatism in their eye. Even though this technically requires an 'aspheric' lens, aspheric and atoric are reserved for lenses which correct errors induced by cosmetic lens flattening.