Abbe number

In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion (variation of refractive index versus wavelength), with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it.

Refractive index variation for SF-11 flint glass (upper graph), BK-7 borosilicate glass (middle curve), and fused quartz (dashed curve).

The Abbe number,[1][2] VD, of a material is defined as

where nD, nF and nC are the refractive indices of the material at the wavelengths of the Fraunhofer D-, F- and C- spectral lines (589.3 nm, 486.1 nm and 656.3 nm respectively).

Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have V < 55 whereas the lower dispersion crown glasses have larger Abbe numbers. Values of V range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses.

Most of the human eye's wavelength sensitivity curve, shown here, is bracketted by the Abbe number reference wavelengths of 486.1 nm (blue) and 656.3 nm (red)

Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used.

Abbe diagram

Abbe-diagram 2
An Abbe diagram, also known as 'the glass veil', plots the Abbe number against refractive index for a range of different glasses (red dots). Glasses are classified using the Schott Glass letter-number code to reflect their composition and position on the diagram.
SpiderGraph Abbe Number-en
Influences of selected glass component additions on the Abbe number of a specific base glass.[3]

An Abbe diagram, also called 'the glass veil', is produced by plotting the Abbe number Vd of a material versus its refractive index nd. Glasses can then be categorised and selected according to their positions on the diagram. This can be a letter-number code, as used in the Schott Glass catalogue, or a 6-digit glass code.

Glasses' Abbe numbers, along with their mean refractive indices, are used in the calculation of the required refractive powers of the elements of achromatic lenses in order to cancel chromatic aberration to first order. Note that these two parameters which enter into the equations for design of achromatic doublets are exactly what is plotted on an Abbe diagram.

Due to the difficulty and inconvenience in producing sodium and hydrogen lines, alternate definitions of the Abbe number are often substituted (ISO 7944).[4] Rather than the standard definition, above, using the refractive index variation between the F and C hydrogen lines, an alternative measure using the subscript "e"

takes the difference between the refractive indices of the blue and red cadmium lines at 480.0 nm and 643.8 nm (with ne referring to the wavelength of the mercury e-line, 546.073 nm). Other definitions can similarly be employed; the following table lists standard wavelengths at which n is commonly determined, including the standard subscripts employed.[5]

λ in nm Fraunhofer's symbol Light source Color
365.01 i Hg UV-A
404.66 h Hg violet
435.84 g Hg blue
479.99 F' Cd blue
486.13 F H blue
546.07 e Hg green
587.56 d He yellow
589.3 D Na yellow
643.85 C' Cd red
656.27 C H red
706.52 r He red
768.2 A' K IR-A
852.11 s Cs IR-A
1013.98 t Hg IR-A

See also


  1. ^ Hovestadt, H. (1902). Jena Glass and Its Scientific and Industrial Applications. London: Macmillan and Co. pp. 1–81.
  2. ^ Bergmann, Ludwig; Clemens Schaefer (1999). Optics of Waves and Particles. Berlin: Walter de Gruyter. pp. 198–201. ISBN 3-11-014318-6.
  3. ^ Abbe number calculation of glasses
  4. ^ Meister, Darryl. "Understanding Reference Wavelengths" (PDF). Carl Zeiss Vision. Retrieved 2013-03-13.
  5. ^ L. D. Pye, V. D. Frechette, N. J. Kreidl: "Borate Glasses"; Plenum Press, New York, 1977

External links

Achromatic lens

An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane.

The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion. Typically, one element is a negative (concave) element made out of flint glass such as F2, which has relatively high dispersion, and the other is a positive (convex) element made of crown glass such as BK7, which has lower dispersion. The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.

In the most common type (shown), the positive power of the crown lens element is not quite equalled by the negative power of the flint lens element. Together they form a weak positive lens that will bring two different wavelengths of light to a common focus. Negative doublets, in which the negative-power element predominates, are also made.


CR-39, or allyl diglycol carbonate (ADC), is a plastic polymer commonly used in the manufacture of eyeglass lenses. The abbreviation stands for "Columbia Resin #39", which was the 39th formula of a thermosetting plastic developed by the Columbia Resins project in 1940.The first commercial use of CR-39 monomer was to help create glass-reinforced plastic fuel tanks for the B-17 bomber aircraft in World War II, reducing weight and increasing range of the bomber. After the War, the Armorlite Lens Company in California is credited with manufacturing the first CR-39 eyeglass lenses in 1947. CR-39 plastic has an index of refraction of 1.498 and an Abbe number of 58. CR-39 is now a trade-marked product of PPG Industries.An alternative use includes a purified version that is used to measure neutron radiation, a type of ionizing radiation, in neutron dosimetry.

Although CR-39 is a type of polycarbonate, it should not be confused with the general term polycarbonate, a tough homopolymer usually made from bisphenol A.

Chromatic aberration

In optics, chromatic aberration (abbreviated CA; also called chromatic distortion and spherochromatism) is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light. The refractive index of most transparent materials decreases with increasing wavelength. Since the focal length of a lens depends on the refractive index, this variation in refractive index affects focusing. Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image.

Cocaine (data page)

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Corrective lens

A corrective lens is a lens typically worn in front of the eye to improve vision. The most common use is to treat refractive errors: myopia, hypermetropia, 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. Intraocular lenses are surgically implanted most commonly after cataract removal, but can be used for purely refractive purposes.

Diborane (data page)

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Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity.

Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves (ocean waves), and for telecommunication signals along transmission lines (such as coaxial cable) or optical fiber.

In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

Ernst Abbe

Ernst Karl Abbe HonFRMS (23 January 1840 – 14 January 1905) was a German physicist, optical scientist, entrepreneur, and social reformer. Together with Otto Schott and Carl Zeiss, he laid the foundation of modern optics. Abbe developed numerous optical instruments. He was a co-owner of Carl Zeiss AG, a German manufacturer of research microscopes, astronomical telescopes, planetariums and other optical systems.

Flint glass

Flint glass is optical glass that has relatively high refractive index and low Abbe number (high dispersion). Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refractive indices ranging between 1.45 and 2.00. A concave lens of flint glass is commonly combined with a convex lens of crown glass to produce an achromatic doublet lens because of their compensating optical properties, which reduces chromatic aberration (colour defects).

With respect to glass, the term flint derives from the flint nodules found in the chalk deposits of southeast England that were used as a source of high purity silica by George Ravenscroft, c. 1662, to produce a potash lead glass that was the precursor to English lead crystal.

Traditionally, flint glasses were lead glasses containing around 4–60% lead(II) oxide; however, the manufacture and disposal of these glasses were sources of pollution. In many modern flint glasses, lead oxides are replaced with other metal oxides such as titanium dioxide and zirconium dioxide without significantly altering the optical properties of the glass.

Flint glass (disambiguation)

Flint glass is a form of glass characterised by having a high refractive index and a low Abbe number.

Flint Glass may also refer to:

Flint Glass, an electronic music project by Gwenn Tremorin

Fraunhofer lines

In physics and optics, the Fraunhofer lines are a set of spectral lines named after the German physicist Joseph von Fraunhofer (1787–1826). The lines were originally observed as dark features (absorption lines) in the optical spectrum of the Sun.

Glass code

A glass code is a method of classifying glasses for optical use, such as the manufacture of lenses and prisms. There are many different types of glass with different compositions and optical properties, and a glass code is used to distinguish between them.

There are several different glass classification schemes in use, most based on the catalogue systems used by glass manufacturers such as Pilkington and Schott Glass. These tend to be based on the material composition, for example BK7 is the Schott Glass classification of a common borosilicate crown glass.

The international glass code is based on U.S. military standard MIL-G-174, and is a six-digit number specifying the glass according to its refractive index nd at the Fraunhofer d- (or D3-) line, 589.3 nm, and its Abbe number Vd also taken at that line. The resulting glass code is the value of nd-1 rounded to three digits, followed by Vd rounded to three digits, with all decimal points ignored. For example, BK7 has nd = 1.5168 and Vd = 64.17, giving a six-digit glass code of 517642.

Consequently, a linear approximation for the refractive index dispersion close that wavelength is given by:

where is the wavelength in nanometers.

The following table shows some example glasses and their glass code. Note that the glass properties can vary slightly between different manufacturer types.

High-refractive-index polymer

A high-refractive-index polymer (HRIP) is a polymer that has a refractive index greater than 1.50.Such materials are required for anti-reflective coating and photonic devices such as light emitting diodes (LEDs) and image sensors. The refractive index of a polymer is based on several factors which include polarizability, chain flexibility, molecular geometry and the polymer backbone orientation.As of 2004, the highest refractive index for a polymer was 1.76. Substituents with high molar fractions or high-n nanoparticles in a polymer matrix have been introduced to increase the refractive index in polymers.

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Leaded glass

Leaded glass may refer to:

Lead glass, potassium silicate glass which has been impregnated with a small amount of lead oxide in its fabrication

Lead came glasswork, glass panels made by combining multiple small pieces of glass, which may be stained, textured or beveled, with cames or copper foil

Flint glass, an optical glass that has relatively high refractive index and low Abbe number

Leadlight or leaded lights, decorative windows made of small sections of glass supported in lead cames

Low-dispersion glass

Low-dispersion glass (LD glass) is a type of glass with low dispersion. Crown glass is an example of a relatively inexpensive low-dispersion glass.

Special low dispersion glass (SLD glass) and extraordinary low-dispersion glass (ELD glass) are glasses with yet lower dispersion (and yet higher price). Other glasses in this class are extra-low-dispersion glass (ED glass), and ultra-low-dispersion glass (UL glass).

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 precision glass lenses for consumer products such as digital cameras, and high-end products like medical systems. The main advantage over mechanical lens production is that complex lens geometries such as aspheres can be produced cost-efficiently.

Trimethylarsine (data page)

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