Editing Chromatic aberration (section)

==Minimization==
[[File:Comparison chromatic focus shift plots.svg|thumb|upright=1.2|alt=Graph show degree of correction by different lenses and lens systems|Chromatic correction of visible and near infrared wavelengths. Horizontal axis shows degree of aberration, 0 is no aberration. Lenses: 1: simple, 2: achromatic doublet, 3: apochromatic and 4: superachromat.]]

In the earliest uses of lenses, chromatic aberration was reduced by increasing the focal length of the lens where possible.  For example, this could result in extremely long [[Refracting telescope#Keplerian Telescope|telescopes]] such as the very long [[aerial telescope]]s of the 17th century. [[Isaac Newton]]'s theories about [[Electromagnetic spectrum#Visible radiation (light)|white light]] being composed of a [[spectrum]] of colors led him to the conclusion that uneven refraction of light caused chromatic aberration (leading him to build the first [[reflecting telescope]], his [[Newtonian telescope]], in 1668.<ref name="books.google.com">{{cite book|author= Hall, A. Rupert|title=Isaac Newton: Adventurer in Thought|url=https://archive.org/details/isaacnewtonadven0000hall|url-access= registration|date= 1996|publisher=Cambridge University Press|isbn=978-0-521-56669-8|page=[https://archive.org/details/isaacnewtonadven0000hall/page/67 67]}}</ref>)

Modern telescopes, as well as other [[catoptric]] and [[catadioptric system]]s, continue to use mirrors, which have no chromatic aberration.

There exists a point called the ''[[circle of least confusion]]'', where chromatic aberration can be minimized.<ref>{{Cite journal
 | pmid = 17514263|doi=10.1364/AO.46.003107
| year = 2007
| last1 = Hosken
| first1 = R. W.
| title = Circle of least confusion of a spherical reflector
| journal = Applied Optics
| volume = 46
| issue = 16
| pages = 3107–17
|bibcode = 2007ApOpt..46.3107H }}</ref> It can be further minimized by using an [[achromatic lens]] or ''achromat'', in which materials with differing dispersion are assembled together to form a compound lens. The most common type is an achromatic [[doublet (lens)|doublet]], with elements made of [[Crown glass (optics)|crown]] and [[flint glass]]. This perfectly corrects the aberration at two wavelengths and reduces the amount of chromatic aberration over a range of nearby wavelengths. By combining more than two lenses of different composition, the degree of correction can be further increased, as seen in an [[apochromatic lens]] or ''apochromat'', which provides perfect correction at three wavelengths. In general, correcting at three wavelengths will make the error on other wavelengths quite small, but an achromat made with low dispersion glass may still provide better correction than an apochromat made with more conventional glass.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/aber2.html "Chromatic Aberration"]. hyperphysics.phy-astr.gsu.edu</ref>

Many types of [[glass]] have been developed to reduce chromatic aberration. These are [[low dispersion glass]], most notably, glasses containing [[fluorite]].<ref>{{Cite web |last=Staff |first=By |title=Defocus Spectacle Lenses May Help Slow Low-Level Myopia |url=https://www.reviewofoptometry.com/article/defocus-spectacle-lenses-may-help-slow-lowlevel-myopia |access-date=2025-03-27 |website=www.reviewofoptometry.com}}</ref> These hybridized glasses have a very low level of optical dispersion; only two compiled lenses made of these substances can yield a high level of correction.<ref>Elert, Glenn. [http://physics.info/aberration/ "Aberration."] – The Physics Hypertextbook.</ref>

The use of achromats was an important step in the development of [[Microscope|optical microscopes]] and [[telescopes]].

An alternative to achromatic doublets is the use of diffractive optical elements. Diffractive optical elements are able to generate arbitrary complex wave fronts from a sample of optical material which is essentially flat.<ref>{{cite journal|url=http://ntv.ifmo.ru/en/article/11431/preimuschestva_ispolzovaniya_difrakcionnyh_opticheskih_elementov_v_prostyh_opticheskih_izobrazhayuschih_sistemah.htm|title=Advantages of diffractive optical elements application in simple optical imaging systems.|author1=Zoric N.Dj. |author2=Livshits I.L. |author3=Sokolova E.A. |journal=Scientific and Technical Journal of Information Technologies, Mechanics and Optics|volume=15|issue=1|pages=6–13|year=2015|doi=10.17586/2226-1494-2015-15-1-6-13|doi-access=free}}</ref> Diffractive optical elements have negative dispersion characteristics, complementary to the positive Abbe numbers of optical glasses and plastics. Specifically, in the visible part of the spectrum diffractives have a negative [[Abbe number]] of −3.5. Diffractive optical elements can be fabricated using [[diamond turning]] techniques.<ref>{{Cite journal
 | pmid = 18026340|doi=10.1364/OL.27.000969
| year = 2002
| last1 = Amako
| first1 = J
| title = Chromatic-distortion compensation in splitting and focusing of femtosecond pulses by use of a pair of diffractive optical elements
| journal = Optics Letters
| volume = 27
| issue = 11
| pages = 969–71
| last2 = Nagasaka
| first2 = K
| last3 = Kazuhiro
| first3 = N
|bibcode = 2002OptL...27..969A }}</ref>

Telephoto lenses using diffractive elements to minimize chromatic aberration are commercially available from [[Canon Inc.|Canon]] and [[Nikon]] for interchangeable-lens cameras; these include 800mm f/6.3, 500mm f/5.6, and 300mm f/4 models by Nikon (branded as "phase fresnel" or PF), and 800mm f/11, 600mm f/11, and 400mm f/4 models by Canon (branded as "diffractive optics" or DO). They produce sharp images with reduced chromatic aberration at a lower weight and size than traditional optics of similar specifications and are generally well-regarded by wildlife photographers.<ref>{{cite web |last1=Hogan |first1=Thom |title=Nikon 500mm f/5.6E PF Lens Review |url=https://www.dslrbodies.com/lenses/nikon-lens-reviews/nikkor-prime-lens-reviews/nikon-500mm-f56e-pf-lens.html |website=byThom |access-date=10 October 2022}}</ref>

{{Multiple image
| align             = left
| direction         = horizontal
| header            = 
| footer            = 
| width1            = 250
| image1            = Chromatic aberration lens diagram.svg
| alt1              = Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths.
| caption1          = Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths.
| width2            = 272
| image2            = diffractive.png
| alt2              = Diffractive optical element with complementary dispersion properties to that of glass can be used to correct for color aberration
| caption2          = Diffractive optical element with complementary dispersion properties to that of glass can be used to correct for color aberration.
| width3            = 250
| image3            = Lens6b-en.svg
| alt3              = For an [[achromatic doublet]], visible wavelengths have approximately the same focal length.
| caption3          = For an [[achromatic doublet]], visible wavelengths have approximately the same focal length.
}}
{{Clear}}

===Mathematics of chromatic aberration minimization===

For a doublet consisting of two thin lenses in contact, the [[Abbe number]] of the lens materials is used to calculate the correct focal length of the lenses to ensure correction of chromatic aberration.<ref>Sacek, Vladmir. [http://www.telescope-optics.net/designing_doublet_achromat.htm "9.3. DESIGNING DOUBLET ACHROMAT."] telescope-optics.net</ref> If the focal lengths of the two lenses for light at the yellow [[Fraunhofer lines|Fraunhofer]] D-line (589.2&nbsp;nm) are ''f''<sub>1</sub> and ''f''<sub>2</sub>, then best correction occurs for the condition:
:<math>f_1 \cdot V_1 + f_2 \cdot V_2 = 0</math>
where ''V''<sub>1</sub> and ''V''<sub>2</sub> are the Abbe numbers of the materials of the first and second lenses, respectively. Since Abbe numbers are positive, one of the focal lengths must be negative, i.e., a diverging lens, for the condition to be met.

The overall focal length of the doublet ''f'' is given by the standard formula for thin lenses in contact:
:<math>\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}</math>
and the above condition ensures this will be the focal length of the doublet for light at the blue and red Fraunhofer F and C lines (486.1&nbsp;nm and 656.3&nbsp;nm respectively). The focal length for light at other visible wavelengths will be similar but not exactly equal to this.

Chromatic aberration is used during a [[duochrome test|duochrome eye test]] to ensure that a correct lens power has been selected. The patient is confronted with red and green images and asked which is sharper. If the prescription is right, then the cornea, lens and prescribed lens will focus the red and green wavelengths just in front, and behind the retina, appearing of equal sharpness. If the lens is too powerful or weak, then one will focus on the retina, and the other will be much more blurred in comparison.<ref>{{Cite journal
 | pmid = 1469739
| year = 1992
| last1 = Colligon-Bradley
| first1 = P
| title = Red-green duochrome test
| journal = Journal of Ophthalmic Nursing & Technology
| volume = 11
| issue = 5
| pages = 220–2
}}</ref>