In
opticsOptics is the branch of physics which studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
,
chromatic aberration (also called
achromatism) is the failure of a
lensA lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens is a lens consisting of a single optical element...
to
focusIn geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
all
colorColor or colour is the visual perceptual property corresponding in humans to the categories called red, yellow, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...
s to the same point. It occurs because lenses have a different
refractive indexThe refractive index of a medium is a measure of how much the speed of light is reduced inside the medium. For example, typical soda-lime glass has a refractive index close to 1.5, which means that in glass, light travels at 1 / 1.5 = 2/3 the speed of light in a vacuum...
for different wavelengths of
lightLight is electromagnetic radiation, particularly radiation of a wavelength that is visible to the human eye ....
(the
dispersionIn optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
of the lens). The refractive index decreases with increasing wavelength.
Chromatic
aberrationAberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge...
manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image, because each color in the optical spectrum cannot be focused at a single common point on the optical axis.
Since the
focal lengthThe focal length of an optical system is a measure of how strongly it converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...
f of a lens is dependent on the refractive index
n, different wavelengths of light will be focused on different positions. Chromatic aberration can be both
longitudinal, in that different wavelengths are focused at a different distance from the lens; and
transverse or
lateral, in that different wavelengths are focused at different positions in the focal plane (because the
magnificationMagnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called magnification...
of the lens also varies with wavelength).
Minimizing chromatic aberration
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 telescopes such as the very long
aerial telescopeAn aerial telescope is a type of very-long-focal-length refracting telescope built in the second half of the 17th century that did not use a tube. Instead, the objective was mounted on a pole, tree tower, building or other structure on a swivel ball-joint. The observer stood on the ground and held...
s of the 17th century.
Isaac NewtonSir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history...
's theories about
white lightWhite Light may refer to:* Light with the color white*White Light/White Heat , The Velvet Underground's second album.*White Light , a 1971 album*White Light a 1980 novel by Rudy Rucker...
being composed of a
spectrumA spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...
of colors led him to the conclusion that uneven refraction of light caused chromatic aberration (leading him to build the first
reflecting telescopeA reflecting telescope is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from...
, his
newtonian telescopeThe Newtonian telescope is a type of reflecting telescope invented by the British scientist Sir Isaac Newton , using a concave primary mirror and a flat diagonal secondary mirror. Newton’s first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope...
, in 1668).
There exists a point called the
circle of least confusion, where chromatic aberration can be minimized. It can be further minimized by using an
achromatic lensAn 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 into focus in the same plane....
or
achromat, in which materials with differing dispersion are assembled together to form a compound lens. The most common type is an achromatic
doubletIn optics, a doublet is a type of lens made up of two simple lenses attached together. The lenses are made from glasses with different refractive indices and different amounts of dispersion. Often one element is made from crown glass and the other from flint glass. This combination produces a...
, with elements made of
crownCrown glass is type of optical glass used in lenses and other optical components.Crown glass is produced from alkali-lime silicates containing approximately 10% potassium oxide...
and
flint glassFlint glass is optical glass that has relatively high refractive index and low Abbe number. 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...
. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. 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.
Many types of
glassIn general Glass refers to a solid, brittle, transparent material, commonly used for windows, bottles, or eyewear. Examples of glassy materials include, but are not limited to, soda-lime glass, borosilicate glass, acrylic glass, sugar glass, Muscovy-glass, or aluminium oxynitride. The term glass...
have been developed to reduce chromatic aberration, most notably, glasses containing
fluoriteFluorite is a halide mineral composed of calcium fluoride, CaF
2. It is an isometric mineral with a cubic habit, though octahedral and more complex isometric forms are not uncommon. Cubic crystals up to 20 cm across have been found at Dalnegorsk, Russia...
. 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.
The use of achromats was an important step in the development of the
optical microscopeA microscope is an instrument to see objects too tiny for the naked eye. The science of investigating small objects using such an instrument is called microscopy. Microscopic means invisible to the eye unless aided by a microscope.-History:An early microscope was made in 1590 in Middelburg, The...
and in telescopes.
An alternative to achromatic doublets is the use of diffractive optical elements. Diffractive optical elements have complementary dispersion characteristics to that of optical glasses and plastics. In the visible part of the spectrum, diffractives have an
Abbe numberIn physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...
of -3.5. Diffractive optical elements can be fabricated using diamond turning techniques.
Mathematics of chromatic aberration minimization
For a doublet consisting of two thin lenses in contact, the
Abbe numberIn physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...
of the lens materials is used to calculate the correct focal length of the lenses to ensure correction of chromatic aberration. If the focal lengths of the two lenses for light at the yellow
FraunhoferFraunhofer may refer to:*Joseph von Fraunhofer , German physicist*Fraunhofer , a lunar crater*Fraunhofer Society , a research society, owner of mp3 technology*Fraunhofer diffraction, far-field diffraction...
D-line (589.2 nm) are
f1 and
f2, then best correction occurs for the condition:
where
V1 and
V2 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:
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 nm and 656.3 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 an 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.
Image processing to reduce chromatic aberration
Post-processing to remove chromatic aberration usually involves scaling the fringed color channel, or subtracting some of a scaled version of the fringed channel.
Since for some lenses, degree of chromatic aberration can have quite a complex relationship to the rectangular geometry of the projected image received by the camera focal plane, geometrical operations to reverse the aberration may be quite complex, and software may not have sufficient complexity and data to be able to properly correct an image, even when the subjects affected are in approximately the same focal plane.
All Panasonic Lumix cameras, and some recent Nikon DSLR's, do such processing automatically in camera.
Photography
The term "
purple fringingIn photography, and particularly in digital photography, purple fringing is the term for an out-of-focus purple ghost image on a photograph. Images taken with high-contrast boundary areas involving daylight or gas discharge lamps are particularly susceptible, since chromatic aberration is worst...
" is commonly used in
photographyPhotography is the process, activity and art of creating still or moving pictures by recording radiation on a sensitive medium, such as a photographic film, or an electronic sensor...
, although not all purple fringing can be attributed to chromatic aberration.
Similar colored fringing around highlights may also be caused by
lens flareLens flare is the light scattered in lens systems through generally unwanted image formation mechanisms, such as internal reflection and scattering from material inhomogeneities in the lens. These mechanisms differ from the intended image formation mechanism that depends on refraction of the image...
. Colored fringing around highlights or dark regions may be due to the receptors for different colors having differing
dynamic rangeDynamic range is a term used frequently in numerous fields to describe the ratio between the smallest and largest possible values of a changeable quantity, such as in sound and light...
or
sensitivityStimulus|Sensitivity may refer to:* Sensitivity * Allergic sensitivity* Sensitivity * Sensitivity * Information sensitivity* Sensitivity and specificity are related concepts in statistics* Sensitivity analysis...
-- therefore preserving detail in one or two color channels, while "blowing out" or failing to register, in the other channel or channels. On digital cameras, the particular
demosaicingA demosaicing algorithm is a digital image process used to reconstruct a full color image from the incomplete color samples output from an image sensor overlaid with a color filter array...
algorithm is likely to affect the apparent degree of this problem. Another cause of this fringing is chromatic aberration in the very small
microlensMicrolenses are small lenses, generally with diameters less than a millimetre and often as small as 10 micrometres . The small sizes of the lenses means that a simple design can give good optical quality but sometimes unwanted effects arise due to optical diffraction at the small features...
es used to collect more light for each CCD pixel; since these lenses are tuned to correctly focus green light, the incorrect focusing of red and blue results in purple fringing around highlights. This is a uniform problem across the frame, and is more of a problem in CCD's with a very small pixel pitch such as those used in compact cameras. Some cameras, such as the Panasonic
LumixLumix is Panasonic's brand of digital cameras, ranging from pocket point-and-shoot models to digital SLRs. Many Lumix models are fitted with Leica lenses that have been designed by Leica's German optical engineers and are assembled in Japan, some are rebadged as Leica cameras with different...
series and newer
Nikon , also known as Nikon or Nikon Corp., is a multinational corporation headquartered in Tokyo, Japan specializing in optics and imaging...
DSLRs, feature a processing step specifically designed to remove it.
On photographs taken using a digital camera, very small highlights may frequently appear to have chromatic aberration where in fact the effect is because the highlight image is too small to stimulate all three color pixels, and so is recorded with an incorrect color. This may not occur with all types of digital camera sensor. Again, the demosaicing algorithm may affect the apparent degree of the problem.
Black-and-white photography
Chromatic aberration also affects black and white photography. Although there are no colors in the photograph, chromatic aberration will blur the image. It can be reduced by using a narrow-band color filter, or by converting a single color channel to black and white. This will, however, require longer exposure. (This of course is only true with panchromatic black and white film, since
orthochromaticOrthochromatic refers to any spectrum of light that is devoid of red light.- Orthochromatic photography :Orthochromatic photography refers to a photographic emulsion that is sensitive to only blue and green light, and thus can be processed with a red safelight. Using it, blue objects appear lighter...
film is already sensitive to only a limited spectrum.)
See also
- Aberration in optical systems
Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge...
- Achromatic telescope
The achromatic telescope is a refracting telescope that uses an achromatic lens to correct for chromatic aberration.-How it works:When an image passes through a lens, the light is diffracted at different angles for different wavelengths. This produces focal lengths that are dependent on the color...
- Apochromatic lens
- Cooke triplet
The Cooke triplet is a photographic lens designed and patented in 1893 by Dennis Taylor who was employed as chief engineer by Cooke of York. It was the first lens system that allowed elimination of most of the optical distortion or aberration at the outer edge of lenses.A Cooke triplet comprises a...
- Superachromat
The superachromat or superachromatic lens was first conceived and developed by Max Herzberger as the ultimately well-corrected lens. The color shift curve of a superachromat is a quartic, meaning that in theory four separate colors can be brought to focus in the same plane, while simultaneously...
- Theory of Colours
Theory of Colours is a book by Johann Wolfgang von Goethe published in 1810. The work comprises three sections: i) a didactic section in which Goethe presents his own observations, ii) a polemic section in which he makes his case against Newton, and iii) a historical section...
External links