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Color

(Redirected from Colors)
For alternative meanings, see color (disambiguation).

Color (American English) or colour (Commonwealth English) is a sensation which (in humans) derives from the ability of the fine structure of the eye to distinguish three differently filtered analyses of a view. The perception of color is influenced by long-term history (nurture) of the observer and also by short-term effects such as the colors nearby. The term color is also used for the property of objects or light sources that can be distinguished by differences in the receptors of the eye.

 Contents

The physics of colour

The colors of the visible light spectrum.

colour wavelength interval frequency interval
red ~ 625-740 nm ~ 480-405 THz
orange ~ 590-625 nm ~ 510-480 THz
yellow ~ 565-590 nm ~ 530-510 THz
green ~ 500-565 nm ~ 600-530 THz
cyan ~ 485-500 nm ~ 620-600 THz
blue ~ 440-485 nm ~ 680-620 THz
violet ~ 380-440 nm ~ 790-680 THz

Continuous optical spectrum

Designed for monitors with gamma 1.5.

Computer "spectrum"

The bars below show the relative intensities of the three
colors mixed to make the color immediately above.

Color, frequency, and energy of light.

Color $\lambda \,\!$/nm $\nu \,\!$/1014 Hz $\nu_b \,\!$/104 cm-1 $E \,\!$/eV $E \,\!$/kJ mol-1
Infrared >1000 <3.00 <1.00 <1.24 <120
Red 700 4.28 1.43 1.77 171
Orange 620 4.84 1.61 2.00 193
Yellow 580 5.17 1.72 2.14 206
Green 530 5.66 1.89 2.34 226
Blue 470 6.38 2.13 2.64 254
Violet 420 7.14 2.38 2.95 285
Near ultraviolet 300 10.0 3.33 4.15 400
Far ultraviolet <200 >15.0 >5.00 >6.20 >598

Electromagnetic radiation is a mixture of radiation of different wavelengths and intensities. When this radiation has a wavelength inside the human visibility range (approximately from 380 nm to 740 nm), it is called light. The light's spectrum records each wavelength's intensity. The full spectrum of the incoming radiation from an object determines the visual appearance of that object, including its perceived color. As we will see, there are many more spectra than color sensations; in fact one may formally define a color to be the whole class of spectra which give rise to the same color sensation, although any such definition would vary widely among different species and also somewhat among individuals intraspecifically.

A surface that diffusely reflects all wavelengths equally is perceived as white, while a dull black surface absorbs all wavelengths and does not reflect (for mirror reflection this is different: a proper mirror also reflects all wavelengths equally, but is not perceived as white, while shiny black objects do reflect).

The familiar colors of the rainbow in the spectrum—named from the Latin word for appearance or apparition by Isaac Newton in 1671—contains all those colors that consist of visible light of a single wavelength only, the pure spectral or monochromatic colors.

The frequencies are approximations and given in terahertz (THz). The wavelengths, valid in vacuum, are given in nanometers (nm). A list of other objects of similar size is available.

Important note!

The color table should not be interpreted as a definite list—the pure spectral colors form a continuous spectrum, and how it is divided into distinct colors is a matter of taste and culture; for example, Issac Newton identified the seven colors red, orange, yellow, green, blue, indigo, and violet, remembered by many school children using mnemonics such as Roy G. Biv and Richard Of York Gave Battle In Vain.

Similarly, the intensity of a spectral color may alter its perception considerably; for example, a low-intensity orange-yellow is brown, and a low-intensity yellow-green is olive-green.

Spectral versus non-spectral colors

Most light sources are not pure spectral sources; rather they are created from mixtures of various wavelengths and intensities of light. To the human eye, however, there is a wide class of mixed-spectrum light that is perceived the same as a pure spectral color. In the table above, for instance, when your computer screen is displaying the "orange" patch, it is not emitting pure light at a fixed wavelength of around 600 nm (which is in fact not a thing most computer screens are even able to do). Rather, it is emitting a mixture of about two parts red to one part green light. Were you to print this page on a color printer, the orange patch on the paper, when lit with white light, would reflect yet another, more continous spectrum. We cannot see those differences (although many animals can), and the reason has to do with the pigments that make up our color vision cells (see below).

A useful quantification of this property is the dominant wavelength, which matches a wavelength of spectral light to a non-spectral source that evokes the same color perception. Dominant wavelength is the formal background for the popular concept of hue.

In addition to the many light sources that can appear to be pure spectral colors but are actually mixtures, there are many color perceptions that by definition cannot be pure spectral colors due to desaturation or because they are purples (which do not appear in the Newtonian pure spectrum). Some examples of necessarily non-spectral colors are the achromatic colors (black, gray and white) and other colors such as pink, tan and magenta. See metamerism (color) for a basic intro to why color matching challenges exist.

Color in the wave equation

The wave equation describes the behavior of light and so we should be able to describe color spectra in terms of the mathematical properties of the solutions of the wave equation. However, to understand which particular color perception will arise from a particular physical spectrum requires knowledge of the specific retinal physiology of the observer. For completeness, we include a simple equation for light traveling in a vacuum:

utt=c2(uxx+uyy+uzz)

where the subscripts denote partial derivatives and c is the speed of light. If we fix (x,y,z) a point in space and look at the solution u(x,y,z,t) as a function of t, we obtain a signal. If we take the Fourier transform of this signal, we obtain a frequency decomposition as described above. Each frequency has an amplitude and phase. The frequency multiplied by Planck's constant h determines the energy of a photon of the relevant component. The square of the amplitude represents the intensity, which is the amount of energy transmitted per second through a unit area of a surface perpendicular to the light propagation. The phase information is much more mysterious because it is difficult to measure and observe. Humans cannot perceive phase effects of light except in special cases of interference (e.g. see thin-film optics) where phase effects lead to perceptible amplitude changes. Most light has randomly distributed phases, but lasers are more efficient when the photons all have the same phase.

Color vision

Though the exact status of color is a matter of current philosophical dispute, color is arguably a psychophysical phenomenon that exists only in our minds. (See Qualia, for some of that dispute.) A "red" apple does not give off "red light", and it is misleading to think of things that we see, or of light itself, as objectively colored at all. Rather, the apple simply absorbs light of various wavelengths shining on it to different degrees, in such a way that the unabsorbed light which it reflects is perceived as red. An apple is perceived to be red only because normal human color vision perceives light with different mixes of wavelengths differently—and we have language to describe that difference.
In 1931, an international group of experts called the Commission Internationale d'Eclairage (CIE) developed a mathematical color model. The premise used by the CIE is that color is the combination of three things: a light source, an object, and an observer. The CIE tightly controlled each of these variables in an experiment that produced the measurements for the system.

Although Aristotle and other ancient scientists speculated on the nature of light and color vision, it was not until Newton that light was correctly identified as the source of the color sensation. Goethe studied the theory of colors, and in 1801 Thomas Young proposed his trichromatic theory which was later refined by Hermann von Helmholtz. That theory was confirmed in the 1960s and will be described below.

Normalized typical human cone responses (and the rod response) to monochromatic spectral stimuli

The retina of the human eye contains three different types of color receptor cells, or cones. One type, relatively distinct from the other two, is most responsive to light that we perceive as violet, with wavelengths around 420 nm (cones of this type are sometimes called short-wavelength cones, S cones, or, most commonly but quite misleadingly, blue cones). The other two types are closely related genetically, and in chemistry and response, and each type is most responsive to light that we perceive as green or greenish. One of these types (sometimes called long-wavelength cones, L cones, or, misleadingly, red cones) is most sensitive to light we perceive as yellowish-green, with wavelengths around 564 nm; the other type (sometimes called middle-wavelength cones, M cones, or green cones) is most sensitive to light perceived as green, with wavelengths around 534 nm. The term "red cones" for the long-wavelength cones is deprecated as this type is actually maximally responsive to light we perceive as greenish, albeit longer wavelength light than that which maximally excites the mid-wavelength/"green" cones.

The sensitivity curves of the cones are roughly bell-shaped, and overlap considerably. The incoming signal spectrum is thus reduced by the eye to three values, sometimes called tristimulus values, representing the intensity of the response of each of the cone types.

Because of the overlap between the sensitivity ranges, some combinations of responses in the three types of cone are impossible no matter what light stimulation is used. For example, it is not possible to stimulate only the mid-wavelength/"green" cones: the other cones must be stimulated to some degree at the same time, even if light of some single wavelength is used (including that to which the target cones are maximally sensitive). The set of all possible tristimulus values determines the human color space. It has been estimated that humans can distinguish roughly 10 million different colors, although the identification of a specific color is highly subjective, since even the two eyes of a single individual perceive colors slightly differently. This is discussed in more detail below.

The rod system (which vision in very low light relies on exclusively) does not by itself sense differences in wavelength; therefore it is not normally implicated in color vision. But experiments have conclusively shown that in certain marginal conditions a combination of rod stimulation and cone stimulation can result in color discriminations not based on the mechanisms described above.

While the mechanisms of color vision at the level of the cones in the retina are well described in terms of tristimulus values (see above), color processing and perception above that base level are organized differently. A dominant theory of the higher neural mechanisms of color vision proposes three opponent processes, or opponent channels, constructed out of the raw input from the cones: a red-green channel, a blue-yellow channel, and a black-white ("luminance") channel. This theory does something to account for the structure of our subjective color experience (see discussion below). Blue and yellow are considered complementary colors, or opposites: you could not experience a bluish yellow (or a greenish red), any more than you could experience a dark brightness or a hot coldness. The four "polar" colors proposed as extremes in the two opponent processes other than black-white have some natural claim to being called primary colors. This is in competition with various sets of three primary colors proposed as "generators" of all normal human color experience (see below).

Clinical issues

If one or more types of a person's color-sensing cones are missing or less responsive than normal to incoming light, that person has a smaller or skewed color space and is said to be color deficient. Another term frequently used is color blind, although this can be misleading; only a small fraction of color deficient individuals actually see completely in black and white, and most simply have anomalous color perception. Some kinds of color deficiency are caused by anomalies in the number or nature of cones of the various types, as just described. Others (like central or cortical achromatopsia) are caused by neural anomalies in those parts of the brain where visual processing takes place.

Some animals may have more than three different types of color receptor (most marsupials, birds, reptiles, and fish; see tetrachromat, below) or fewer (most mammals; these are called dichromats and monochromats).

An unusual and elusive neurological condition sometimes affecting color perception is synaesthesia.

Tetrachromat

A normal human is a trichromat (from Greek: tri=three, chroma=color). In theory it may be possible for a person to have four, rather than three, distinct types of cone cell. Such a person might, depending on the neural processing of the input from these four types, be a tetrachromat (tetra=four). Such a person might have an extra and slightly different copy of either the medium- or long-wave cones. It is not clear that such people exist or that the human brain could actually process the information from such an extra cone type separately from the standard three.

Color perception

There is an interesting phenomenon which occurs when an artist uses a limited color palette: the eye tends to compensate by seeing any grey or neutral color as the color which is missing from the color wheel. E.g.: in a limited palette consisting of red, yellow, black, and white, a mixture of yellow and black will appear as a variety of green, a mixture of red and black will appear as a variety of purple, and pure grey will appear bluish.

When the eye shifts attention after viewing a color for some time, then the complement of that color (the color opposite to it in the color wheel) is perceived by the eye for some time wherever it moves. This effect of color perception was utilised by Vincent van Gogh, a Post-Impressionist painter.

Effect of luminosity

Note that the color experience of a given light mixture may vary with absolute luminosity, because both rods and cones are active at once in the eye, with each having different color curves, and rods taking over gradually from cones as the brightness of the scene is reduced. This effect leads to a change in color rendition with absolute illumination levels that can be summarised in the "Kruithof curve".

Cultural influences

Different cultures have different terms for colors, and may also assign some color names to slightly different parts of the spectrum, or have a different color ontology: for instance, the Japanese color aoi can be interpreted as meaning something between the Western color terms of "blue" and "green": green is regarded as a shade of aoi.

Some argue that color terms evolve. There are a limited number of universal "basic color terms" which begin to be used by individual cultures in a relatively fixed order. For example, a culture would start with only two terms, equivalent to black and white or dark and light, before adding subsequent colors closely in the order of red; green and yellow; blue; brown; and orange, pink, purple, and gray. Older arguments for this theory also stipulated that the acquisition and use of basic color terms further along the evolutionary order indicated a more complex culture with more highly developed technology.

A somewhat dated example of a universal color categories theory is Basic Color Terms: Their Universality and Evolution (1969) by Brent Berlin and Paul Kay . A more recent example of a linguistic determinism theory might be Is color categorisation universal? New evidence from a stone-age culture (1999) by Jules Davidoff et al. The idea of linguistically determined color categories is often used as evidence for the Sapir-Whorf hypothesis (Language, Thought, and Reality (1956) by Benjamin Lee Whorf).

Additionally, different colors are often associated with different emotional states, values, or groups, but these associations can vary between cultures. In one system, red is considered to motivate action; orange and purple are related to spirituality; yellow cheers; green creates cosiness and warmth; blue relaxes; and white is associated with either purity or death. These associations are described more fully in the individual color pages, and under color psychology.

Color constancy

The trichromatric theory discussed above is strictly true only if the whole scene seen by the eye is of one and the same color, which of course is unrealistic. In reality, the brain compares the various colors in a scene, in order to eliminate the effects of the illumination. If a scene is illuminated with one light, and then with another, as long as the difference between the light sources stays within a reasonable range, the colors of the scene will nevertheless appear constant to us. This was discovered by Edwin Land in the 1970s and led to his retinex theory of color constancy.

Contrast

Compare the visibility of the RGB primary and secondary colors against a white background:

 red green blue red+green green+blue red+blue red+green+blue zero light

Again, compare variations on gray backgrounds—#7f7f7f, #5f5f5f & #9f9f9f—the eight RGB primaries are equidistant from #7f7f7f in a 3-d geometrical representation of RGB color space—a reminder of the importance of background color for color perception.

Background = #7f7f7f

 red green blue red+green green+blue red+blue red+green+blue zero light

And let's look at black again, for completeness. (Note that your monitor background probably isn't perfectly black. Turn it off and see for yourself.)

Background = #00000

 red green blue red+green green+blue red+blue red+green+blue zero light

Color models

A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. The resulting set of colors is called color space. This section describes ways in which human color vision can be modeled.

Tristimulus color space

The human tristimulus color space.

One can picture this space as a region in three-dimensional Euclidean space if one identifies the x, y, and z axes with the stimuli for the long-wavelength (L), medium-wavelength (M), and short-wavelength (S) receptors. The origin, (S,M,L) = (0,0,0), corresponds to black. White has no definite position in this diagram; rather it is defined according to the color temperature or white balance as desired or as available from ambient lighting. The human color space is a horse-shoe-shaped cone such as shown here (see also CIE chromaticity diagram below), extending from the origin to, in principle, infinity. In practice, the human color receptors will be saturated or even be damaged at extremely-high light intensities, but such behavior is not part of the CIE color space and neither is the changing color perception at low light levels (see: Kruithof curve).

The most saturated colors are located at the outer rim of the region, with brighter colors farther removed from the origin. As far as the responses of the receptors in the eye are concerned, there is no such thing as "brown" or "gray" light. The latter color names refer to orange and white light respectively, with an intensity that is lower than the light from surrounding areas. One can observe this by watching the screen of an overhead projector during a meeting: one sees black lettering on a white background, even though the "black" has in fact not gotten darker than the white screen on which it is projected before the projector was turned on. The "black" areas have not actually become darker but appear "black" relative to the higher intensity "white" projected onto the screen around it. See also color constancy above.

The human tristimulus space has the property that additive mixing of colors corresponds to the adding of vectors in this space. This makes it easy to, for example, describe the possible colors (gamut) that can be constructed from the red, green, and blue primaries in a computer display.

Tristimulus color space as a mathematical projection

Continuing with our mathematical description of light using the wave equation, a good model for the way our receptors work can be explained in terms of Hilbert spaces and orthogonal projections. Indeed, as mentioned previously, the light going through point (x,y,z) in space is a signal. It is useful to think of this signal as some function in L2, the space of square-integrable functions. This space is a (infinite dimensional!) Hilbert space, which means that it has a useful notion of orthogonal projection.

Each receptor can be thought of as a unit vector. For instance, the red receptor would be some vector r of light, whose Fourier transform would be large in the 405 to 480 THz interval, and smaller elsewhere. If we take the Fourier transform of v and plot its absolute value, we obtain what is called the frequency response curve of the human red receptor.

Then, the amount of "red" present in any color will be the orthogonal projection onto the axis generated by the vector r. In fact, only the magnitude of the orthogonal projection onto r is measured by our receptors. There are two more vectors, one for blue and one for green. Therefore, our color perception is in fact limited to a three-dimensional subspace of the infinite dimensional space of all possible colors.

CIE XYZ color space

One of the first mathematically defined color spaces is the CIE XYZ color space (also known as CIE 1931 color space), created by the International Commission on Illumination in 1931. These data were measured for human observers and a 2-degree field of view. In 1964, supplemental data for a 10-degree field of view were published.

It must be noted that the tabulated sensitivity curves have a certain amount of arbitrariness in them. The shapes of the individual X, Y and Z sensitivity curves can be measured with a reasonable accuracy. However, the overall luminosity curve (which in fact is a weighted sum of these three curves) is subjective, since it involves asking a test person whether two light sources have the same brightness, even if they are in completely different colors. Along the same lines, the relative magnitudes of the X, Y, and Z curves are arbitrary. One could as well define a valid color space with an X sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 and 1964 xyz color space are scaled to have equal areas under the curves.

CIE 1931 chromaticity diagram

The figure on the left shows the related chromaticity diagram with wavelengths in nanometers.

In this diagram, x and y are related to the X, Y, and Z tristimulus values under Human tristimulus color space above according to:

x = X/(X + Y + Z),
y = Y/(X + Y + Z).

Mathematically, x and y are projective coordinates and the colors of the chromaticity diagram occupy a region of the real projective plane. Because the CIE sensitivity curves have equal areas under the curves, light with a flat energy spectrum corresponds to the point (x,y) = (0.333,0.333).

The values for X, Y, and Z are obtained by integrating the product of the spectrum of a light beam and the published color-matching functions. Blue and red wavelengths do not contribute strongly to the luminosity, which is illustrated by the following example:

 red green blue red+green green+blue red+blue red+green+blue zero light

For someone with normal color vision, green is brighter than red, which is brighter than blue. Even though the pure blue appears to be very dark and hardly discernible from black when observed from a distance, blue has a strong coloring power when mixed with green or red.

With some forms of "red-green color blindness" the green is very slightly brighter than the blue, and the red is so dark it can barely be made out. Red traffic lights in bright daylight appear broken (no light). The green traffic light appears dirty white and hard to distinduish from night street lights.

The CIE-xyz color space is a prism, as opposed to the cone-shaped tristimulus space above. In the two-dimensional xy representation, all possible additive mixtures of two colors A and B form a straight line. However, the additive mixture of two colors does generally not lie on the mid-point of this line.

RGB color space

Media that transmit light (such as television) use additive color mixing with primary colors of red, green, and blue, each of which stimulates one of the three types of the eye's color receptors with as little stimulation as possible of the other two. This is called "RGB" color space—see also RGB color model. Mixtures of light of these primary colors cover a large part of the human color space and thus produce a large part of human color experiences. This is why color television sets or color computer monitors need only produce mixtures of red, green and blue light. See Additive color.

Other primary colors could in principle be used, but with red, green and blue the largest portion of the human color space can be captured. Unfortunately there is no exact consensus as to what loci in the chromaticity diagram the red, green, and blue colors should have, so the same RGB values can give rise to slightly different colors on different screens.

CMYK color model

It is possible to achieve a large range of colors seen by humans by combining cyan, magenta, and yellow transparent dyes/inks on a white substrate. These are the subtractive primary colors. Often a fourth black is added to improve reproduction of some dark colors. This is called "CMY" or "CMYK" color space.

The cyan ink will reflect all but the red light, the yellow ink will reflect all but the blue light and the magenta ink will reflect all but the green light. This is because cyan light is an equal mixture of green and blue, yellow is an equal mixture of red and green, and magenta light is an equal mixture of red and blue.

HLS color space

The HLS color space, also called HSL, stands for "Hue, Saturation, Lightness". While HSV (Hue, Saturation, Value) can be viewed graphically as a color cone or hexcone, HSL is drawn as a double cone or double hexcone. Both systems are non-linear deformations of the RGB color cube. The two apexes of the HLS double hexcone correspond to black and white. The angular parameter corresponds to hue, distance from the axis corresponds to saturation, and distance along the black-white axis corresponds to lightness.

HSV color space

The RGB and CMYK color spaces are most useful for technical reproduction of color scenes. A color space used in computer graphics that more closely models the human experience is the HSV color space which arranges colors in a cylinder, somewhat similar to the CIE-xyz space discussed above. The cross-section of the cylinder is a color wheel, but instead of pure spectral colors, the edge consists of additive mixtures of red, green, and blue. In the HSV color space, every color is specified by its hue (position on the circle), saturation (distance from the circle's center) and value (luminosity). The basic idea of the HSV color space was already used by 19th century physiologist Ewald Hering, although the modern definition dates from the 1970s. The HSV color space is also sometimes referred to as the HSB (hue-saturation-brightness) color space.

Color systems

There are various types of color systems that classify color and analyse their effects. The Munsell color system is a famous classification that organises various colors into a color solid based on hue, saturation and value.

Reproduction of color

Two different light spectra which have the same effect on the three color receptors in the human eye will be perceived as the same color. This is exemplified by the white light that is emitted by fluorescent lamps, which typically has a spectrum consisting of a few narrow bands, while daylight has a continuous spectrum. The human eye cannot tell the difference between such light spectra just by looking into the light source, although reflected colors from objects can look different.

Similarly, most human color perceptions can be generated by a mixture of three colors called primaries. This is used to reproduce color scenes in photography, printing, television, and other media.

No mixture of colors, though, can produce a fully pure color perceived as completely identical to a spectral color, although one can get very close for the longer wavelengths, where the chromaticity diagram above has a nearly straight edge. For example, mixing green light (530 nm) and blue light (460 nm) produces cyan light that is slightly desaturated, because response of the red color receptor would be greater to the green and blue light in the mixture than it would be to a pure cyan light at 485 nm that has the same intensity as the mixture of blue and green.

Because of this, and because the primaries in color printing systems generally are not pure themselves, the colors reproduced are never perfectly saturated colors, and so spectral colors cannot be matched exactly. However, natural scenes rarely contain fully saturated colors, thus such scenes can usually be approximated well by these systems. The range of colors that can be reproduced with a given color reproduction system is called the gamut. The CIE chromaticity diagram can be used to describe the gamut.

Another problem with color reproduction systems is connected with the acquisition devices, like cameras or scanners. The characteristics of the color sensors in the devices are often very far from the characteristics of the receptors in the human eye. In effect, acquisition of colors that have some special, often very "jagged", spectra caused for example by unusual lighting of the photographed scene can be relatively poor.

Species that have color receptors different from humans, e. g. birds that may have four receptors, can differentiate some colors that look the same to a human. In such cases, a color reproduction system `tuned' to a human with normal color vision may give very inaccurate results for the other observers.

Pigments and reflective media

When producing a color print or painting a surface, the applied paint changes the surface; if the surface is then illuminated with white light (which consists of equal intensities of all visible wavelengths), the reflected light will have a spectrum corresponding to the desired color. If a dab of paint looks red in white light, that is because the reflection of all non-red wavelengths is interrupted by the pigment, such that only red light is reflected into one's eye.

Structural color

Structural color is a property of some surfaces that are scored with fine parallel lines, formed of many thin parallel layers, or otherwise composed of periodic microstructures on the scale of the color's wavelength, to make a diffraction grating. The grating reflects some wavelengths more than others due to interference phenomena, causing white light to be reflected as colored light. Variations in the pattern's spacing often give rise to an iridescent effect, as seen in peacock feathers, films of oil, and mother of pearl, because the reflected color depends upon the viewing angle.

Structural color is studied in the field of thin-film optics. A layman's term that describes particularly the most ordered structural colors is iridescence.