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Color

For alternate meanings, see color (disambiguation).

Table of contents

1 The physics of color 1.1 Spectral versus non-spectral colors 1.2 Color in the wave equation 2 Color vision 3 Human color models 3.3 Tristimulus color space 3.4 Tristimulus color space as a mathematical projection 3.5 CIE XYZ color space 4 Reproduction of color 4.6 Pigments and reflective media 4.7 RGB color space 4.8 CMYK color model 4.9 HSV color space 5 Color perception 5.10 Effect of luminosity 5.11 Cultural influences 5.12 Color constancy 6 Miscellaneous 6.13 Structural color 6.14 Associations 6.15 Color systems 6.16 Contrast 7 See also 8 External links

The physics of color

The colors of the visible light spectrum.

color	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 spectrum Designed for monitors with gamma 1.5.

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 rainbow spectrum—named from the Latin word for image by Isaac Newton in 1666—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.

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, 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 will be perceived as the same color as a pure spectum. In the table above, for instance, the "orange" patch is not emitting pure light at a fixed wavelength of around 600nm. Instead, you see a mixture of about two parts red to one part green light. We cannot tell the difference, and the reason has to do with the pigments that make up our color vision cells (see below).

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

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:

u_tt=c²(u_xx+u_yy+u_zz)

Color vision

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.

The human eye contains three different types of color receptor cells, or cones. The first ("red" or "long-wavelength") are most responsive to wavelengths around 565 nm, the second ("green" or "middle-wavelength") to those around 535 nm, and the third ("blue" or "short-wavelength") to those around 445 nm. 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, representing the intensity of the response of each of these types of color receptors. Note that the sensitivity curves do not really peak at red, green, and blue; hence the more correct names "short", "medium", and "long".

Because of the overlap between the sensitivity ranges, not all combinations of stimuli are actually possible. For example, it is not possible to stimulate only the "green" cone: at least one of the other cones will always be stimulated to some degree at the same time. The set of all combinations of stimuli that are possible make up the human color space. This is discussed in more detail in Human color space elsewhere in this article.

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 eyes of a single individual perceive colors slightly differently. If one or more types of a person's color-sensing cones isn't responding correctly to incoming light, that person has a smaller 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, most simply have anomalous color perception. Other animals may have more than three different color receptors (some birds and reptiles) or fewer (most mammals).

Human 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 into, 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 the same spectrum and intensity as the white screen on which it is projected. See also color constancy below.

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 whan 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 at 1931. This color space is based on the Standard Colorimetric Observer functions. The figure shows the related chromaticity diagram with wavelengths in nanometers.

In this diagram, x and y are related to the S, M, and L stimuli under Human tristimulus color space above according to:

x = L/(S + M + L),

y = M/(S + M + L).

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.

It must be noted that the tabulated sensitivity curves have a certain amount of arbitraryness in them. The shapes of the individual S, M, and L 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 S, M, and L curves are arbitrary. One could as well define a valid color space with an S sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 xyz color space are scaled to have equal areas under the curves. This scaling means that light with a flat energy spectrum corresponds to the point (x,y) = (0.333,0.333).

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.

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 below 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 reproduction 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.

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.

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.

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
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