Chromaticity

[kroh-muh-tis-i-tee]

Chromaticity is an objective specification of the quality of a color regardless of its luminance, that is, as determined by its colorfulness (or saturation, chroma, intensity, or excitation purity) and hue.

In color science, the white point of an illuminant or of a display is a neutral reference characterized by a chromaticity; for example, the white point of an sRGB display is an x,y chromaticity of [0.3127,0.3290]. All other chromaticities may be defined in relation to this reference using polar coordinates. The hue is the angular component, and the purity is the radial component, normalized by the maximum radius for that hue.

Chromaticity in color science

Purity is roughly equivalent to the term "saturation" in the HSV color model. The property "hue" is as used in general color theory and in specific color models such as HSV or HSL, though it is more perceptually uniform in color models such as Munsell, CIELAB or CIECAM02.

Some color spaces separate the three dimensions of color into one luminance dimension and a pair of chromaticity dimensions. For example, the chromaticity coordinates are a and b in Lab color space, u and v in Luv color space, x and y in xyY space, etc. These pairs define chromaticity vectors in a rectangular 2-space, unlike the polar coordinates of hue angle and saturation that are used in HSV color space.

On the other hand, some color spaces such as RGB and XYZ do not separate out chromaticity; chromaticity coordinates such as r and g or x and y can be calculated by an operation that normalizes out intensity.

The xyY space is a cross between the CIE XYZ color space and its normalized chromaticity coordinates xyz, such that the luminance Y is preserved and augmented with just the required two chromaticity dimensions.

Chromaticity in accelerator physics

There are many parallels between accelerator physics and optics. Since a bunch of charged particles has a tendency to disperse over time, it is important to include numerous magnets of different types along the beam line in order to keep the beam well controlled, and tightly bunched. When quadrupole magnets are used, this is known as beam focusing. Focusing the beam in this way, however, can lead to problems if the bunch contains particles of differing energy. In this case, the low energy particles will be focused much more tightly than high energy particles -- exactly in the same way that longer wavelengths of light (i.e. the lower energy photons), will be brought to a focus more quickly than short wavelengths.

In the case of a storage ring, a high degree of chromaticity can lead to instabilities in the beam's motion, which will result in large movements of the beam. This will eventually cause the beam to hit the wall of the chamber and be lost and/or damage the machine. For this reason it is advantageous to correct the chromaticity introduced by bending and focusing magnets. This can be done with sextupole magnets.

Thus it can be seen that the chromaticity of a beam is an indication of the energy spread of its constituent particles, in much the same way that the chromaticity of light is an indication of the energy spread of its constituent photons.