# USC Diagrams; Uniform Chromaticity Scales; Yu′v′

**DOI:**https://doi.org/10.1007/978-1-4419-8071-7_10

## Definition

*XYZ*tristimulus value or from the

*xy*chromaticity coordinates thus:

*u*′

*v*′ chromaticity diagram was obtained by stretching the

*v*-axis of the UCS diagram (

*u*′ =

*u*,

*v*′ = 1.5

*v*), and the coordinates are calculated thus:

*U*′ = 4

*X*/9,

*V*′ =

*Y*, and

*W*′ = −

*X*/3 + 2

*Y*/3 +

*Z*/3 and

*u*′ =

*U*′ /(

*U*′ +

*V*′ +

*W*′) and

*v*′ =

*V*′ /(

*U*′ +

*V*′ +

*W*′).

Both the CIE 1960 UCS diagram and the 1976 CIE *u*′*v*′ chromaticity diagram are associated with the 1931 *Y* tristimulus value to provide a complete trichromatic specification since *V* = *V′* = *Y*.

## Historical Development

The 1931 CIE system of colorimetry [1] allowed color stimuli to be defined in terms of tristimulus values XYZ but does not provide a particularly uniform representation of color stimuli in visual terms. If lines are drawn on the CIE 1931 chromaticity diagram that represent equal perceptual steps, then the disparity in the lengths of the lines is as great as 20 times, with the lines in the green region, for example, being much longer than those in the blue region [2].

*uv*-diagram for use whenever a projective transformation of the CIE

*xy*-diagram is desired to give uniform chromaticity spacing [4]. This space became known as the CIE 1960 UCS diagram (Fig. 1).

*u*′

*v*′-diagram stretching the v-axis (

*v*′ = 1.5v). The resulting diagram was adopted as the CIE 1976 UCS diagram (Fig. 2).

## Properties and Current Status

All chromaticity diagrams, whether *xy*, *uv*, or *u*′*v*′, have the property that additive mixtures of colors are represented by points lying on the straight line joining the points representing the constituent colors [5]. However, the CIE 1960 UCS diagram and the 1976 CIE *u*′*v*′ diagram represent substantial improvements over the 1931 CIE *xy* chromaticity diagram in terms of the visual uniformity of the spaces. Whereas lines that represent equal perceptual steps drawn on the CIE 1931 chromaticity diagram differ in length by as much as 20 times, the same lines drawn on the CIE 1976 *u*′*v*′ diagram differ in length by about four times (and over much of the diagram, the difference is not greater than two to one) [2].

CIE 1976 UCS is useful for showing the relationships between colors whenever interest lies in their discriminability. However, it is mainly used for the representation of self-emissive colors on display devices or those produced directly from light sources since the diagram assumes that colors are of equal luminance (this condition is rarely met in practice with reflective surface colors). Note, however, that CIELUV, the first approximately uniform three-dimensional space, is a transformation of the CIE 1976 UCS chromaticity coordinates *u*′, *v*′, and *Y*.

## Cross-References

### References

- 1.CIE Pub. No. 15: Colorimetry, Central Bureau of the CIE, Vienna (2004)Google Scholar
- 2.Hunt, R.W.G.: The Reproduction of Colour, 6th edn. Wiley, Chichester (2004)CrossRefGoogle Scholar
- 3.Judd, D.B., Yonemura, G.T.: CIE 1960 UCS diagram and the muller theory of color vision. J. Res. Natl. Bur. Stand. A. Phys. Chem.
**74A**(1), 23–30 (1970)CrossRefGoogle Scholar - 4.Wright, H.: The Measurement of Colour, 4th edn. Adam Hilger, London (1969)Google Scholar
- 5.Hunt, R.W.G., Pointer, M.R.: Measuring Colour, 4th edn. Wiley, Hoboken (2011)CrossRefGoogle Scholar