# Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

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

• Stephen Westland
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_10

## Definition

The coordinates of the CIE 1960 UCS diagram are calculated from the 1931 CIE XYZ tristimulus value or from the xy chromaticity coordinates thus:
$$\begin{array}{l}u=4X/\left(X+15Y+3Z\right)=4x/\left(-2x+12y+3\right),\\ {}v=6Y/\left(X+15Y+3Z\right)=6y/\left(-2x+12y+3\right).\end{array}$$
(1)
The 1976 CIE uv′ chromaticity diagram was obtained by stretching the v-axis of the UCS diagram (u′ = u, v′ = 1.5v), and the coordinates are calculated thus:
$$\begin{array}{l}u^{\prime }=4X/\left(X+15Y+3Z\right)=4x/\left(-2x+12y+3\right),\\ {}v^{\prime }=9Y/\left(X+15Y+3Z\right)=9y/\left(-2x+12y+3\right),\end{array}$$
(2)
where, alternatively, U′ = 4X/9, V′ = Y, and W′ = −X/3 + 2Y/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 uv′ 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].

However, many years earlier it had been suggested, by König, for example, that “it ought not to be difficult in the construction of a chromaticity diagram so to modify the adopted arbitrary assumptions that the separation of two points on it would give a measure for the difference in sensation between the colors corresponding to them” [3]. Following work by Judd, in 1935 a Maxwell triangle yielding approximately uniform chromaticity scales (known as the UCS diagram) was defined by reference to the CIE system, and in 1937 MacAdam developed a rectangular coordinate system based on the simple transformation of tristimulus values. In 1959 at a meeting in Brussels, the CIE recommended the 1937 MacAdam 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).
If compared with the 1931 chromaticity diagram, the effect of the linear transformation was to elongate the blue-red portions of the diagram and to relocate the white point to reduce the size of the green area. Although not perfectly uniform, the UCS diagram was thought to be an almost optimal transformation from the 1931 space [2] and was deemed to be sufficient for most practical purposes [4]. However, at a meeting in London in 1975, the CIE proposed modifying the UCS diagram and replaced it with the uv′-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 uv′, 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 uv′ 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 uv′ 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.

## References

1. 1.
CIE Pub. No. 15: Colorimetry, Central Bureau of the CIE, Vienna (2004)Google Scholar
2. 2.
Hunt, R.W.G.: The Reproduction of Colour, 6th edn. Wiley, Chichester (2004)
3. 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)
4. 4.
Wright, H.: The Measurement of Colour, 4th edn. Adam Hilger, London (1969)Google Scholar
5. 5.
Hunt, R.W.G., Pointer, M.R.: Measuring Colour, 4th edn. Wiley, Hoboken (2011)