## CIE – 1931-System

In the early 20th century, the wish for an objective method of determining colours became increasingly apparent. A colour-system was required without the need for samples. The *(Detailed text)*

Mathematical constructions can certainly have their aesthetic appeal, and the colour diagram which we show here is no exception. This type of

In the early 20th century, the wish for an objective method of determining colours to overcome this weakness became increasingly apparent. A colour system was required without the need for samples, so the CIE («Commission International d’Eclairage») was engaged to produce a «

Its starting point was the indirect method of comparison which we have already described («colour match»). Here, a colour is measured by enabling an observer to compare it, using a suitable apparatus, with an (additive) mixture of three elementary colours. The term used here is the «tristimulus value». «Colour» in this case means «wavelength», and using the method described, we can establish the proportions of red, green and blue which will be seen in light with a wavelength, for example of 520 nm. An observer makes the appropriate adjustment to his apparatus and the result obtained is recorded as three digits, to which we shall assign the letters R, G and B. (That we are here concerned with the energy of the specific radiation being measured is of no consequence to the CIE diagram.)

Such experiments have been providing the basis for objective colour measurement since the establishment of «colour matching functions» in the 1920s, mainly by W. D. Wright and J. Gould in England. Wright and Gould required a large number of normally sighted people to manipulate three constant-energy sources of monochromatic light (light of only one wavelength), in order to achieve a match with the primary colours. From the tristimulus values thus obtained, mean values can be derived which in turn are used to construct the colour matching functions by plotting their locus according to wavelength. These figures were accepted by the CIE in 1931, and related to a hypothetical «standard observer». In addition, the CIE stipulated that a colour-sample was to be measured under conditions of average daylight — identified as ‘C’ — which at that time still had to compete with a defined artificial light source ‘A’ and the sunlight of midday ‘B’ for recognition as the standard reference. (These letters can be seen in the diagram.)

The CIE adopted these measured colour matching functions — but not without first giving them a mathematical tweak so that only positive values would arise for the new colour matches. This certainly proved advantageous when making calculations, but caused a lack of clarity in the reference values used. While the old Maxwellian trichromatic values R, G and B could still be related to primary colours, this was no longer possible with the CIE’s new «tristimulus values» of X, Y and Z (in spite of the choice being such that white is represented by equal values for X, Y and Z). Nevertheless, they can still be converted in the same way as Maxwell had done, and this will result in the colour-table shown.

The CIE wished to promote the study of colours using a colour-map similar to the way the study of geography is simplified by using two dimensional maps. In order, therefore, to omit one dimension, three new variables x, y and z (colour-masses) were derived from the three measured values of X, Y and Z by dividing each of these numbers by their total sum: x = X/(X + Y + Z) and so forth. With this conversion, it is important that the sums of the colour-masses add up to one (x + y + z = 1). Only two of the new values thus remain independent, and these can be shown on a two-dimensional chart (a map, in fact). The CIE diagram does just this: the horizontal axis represents the values for x, and the vertical axis the values for y.

The chromaticity diagram shown will result if a line is drawn through the points which plot the positions of the converted tristimulus values relating to the various specified wavelengths. Since the range of wavelengths between 770 nm and 450 nm is concerned with the spectral colours, we also call these positions «spectrum loci». If spectral light with a wavelength of 400 nm (left-hand edge intersection) is mixed with light of 770 nm (right-hand end point), we can see that all resulting colours must lie on the line which connects these two points. By plotting this, the so-called purple line will result, to complete the diagram.

Although the CIE diagram is based on the ability of the human eye to match colours, it is a mathematical construction all the same, with the advantage that the position of each colour in relation to each of the primary colours can be calculated — indeed independently from any particular source of illumination. The chromaticity diagram also gains significance because all existing colours must lie within the tongue shape delineated by both the above-mentioned lines. The light sources A, B and C must first be specified, however. They are located on a curve which is marked with digits. These digits represent temperatures based on a law of physics which states that light radiating from a black-body — a colour therefore — is linked with its temperature. If, for example, glowing coal or boiling steel are subjected to further heating, their colour will change. Colours and temperature are interrelated; physics will state that the midday light of the sun has a value of 4870° Kelvin and a typical lamp perhaps 2854° K. The light of the rising sun is approximately 1800° K in warmth (Kelvin is the unit of value on the absolute temperature scale. 0° Kelvin (absolute zero) = -273.16 °C).

The CIE diagram is only one plane within a colour-space which records the sensation of light. Other planes represent

In addition to the measurement of colour, the CIE diagram can also be used to name colours. The division shown below and to the right originates with

**Date:** The so-called “Colour Standard Table” of the “Commission International d’Eclairage” has existed since 1931.

**Country of origin:** Commission Internationale d’Eclairage

**Basic colours:** Red, green and blue

**Form:** Diagram

**Related systems:**

**Bibliography:** G. Wyszecki und W. S. Stiles, «Color Science», New York 1967; D. B. Judd und G. Wyszecki, «Color in Business, Science, and Industry», New York 1975; G. A. Agoston, «Color Theory and Its Application in Art and Design», Heidelberg 1979.