colorsystem

The basis of this plate is the CIE standard colour-scale, which has been altered, distorted or transformed to create a Uniform Chromaticity Scale (UCS) — a type of Uniform Colour Scale. Ideally, colours should be distributed within it so that the spacing between them is as proportional as possible to their visually perceived differences. UCS diagrams are not actually colour-systems because they are not represented by colour standards and only cover a small area of colour space. For the practical measurement of colour, however, they are significant.

We cannot examine here the many mathematical details worked out in 1944 by David L. MacAdam, the former chairman of the Optical Society of America, for his paper Concerning the Geometry of Colour Space. These calculations were made in order to arrive at the illustration shown here, which attempts to graphically show small differences in colour. For our purposes, it is more important to simply enjoy the variety of geometrical forms which, in turn, bring forth the diversity of colours.

The starting point on the way to the illustrations shown here is the tongue-like CIE diagram which MacAdam first of all breaks down into squares with sides of uniform length. These squares are then transformed into strips which are then arranged so that the original sequence of squares is maintained. The three-digit numbers on the strips indicate the wavelength of light (in nanometers). The two-digit numbers on the lines which cross the strips reproduce the value of the x-coordinates from the CIE diagram. However, in front of these coordinates we must imagine a decimal point (this has become lost not only in this reproduction but also on MacAdam’s original). Joining of the strips so that their edges become «bonded» together will create an undulating surface. The curves on this surface denote the locations on which the values for x and y from the CIE diagram remain constant.

The transformation from squares into strips has its origin in so-called MacAdam ellipses. These ellipses can be placed around the base-colours specified in the CIE diagram to indicate their area of tolerance. These should be seen as nothing else but nominal colours. The ellipses, which are determined experimentally, point to the positions of those colours which can be distinguished from the nominal colour. There is no analytical term for these threshold ellipses, but MacAdam gives a graphic representation of so-called «ellipse constants», which are applied to the squares from the CIE diagram in order to transform them into rectangles of similar sensitivity.

The objective of all these distortions and constructions is to obtain information about sensitivity to differences in colour. David L. MacAdam is the pioneer in these investigations. In 1981, in his book Colour Measurement, he concerns himself with the basics of colour difference:

«Analogous to Mercator charts and other kinds of maps of the world that misrepresent the ratios of distances, the chromaticity diagram does not represent perceptually equal colour differences by equal distances between points that represent equally luminous colours. The noticeability of colour differences was not considered — very little data was available — when the chromaticity diagram was devised and adopted. However, as soon as it came into use, anomalies were encountered in interpreting the points configured on the diagram. Inconsistencies between distances and perceived magnitudes of colour-differences were evident. The analogy with geographical maps was quickly noted, and suggestions were made about changing the representation so that equal distances would represent equally noticeable colour-differences. A chromaticity diagram that possessed such properties came to be called ‘uniform’. The search for such a diagram has extended over 50 years and is no nearer its goal. In fact, much of the evidence accumulated indicates that the goal is unattainable: a flat diagram cannot represent equal colour-differences by equal distances any more than a flat map of the world can represent equal geographical distances by equal distances on the map.»