All possible colours, either as coloured lights, translucent filters or reflecting objects, can be colour matched by negative, nil or positive amounts of three primary lights under predefined viewing conditions. To achieve this, two problems have still to be resolved. First, if the colour matching is to be performed by a machine then a numerical description of the response to colour of the normal human observer has to be determined; and secondly, the problem of negative quantities of the primary stimuli has to be overcome.
The solution to the first problem was achieved by the statistical evaluation of the colour matching properties of a number of observers with normal colour vision. As approximately 95% of all observers are regarded as colour normal their colour matching properties can be evaluated to produce an average normal observer. In 1931 the CIE defined the colour matching properties of a standard observer suitable for application to matching fields of one to four degrees angular subtense. These colour matching functions are based on the experimental work of Wright (1928-1929) and Guild (1931) using a 2
degree bipartite matching field; the experiments have been summarised by Wyszecki and Stiles (1982). The colour matching functions xbar(lambda), ybar(lambda) and zbar(lambda) which define the colour matching properties of the CIE 1931 (2
degree) standard observer have been published in tabular form by the CIE. This table was later expanded by the CIE (1986) and the colour matching functions are now defined between the wavelengths of 380nm to 780nm at 5nm intervals. In 1964 the CIE recommended a supplementary standard observer suitable for application to colour matching fields of greater than four degrees angular subtense. The colour matching functions of the 1964 10 degree angular subtense standard observer, xbar10(lambda), ybar10(lambda) and zbar10(lambda) are based on the experimental work of Stiles and Burch (1959) and Speranskaya (1959). The colour matching functions of the CIE 1964 standard observer have been tabulated over the wavelengths 380nm to 780nm at 5nm intervals and the table published by the CIE (1986). The precision of large-field colour matching is generally somewhat greater than that of small-field colour matching. For a 10
degree as compared with a 2 degree field, colour matching is estimated to be two or three times as precise (Wyszecki and Stiles, 1982).
The remaining problem of requiring negative amounts of one or two of the primary stimuli for colour matching cannot be overcome by using any combination of real primary stimuli. However, unreal or imaginary primary stimuli can be chosen such that all possible colours can be matched by an additive mixture of nil or positive amounts of these three primaries. Although such primaries cannot be realised, the amounts of these primaries needed to colour match any given colour can be easily calculated by application of Grassmann's (1853, 1854) laws. The laws state that the colour matching functions, or tristimulus values of the spectrum colours, can be calculated for any specified set of primaries if they are known for one set of primaries. In 1931 the CIE adopted a transformation of the trichromatic system based on the R, G, B primary stimuli to one based on the imaginary X, Y, Z primary stimuli. The colour matching functions xbar(lambda), ybar(lambda) and zbar(lambda) were calculated from the colour matching functions of the R, G, B system, rbar(lambda), gbar(lambda) and bbar(lambda) which were originally determined experimentally.
The standard coordinates of the 1931 CIE colorimetric system by which all possible colours can be uniquely identified are the CIE tristimulus values X, Y and Z. CIE colour space is thus three-dimensional, and originally such tristimulus colour space had axes at right angles to each other. The R, G, B system is such a system and as a result the unit plane, R + G + B = 1, is an equilateral triangle and defines the (r,g) chromaticity diagram. The CIE adopted an axis arrangement for the X, Y, Z system which produces an isosceles right-angled triangle on the unit plane X + Y + Z = 1. This defines the CIE (x,y) 1931 chromaticity diagram. All tristimulus vectors, the result of a colour match with the X, Y, Z primaries, must intersect this unit plane. The point of intersection with this plane defines the chromaticity of the matched object; that is, the qualities of a colour other than luminance. The coordinates x, y and z are the CIE chromaticity coordinates and are defined by the ratios of the CIE tristimulus values to their sum.
As a consequence of this relationship the sum of the CIE x,y,z chromaticity coordinates is equal to unity, and as such they provide only two of the three coordinates required to uniquely define a colour.
To uniquely identify a colour in terms of the CIE chromaticity coordinates, one of the tristimulus values must also be specified. The tristimulus value usually used for this purpose is Y. The CIE Y tristimulus value defines the luminance of a colour as ybar(lambda) duplicates the spectral luminous efficiency V(lambda). Any two of the chromaticity coordinates specify the chromaticness of a colour while the CIE Y tristimulus value defines a colour's luminance. Thus a point in CIE colour space can be identified in two ways, in terms of the colour's X, Y, Z tristimulus values, or in terms of the colour's x, y chromaticity coordinates and Y tristimulus value.
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