Appendix A: Calculating chromaticity coordinates

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Volume 8 Issue 1	October 2004

Color rendering index (CRI) - A measure of the degree of color shift that objects undergo when illuminated by a lamp, compared with those same objects when illuminated by a reference source of comparable correlated color temperature (CCT). A CRI of 100 represents the maximum value. A lower CRI value indicates that some colors may appear unnatural when illuminated by the lamp. Incandescent lamps have a CRI above 95. The cool white fluorescent lamp has a CRI of 62; fluorescent lamps containing rare-earth phosphors are available with CRI values of 80 and above. Correlated color temperature (CCT) - A specification of the apparent color of a light source relative to the color appearance of an ideal incandescent source held at a particular temperature and measured on the Kelvin (K) scale. The CCT rating for a lamp is a general indication of the warmth or coolness of its appearance. As CCT increases, the appearance of the source shifts from reddish white toward bluish white; therefore, the higher the color temperature, the cooler the color appearance. Lamps with a CCT rating below 3200 K are usually considered warm sources, whereas those with a CCT above 4000 K usually considered cool in appearance. Efficacy - The ratio of the light output of a lamp (lumens) to its active power (watts), expressed as lumens per watt. Spectral power distribution (SPD) - A representation of the radiant power emitted by a light source as a function of wavelength. Blackbody radiator - A temperature radiator of uniform temperature whose radiant output in all parts of the spectrum is the maximum obtainable from any temperature radiator at the same temperature. Such a radiator is called a blackbody because it absorbs all the radiant energy that falls upon it. All other temperature radiators can be classed as non-blackbodies. Non-blackbodies radiate less in some or all wavelength intervals than a blackbody of the same size and the same temperature. Chromaticity - The dominant or complementary wavelength and purity aspects of the color taken together, or of the aspects specified by the chromaticity coordinates of the color taken together. It describes the properties of light related to hue and saturation, but not luminance (brightness). Color appearance - The resultant color perception that includes the effects of spectrum, background contrast, chromatic adaptation, color constancy, brightness, size and saturation. Color consistency - The measure of how close in color appearance random samples of a lamp or source tend to be. Color matching - The action of making a color appear the same as a given color. Often used as a method of evaluating the ability of a light source to render colors faithfully. Color stability - The ability of a lamp or light source to maintain its color rendering and color appearance properties over its life. The color properties of some discharge light sources may tend to shift over the life of the lamp. Full-spectrum index (FSI) - A mathematical measure of how much a light source's spectrum deviates from an equal energy spectrum, based on the slope of its cumulative spectrum. Full-spectrum color index (FSCI) - A mathematical transformation of full-spectrum index into a zero to 100 scale, where the resulting values are directly comparable to color rendering index. An equal energy spectrum is defined as having an FSCI value of 100, a “standard warm white” fluorescent lamp has an FSCI value of 50, and a monochromatic light source (e.g., low pressure sodium) has an FSCI value of 0. Gamut area - A measure of color rendering based upon volume in color space. It is the range of colors achievable on a given color reproduction medium (or present in an image on that medium) under a given set of viewing conditions. Hue - The attribute of a light source or illuminated object that determines whether it is red, yellow, green, blue, or the like. Isotemperature - A set of coordinates within which all points have the same temperature. In a color space diagram, isotemperature lines represent lights with identical correlated color temperatures. Metamers - Lights of the same color but of different spectral power distribution. Photopic - Vision mediated essentially or exclusively by the cones. It is generally associated with adaptation to a luminance of at least 3.4 cd/m². Primary - Any one of three lights in terms of which a color is specified by giving the amount of each required to match it by additive combination.

The 1931 CIE (x, y) chromaticity coordinates are calculated from the spectral power distribution of the light source and the CIE color-matching functions (Figure A-1). The
x, y, z,
color-matching functions give the tristimulus value X,Y and Z:

X=∫ p x dλ, Y=∫ p y dλ, Z=∫ p z dλ

where p is the SPD of the light source. From X, Y and Z, the chromaticity coordinates x, y, z can be obtained as follows:

Figure A-1. The CIE color-matching functions

Using x, y as the coordinates, a two-dimensional chromaticity diagram (the CIE 1931 color space diagram) can be plotted as shown in Figure 6. In Figure 6, the spectral locus, the purple boundary, and the blackbody locus comprise the chromaticity diagram. The blackbody locus represents the chromaticities of blackbodies having various (color) temperatures.

The CIE 1976 chromaticity diagram was constructed by mathematically transforming the x, y chromaticity coordinates to u’, v’:

In the u’, v’ color space, the same distance between any two points are presumed to be perceptually equal.