Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

CIE 1931 and 1964 Standard Colorimetric Observers: History, Data, and Recent Assessments

  • János Schanda
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_323



CIE color-matching functions

Functions \( \overline{x}\left(\lambda \right),\overline{y}\left(\lambda \right),\overline{z}\left(\lambda \right) \) in the CIE 1931 standard colorimetric system or \( {\overline{x}}_{10}\left(\lambda \right),{\overline{y}}_{10}\left(\lambda \right),{\overline{z}}_{10}\left(\lambda \right) \) in the CIE 1964 standard colorimetric system

CIE 1931 standard colorimetric observer

ideal observer whose color-matching properties correspond to the CIE color-matching functions \( \overline{x}\left(\lambda \right),\overline{y}\left(\lambda \right),\overline{z}\left(\lambda \right) \) adopted by the CIE in 1931

CIE 1964 standard colorimetric observer

ideal observer whose color-matching properties correspond to the CIE color-matching functions \( {\overline{x}}_{10}\left(\lambda \right),{\overline{y}}_{10}\left(\lambda \right),{\overline{z}}_{10}\left(\lambda \right) \) adopted by the CIE in 1964


Colors with different spectral compositions can look alike (i.e., be metameric). An important function of colorimetry is to determine which spectral compositions appear metameric. The use of visual colorimeters for this purpose is handicapped by variations in the color matches made among observers classified as having normal color vision, so that different observers make different matches. Visual colorimetry also tends to be time-consuming. For these reasons, it has long been the practice in colorimetry to make use of sets of mean or standard color-matching functions to calculate tristimulus values for colors: Equality of tristimulus values for a pair of colors indicates that the color appearances of the two colors should match, when viewed under the same conditions by an observer for whom the color-matching functions apply. The use of standard sets of color-matching functions makes the comparison of tristimulus values obtained at different times and locations possible [1]. The standard colorimetric observers are defined by their color-matching functions.

According to Grassman’s laws, a test color stimulus can be matched by the additive mixture of three properly selected matching primary stimuli (properly selected includes independence; i.e., none of the primary stimuli can be matched by the additive mixture of the other two). The test stimulus is projected on one side of a bipartite field; the additive mixture of the three matching primary stimuli (it is practical to use monochromatic red, green, and blue primary lights, see later) is projected onto the other side of the field. By using adjustable light attenuators, the light flux of the three matching stimuli is adjusted to obtain a color appearance match between the two fields. When this situation is reached, the test stimulus can be characterized by the three luminance values of the matching stimuli reaching the eye of the observer. This is described by the following equation:
$$ \left[\mathrm{C}\right]\equiv R\left[\mathrm{R}\right]+G\left[\mathrm{G}\right]+B\left[\mathrm{B}\right] $$
where [C] is the test stimulus; [R], [G], and [B] are the unit values of the three matching stimuli; and R, G, and B are the amount taken from [R], [G], and [B] to match the stimulus [C]. The ≡ sign means “matches” (for more details, see [2]). Invariably, one of the primary stimuli has to be added to the test stimulus to complete the match.

If one uses monochromatic test stimuli of equal power, wavelength to wavelength along the visible spectrum (theoretically between 360 nm and 830 nm, practically between 380 nm and 780 nm), and matches these monochromatic radiations with the three selected matching stimuli (in different wavelength regions, one of the matching stimuli has to be added to the test stimulus to get a color match, and in that case the matching stimulus is shown in Eq. 1 as it would be subtracted from the other two matching stimuli), one can build up the color-matching functions.

Using 1 cd∙m−2 monochromatic red light of 700 nm as [R], 4.5907 cd∙m−2 monochromatic green light of 546.1 nm as [G] and 0.0601 cd∙m−2 monochromatic blue light of 435.8 nm as [B] for the units of the matching stimuli, one gets for unit power of monochromatic lights of the spectrum curves as shown in Fig. 1 called color-matching functions (CMFs) and usually written in the following form: \( \overline{r}\left(\lambda \right),\overline{g}\left(\lambda \right),\overline{b}\left(\lambda \right) \).
CIE 1931 and 1964 Standard Colorimetric Observers: History, Data, and Recent Assessments, Fig. 1

Color-matching functions of the CIE 1931 RGB system

Visual experiments have shown that color stimuli are additive, i.e., if the test stimulus is composed of two sub-stimuli [C(λ1)] and [C(λ2)] of different wavelengths, the amounts of the [R], [G], and [B] matching stimuli, also called primaries, that are used to match [C(λ1)] and [C(λ2)] have to be added to match the additive mixture of the two test stimuli \( \left[{C}_{1+2}\right] \). This can be expanded to a spectrum that has different spectral radiance values at different wavelength: the color of the compound spectrum S(λ) can be described by three tristimulus values:
$$ R={\displaystyle \underset{380\mathrm{nm}}{\overset{780\mathrm{nm}}{\int }}\overline{r}\left(\lambda \right)S\left(\lambda \right)\mathrm{d}\lambda }, G={\displaystyle \underset{380\mathrm{nm}}{\overset{780\mathrm{nm}}{\int }}\overline{g}\left(\lambda \right)S\left(\lambda \right)\mathrm{d}\lambda, }B={\displaystyle \underset{380\mathrm{nm}}{\overset{780\mathrm{nm}}{\int }}\overline{b}\left(\lambda \right)S\left(\lambda \right)\mathrm{d}\lambda } $$

In many applications, it is inconvenient to use negative lobes of the \( \overline{r}\left(\lambda \right),\overline{g}\left(\lambda \right),\overline{b}\left(\lambda \right) \) functions; therefore, the CIE decided in 1931 to transform the \( \overline{r}\left(\lambda \right),\overline{g}\left(\lambda \right),\overline{b}\left(\lambda \right) \) functions using a matrix transformation to imaginary CMFs (non-real in the sense that they cannot be physically realized). The transformed CMFs are the \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), and \( \overline{z}\left(\lambda \right) \) functions, and the tristimulus values determined using these functions are the X, Y, and Z tristimulus values. Their calculation is similar at those of the R,G, and B values shown in Eq. 2.

The transformation matrix has the following form:
$$ \left|\begin{array}{l}X\\ {}Y\\ {}Z\end{array}\right|=\left|\begin{array}{ccc}\hfill 2.768\ 892\hfill & \hfill\ 1.751\ 748\hfill & \hfill 1.130\ 160\hfill \\ {}\hfill 1.000\ 000\hfill & \hfill 4.590\ 700\hfill & \hfill 0.060\ 100\hfill \\ {}\hfill 0\hfill & \hfill 0.056\ 508\hfill & \hfill 5.594\ 292\hfill \end{array}\right|\bullet \left|\begin{array}{l}R\\ {}G\\ {}B\end{array}\right| $$

The original color-matching experiments were conducted with small, approximately 2° diameter homogeneous color patches, seen foveally. The central part of the fovea is covered by a yellow pigmentation, the yellow spot or macula lutea. If larger-colored fields are viewed or slightly off-axis objects are viewed, the above CMFs do not hold anymore, as the yellow pigmentation absorbs light in a part of the visible spectrum.

In 1964 CIE standardized CMFs for a 10° visual field, the so-called large field CMFs. Based on similar direct visual investigations performed mainly by Stiles and Burch [3] with contributions by Speranskaya [4], these functions are now used in many applications. To distinguish between values determined using the 2° or the 10° functions, the latter are distinguished by the subscript “10,” and thus the 10° observer’s CMFs are termed \( {\overline{x}}_{10}\left(\lambda \right), {\overline{y}}_{10}\left(\lambda \right), {\overline{z}}_{10}\left(\lambda \right) \) (Fig. 2).
CIE 1931 and 1964 Standard Colorimetric Observers: History, Data, and Recent Assessments, Fig. 2

The \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), and \( \overline{z}\left(\lambda \right) \) color-matching functions of the CIE 1931 standard (2°) colorimetric observer (full lines) and the \( {\overline{x}}_{10}\left(\lambda \right),{\overline{y}}_{10}\left(\lambda \right),{\overline{z}}_{10}\left(\lambda \right) \) CMFs of the CIE 1964 standard (10°) colorimetric observer (shown by dashed line)

Regarding the use of the tristimulus values and further colorimetric calculations, see chapters on “CIE chromaticity co-ordinates,” “CIE chromaticity diagram,” “CIE illuminants,” and “CIELAB” and other chapters on advanced colorimetry.

Short History of the CIE Colorimetric Observer

CIE colorimetry is based on the tristimulus theory developed by the greatest scientists of the nineteenth century, including Thomas Young, Helmholtz, and Maxwell (see [5]). Maxwell’s demonstrations and ideas, in particular, lead to the specification of the trichromatic theory; he showed, e.g., the three color mixture curves of the spectrum and plotted the spectrum locus in the color triangle.

Photometry and colorimetry were further developed in the USA that lead to the so-called OSA excitation curves.

During the second decade of the twentieth century, two groups in the UK performed detailed investigations of color matching: John Guild at the NPL and David Wright at the Imperial College, London. The two researchers used different primaries, and it was a great surprise that after their transformation into a common system, they matched reasonably well.

During those years the CIE formulated the wish to develop a colorimetric description of colored glasses used for traffic control. At the 1931 meetings of the CIE, the USA and UK groups discussed in detail the pros and cons of different systems and finally agreed that a mean of the Guild and Wright data should be adopted, but transformed to a system with nonnegative CMFs. These were the \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), and \( \overline{z}\left(\lambda \right) \) CMFs that we still use today.

One major problem with the CIE 1931 XYZ system is that the values of the primaries were determined photometrically, so that the \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), and \( \overline{z}\left(\lambda \right) \) functions had to be reconstructed using V(λ) function, the visibility function (now called spectral luminous efficiency for photopic vision). As it turned out later, the V(λ) dataset is in error in the blue part of the spectrum, and this error has been transferred to the color-matching functions.

Experiments carried out in the 1950s at NPL by Stiles and Burch led to a new set of 10-deg CMFs; this time the primaries and test lights were radiometrically calibrated, so they were not contaminated by photometric errors. As mentioned in the Overview, the NPL data were harmonized with data measured by Speranskaya, and these were standardized as the CIE 10° observer in 1964.

Recently, the fundamental experimental data have been reanalyzed, together with new cone spectral sensitivity measurements made in red-green dichromats and blue-cone monochromats of known genotype to produce new cone spectral sensitivity curves of the three cone receptors (the cones are mainly responsible for daylight vision and color perception) as well as transformations to \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), and \( \overline{z}\left(\lambda \right) \)-like curves [6, 7]; see Chapter on CIE Physiologically-Based Colour-Matching Functions and Chromaticity Diagrams. The cone fundamentals are known as the fundamental CMFs or \( \overline{l}\left(\lambda \right) \), \( \overline{m}\left(\lambda \right) \), and \( \overline{s}\left(\lambda \right) \). Both the 2° and the 10° CMFs have been published by the Colour & Vision Research Laboratory at http://www.cvrl.org (see Fig. 3) − at the time of submitting this manuscript, CIE TC 1-36 has not endorsed the transformation from the LMS cone fundamentals to the CMFs shown here.
CIE 1931 and 1964 Standard Colorimetric Observers: History, Data, and Recent Assessments, Fig. 3

The \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), \( \overline{z}\left(\lambda \right) \), and \( {\overline{x}}_{10}\left(\lambda \right), {\overline{y}}_{10}\left(\lambda \right), {\overline{z}}_{10}\left(\lambda \right) \) color-matching functions transformed from the LMS cone fundamentals



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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.VeszprémHungary