Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

CIE Tristimulus Values

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_371




Tristimulus values are defined as the amounts of the 3 reference color stimuli, in a given trichromatic system, required to match the color of the stimulus considered


The International Commission on Illumination (CIE) recommended CIE color specification system as the basis for colorimetry [1]. The ISO and CIE are also provided a series of joint standards [2, 3, 4]. The fundamental of colorimetry is Tristimulus Values [4]. They are used for color communication and reproduction. The three key elements of color perception are: human vision system, light, and object. If missing one of three elements, we will not be able to perceive color. These elements have been defined by CIE as color matching functions of \( \overline{x}\left(\lambda \right) \), \( \overline{y}\left(\lambda \right) \), and \( \overline{z}\left(\lambda \right) \), or \( {\overline{x}}_{10}\left(\lambda \right), \)\( {\overline{y}}_{10}\left(\lambda \right), \)and \( {\overline{z}}_{10}\left(\lambda \right) \) for 2° and 10° fields of viewing respectively, across visual spectrum to represent the human population having normal color vision. They also known as CIE 1931 and 1964 standard colorimetric observers (see [2]). CIE also standardized some illuminants in terms of Spectral Power Distribution (SPD) (S(λ)) [3]. Additionally, CIE specified the illuminating and viewing geometry for measuring a reflecting surface. Each surface is defined by spectral reflectance, R(λ), a ratio of the reflected light from a sample to that reflected by a perfect diffuser identically illuminanted [1]. The typical instrument for measuring spectral reflectance is a spectrophotometer.

Thus any color can be specified by a triad of numbers called Tristimulus Values, or XYZ values (see Eq. 1). The details can be found in references [1] and [4]. An easier explanation can be a color is matched by the amounts of standard red, green, and blue lights by a normal color vision observer under a particular standard illuminant. These are the integration of the products of the functions in three components over the visible spectrum, say 380 to 700 nm.
$$ \begin{array}{l}X=k{\displaystyle \underset{\lambda }{\int }S\left(\lambda \right)R\left(\lambda \right)\overline{x}\left(\lambda \right)d\lambda}\\ {}Y=k{\displaystyle \underset{\lambda }{\int }S\left(\lambda \right)R\left(\lambda \right)\overline{y}\left(\lambda \right)d\lambda}\\ {}Z=k{\displaystyle \underset{\lambda }{\int }S\left(\lambda \right)R\left(\lambda \right)\overline{z}\left(\lambda \right)d\lambda}\end{array} $$
where k constant was chosen so that Y = 100 for the perfect reflecting diffuser. If the CIE1964 standard colorimetric observer is used in Eqs. 1 and 2 all terms except k, S(λ) and R(λ) should include a subscript of 10.
For measuring self-luminous colors such as color displays, TV, light sources, Eq. 2 should be used instead of Eq. 1. This is due to the fact that the object and illuminant are not defined. The P function represents the spectral radiance or spectral irradiance of the target stimulus. The areas of colors considered in display applications usually have quite small angular subtense and the CIE 1931 standard colorimetric observer is the appropriate one to use. The typical instrument for measuring spectral radiance or irradiance is a spectroradiometer.
$$ \begin{array}{l}X=k{\displaystyle \underset{\lambda }{\int }P\left(\lambda \right)\overline{x}\left(\lambda \right)d\lambda}\\ {}Y=k{\displaystyle \underset{\lambda }{\int }P\left(\lambda \right)\overline{y}\left(\lambda \right)d\lambda}\\ {}Z=k{\displaystyle \underset{\lambda }{\int }P\left(\lambda \right)\overline{z}\left(\lambda \right)d\lambda}\end{array} $$
where k constant is chosen so that Y = 100 for the appropriate reference white.



  1. 1.
    CIE Pub. No. 15:2004: Colorimetry (Central Bureau of the CIE, Vienna)Google Scholar
  2. 2.
    ISO 11664-1:2007(E)/CIE S 014-1/E:2006 Joint ISO/CIE Standard: Colorimetry — Part 1: CIE Standard Colorimetric Observers (Central Bureau of the CIE, Vienna)Google Scholar
  3. 3.
    ISO 11664-2:2007(E)/CIE S 014-2/E:2006 Joint ISO/CIE Standard: Colorimetry — Part 2: CIE Standard Illuminants for Colorimetry (Central Bureau of the CIE, Vienna)Google Scholar
  4. 4.
    ISO 11664-3:2012(E)/CIE S 014-3/E:2012 Joint ISO/CIE Standard: Colorimetry — Part 3: CIE Tristimulus Values (Central Bureau of the CIE, Vienna)Google Scholar

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© Her Majesty the Queen in Right of United Kingdom 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Modern Optical InstrumentationZhejiang UniversityHangzhouChina
  2. 2.School of DesignUniversity of LeedsLeedsUK
  3. 3.Graduate Institute of Colour and IlluminationNational Taiwan University of Science and TechnologyTaipeiRepublic of China