Tristimulus value

The tristimulus values result from the natural sensitivity of the human eye to colors. There are three types of sensor cells in the human eye that respond to three regions of the visible light. The basic idea 

and b are the response functions in order to match the sensitivity functions of the average human eye to get a certain impression of a color. Note that f, g, and b differ from the sensitivity functions, because the light sources may have - and actually have - a spectrum that is different from the human sensitivity functions. Therefore, also negative values of the response functions occur. 

However, by suitable transformations the color matching func- 

In summary, the tristimulus values are orientated according to the average sensitivity of the human eye. Light with a different spectral distribution may have the same effect on the three color receptors in the human eye. This will result in the perception of the same color. 

---

The science of color measurement has been explored by various authors (127,128). AATCC evaluation procedure no. 6 describes a method for instmmental measurement of color of a textile fabric. AATCC evaluation procedure no. 7 may be used to determine the color difference between two fabrics of a similar shade. Instmmentation may be either a spectrophotometer for measuring reflectance versus wavelength, or a colorimeter for measuring tristimulus values under specified illumination. If a spectrophotometer is used, however, the instmment must be equipped with tristimulus integrators capable of producing data in terms of CIE X, Y, and Z tristimulus values. 

Another test method appHcable to textiles is ASTM E313, Indexes of Whiteness and Yellowness of Near-White, Opaque Materials. The method is based on obtaining G, ie, green reflectance, and B, ie, blue reflectance, from X, Y, and Z tristimulus values. Whiteness and yellowness index are then calculated from the G and B values. This method has particular appHcability to measurement of whiteness of bleached textiles. AATCC test method 110 also addresses measurement of the whiteness of textiles. 

CIE used the 1931 CIE standard observer to estabUsh a color representation system in which the hue and saturation could be represented on a two-dimensional diagram. Three tristimulus values X, Y, and Z are first obtained, based on the standard observer, so that the hue and saturation of two... 

The spectral characteristics of the source, photocells, and the three filters are such that approximate I.C.I. tristimulus values may be calculated (5) and from these a specification in terms of luminous reflectance, dominant wave length, and purity can be obtained. Hardy has cautioned (3), however, that the usefulness of such an instrument as a tristimulus colorimeter depends upon the standardization and constancy of the spectral characteristics of the light source, cell, and filters. 

We finally arrive at the result we want, since we can now set up "Tristimulus Filters" to use in defining colors. We can now define "y as our standard luminosity curve for the human eye (photopic vision). Note that x, the red tristimulus value, has a certain amount of blue in it in order to duplicate the response of the red preceptor in the retina. 

Therefore if we take the spectral curve, and multiply it by the overlap of each tristimulus response curve, we get TRISTIMULUS VALUES, i.e.-... 

However, we find that these values are difficult to use since each color give a set of tristimulus values, but each set does not have a specific relation to any other. The reason for this is that the intensity of Ir Iq Ib Therefore, we... 

Many whiteness (W) formulae have been proposed. All are based on CIE colour space and the X,Y,Z tristimulus values. Three of these equations are those of Berger [23] (Equation 11.1), Stensby [24] (Equation 11.2) and the CIE 1982 formula (Equation 11.3). 

The R,G,B values of the Berger formula measured by tristimulus colorimeters are linearly related to the X,Y,Z tristimulus values of the CIE system. The Stensby formula incorporates the L,a,b tristimulus values of the Hunter system. In the CIE 1982 formula, x and yn are the chromaticity coordinates of the D65 (2° or 10° observer) light source. 

The most successful quantitative expression of color is that known as the CIE (Commission Internationale de l Eclairage) system [13]. This methodology assumes that color may be expressed as the summation of selected spectral components (blue, green, and red hues) in a three-dimensional manner. The CIE system is based on the fact that human sight is trichromatic in its color perception, and that two stimuli will produce the same color if each of the three tristimulus values (X, Y, and Z) are equal for the two. Detailed summaries of the CIE and other quantitative systems for color measurement are available [14,15],... 

In Eqs. (7)—(10), 5(A) is the spectral power distribution of the illuminant, and R A) is the spectral reflectance factor of the object. Jc(A), y(A), and 5(A) are the color-matching functions of the observer. In the usual practice, k is defined so that the tristimulus value, Y, for a perfect reflecting diffusor (the reference for R A)) equals 100. Using the functions proposed by the CIE in 1931, y(A) was made identical to the spectral photopic luminous efficiency function, and consequently its tristimulus value, Y, is a measure of the brightness of objects. The X and Z values describe aspects of color that permit identification with various spectral regions. 

The proper implementation of the CIE system requires use of a standard illumination source for calculation of the tristimulus values. Three standard sources were recommended in the 1931 CIE system, and these may be presented in terms of color temperatures (the temperature at which the color of a black-body radiator matches that of the illuminant). The, simplest source is an incandescent lamp, operating at a color temperature of 2856 K. The other two sources are combinations of lamps and solution filters designed to provide the equivalent of sunlight at noon, or the daylight associated with an overcast sky. The latter two sources are equivalent to color temperatures of 5000 K and 6800 K, respectively. 

Since color is a perceived quantity, a strict mathematical relation relating tristimulus values to a concept of color is not possible. An equation has been proposed, however, that relates the perception of a color to these values. The trichromatic equation for tristimulus values is normally put into the general form... 

With the introduction of computers and microprocessor-controlled instrumentation, it has become possible to use spectrophotometry to obtain far more accurate determinations of color. The tristimulus values are obtained after integration of the data according to Eqs. (7)—(9). This degree of sophistication permits the use of more advanced methods of color quantitation, such as the 1976 CIE L u v system [41] or other systems not discussed in the present chapter. 

In a subsequent work, Raff used the CIE system to quantify the colors that could be obtained when using FD C aluminum lakes as colorants in tablet formulations [43]. He reported on the concentration dependence of the tristimulus values obtained when calcium sulfate dihydrate was compressed with various amounts of FD C Blue No. 2 aluminum lake, and one example of the reported data is found in Table 1. 

The Y tristimulus value may be taken as the relative lightness of the tablet... 

Table 1 Tristimulus Values Obtained on a Series of Tablets Colored with FD C Blue No. 2 Aluminum Lake...

In the field of colorimetry, the most important method of characterizing a color is to state the CIE tristimulus values X, Y, Z, which are calculated with the formulas... 

Colors specified in terms of the tristimulus values X, Y, and Z are fairly hard to visualize. For this and other reasons, a variety of different color systems have been devised. The color coordinates in these systems can be calculated from the X, Y, and Z values, which are of central importance to color measurement because of their close link to measurable quantities. 

Opaque minerals like iron oxides are frequently examined in the reflectance mode - and usually give diffuse reflectance spectra. Reflectance spectra provide information about the scattering and absorption coefficients of the samples and hence their optical properties. The parameters of reflectance spectra may be described in four different ways (1) by the tristimulus values of the CIE system (see 7.3.3) (2) by the Kubelka-Munk theory and (3) by using the derivative of the reflectance or remission function (Kosmas et al., 1984 Malengreau et ak, 1994 1996 Scheinost et al. 1998) and, (4) more precisely, by band fitting (Scheinost et al. 1999). 

Figure 3. Spectral tristimulus values according to the 1931 CIE standard observer. These values are dimensionless.

Colorimetry [1.17] - [1.19]. The principles of colorimetry are based on the fact that all color stimuli can be simulated by additively mixing only three selected color stimuli (trichromatic principle). A color stimulus can, however, also be produced by mixing the spectral colors. Thus, it has a spectral distribution, which in the case of nonluminous, perceived colors is called the spectral reflectance q (2). After defining three reference stimuli, the trichromatic principle allows a three-dimensional color space to be built up in which the color coordinates (tristimulus values) can be interpreted as components of a vector (CIE system for standards, see Table 1, Colorimetry CIE = Commission Internationale de l Eclairage). For uncolored illumination the three CIE tristimulus values depend on the spectral reflectance as follows ... 

They are represented as coordinates in a color plane. The chromaticity coordinates x and y are used to specify the saturation and hue of any color in the CIE chromaticity diagram. See Figure 4 a for illumination D 65. The CIE spectral tristimulus value y (2) corresponds to the lightness sensitivity curve of the human eye. Therefore, a third color variable is specified in addition to x and y, namely the CIE tristimulus value Y, which is a measure of lightness. 

Methods of Determination. Lightness. The white pigment powder is compressed in a suitable powder press to give an even, matt surface. The CIE tristimulus value Y is measured with color measuring equipment. For standards, see Table 1 ( Lightness ). Apparatus spectrophotometer or tristimulus colorimeter, powder press, white standard. 

---