# CIE Whiteness

**DOI:**https://doi.org/10.1007/978-1-4419-8071-7_5

## Definition

*W*is given by

*x*,

*y*are the chromaticity coordinates of the sample, and

*x*

_{n},

*y*

_{n}are those of the illuminant. For the CIE 1964 supplementary standard colorimetric observer, the whiteness index

*W*

_{10}is given by

_{10}, y

_{10}and

*x*

_{n,10},

*y*

_{n,10}are the chromaticity coordinates of the sample and the illuminant, respectively.

*T*

_{w}or

*T*

_{w,10}, given by the following formulae, is zero for a sample without reddishness or greenishness. For the CIE 1931 standard colorimetric observer,

*x*

_{10},

*y*

_{10}and

*x*

_{n,10},

*y*

_{n,10}are the chromaticity coordinates of the sample and the illuminant, respectively. The tint coefficient allows two samples with the sample whiteness index,

*W*or

*W*

_{10}, but with different hue to be distinguished. The more positive the value of

*T*

_{w}or

*T*

_{w,10}, the greater is the indicated greenishness, and the more negative, the greater the reddishness [2].

The higher the value of *W* or *W*_{10}, the higher the whiteness of the sample. However, the CIE standard includes the following restriction:

*Y*is the tristimulus value of the sample.

## Development of the CIE Whiteness Formula

Whiteness is a commercially important property of color appearance in a number of industries, most notably those of textiles and paper. According to Wyszecki and Stiles, white is the attribute of a visual sensation according to which a given stimulus appears to be void of any hue and grayness [3]. Alternatively, the percept of whiteness is caused by a combination of high lightness and lack of yellowness [4]. MacAdam published the first instrumental method for the assessment of whiteness in 1934 [5], and by the 1960s, over 100 different methods to predict perceptual whiteness had been proposed. Although color is a three-dimensional percept, whiteness has traditionally been measured using a univariant metric. Hayhurst and Smith suggest that the reason for this is that the color of white textile or paper is often influenced by the quantity of a specific (single) impurity in it [4]; the white color therefore falls on a line in three-dimensional color space, albeit one that is curved. However, especially when different products are being compared, it is important to have a metric that is at least dependent upon all three dimensions of color space even if the metric is condensed to a single number, as is the case with the CIE whiteness method. Many of the early whiteness formulae considered only one or two of the three dimensions of color and therefore had limited general applicability.

*W*

_{G}in 1972 with the following form:

*Y*and

*x*,

*y*are the

*Y*tristimulus value (sometimes called luminous reflectance) and chromaticity coordinates, respectively, of the sample, and

*D*,

*P*,

*Q*, and

*C*are coefficients that could be varied to adjust for various parameters including the illuminant, the observer, and the hue preference. The coefficient of

*D*was set to unity and

*C*=

*P*

_{x,n}+

*Q*

_{y,n}. Ganz suggested three pairs of values for

*P*and

*Q*each corresponding to a different hue preference. The formula was linear in chromaticity space because experience in producing white scales had shown that the chromaticities of uniformly spaced samples turn out to be approximately equidistant in this space [7].

A round-robin test [7], organized by a technical committee (TC-1.3) of the CIE in the 1970s, showed that there are individuals with extreme hue preference for whiteness. This suggests that a single whiteness formula cannot reproduce the whiteness preferences of a sizable portion of the population and this is why Ganz originally suggested three pairs of values for *P* and *Q*. The CIE adopted a form of Eq. 6 with values of *P* and *Q* corresponding to neutral hue preference, and the CIE equation is normally written in the forms of Eqs. 1 and 2. The use of unity for the coefficient *D* has the implication that the whiteness of a perfect reflecting diffuser would be 100. Samples containing fluorescent whitening agents may have *W* or *W*_{10} ≫100. The difference that is just perceptible to an experienced visual assessor is about three CIE whiteness units [4].

The whiteness formula should be used only for the comparison of samples that are commercially white and do not differ much in color or fluorescence. The samples should be measured on the same instrument at the same time. The light source in the spectrophotometer used to measure the reflectance factors should match, as closely as possible, the illuminant D65. The requirement for instruments that could deliver consistent light output (including in the near UV) that closely matches illuminant D65 led to developments in instrument-calibration techniques toward the end of the twentieth century.

## Further Considerations and Future Directions

*L**,

*a**, and

*b**are the CIELAB coordinates of the sample. The upper limit

*W*

_{10}< 5

*Y*− 280 was transformed by a linear approximation yielding

*W*

_{10}< 10.6

*L**− 852. The other limits

*W*

_{10}> 40 and −3 <

*T*

_{w,10}< 3 remained unchanged.

*W*

_{u}where

*W*

_{10}< 5

*Y*− 275 and was found to give better agreement with the visual results than the CIE equation. In a recent study [11], 22 observers were asked to rank 20 samples (with low to high CIE whiteness indices). Results showed a significant consistency between the variations in the ordering decisions of the observers for the white samples with low CIE whiteness index but a high level of disagreement between the observers for the whiter samples.

Recently the generic form of the CIE whiteness equation (Eq. 2) with modified coefficients has been shown to be able to predict the whiteness of human teeth even though many of the samples would not be considered to be commercially white in the textile, plastic, and paper industries in which the CIE whiteness equation has traditionally been applied [12].

## Cross-References

### References

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