Whiteness by numbers

Quite early was recognized that most materials considered white show actually a slightly yellow tint; this is especially true in the ceramic industry, where the color white occupies a central position, however this is a physical white, as presented in the theory section. Many formulas have been developed to express yellowness as a single number, the so-called yellowness index.
Whiteness was well understood as being the opposite of yellow, many attempts were undertaken to express similarly whiteness as a single number. Some formulas still in use are:

W= 4*B-3*G (Taube, incomplete description)

W= 3*B+G-3*A (Berger, green preference)

W= L+3*a-3*b (Stensby, red preference)

Note that formulas are expressed in (A,B,G) system or Hunter Lab coordinates.
Since blue alone is not sufficient to describe whiteness completely, one must also take the red-green axis into consideration; for this reason Taubes formula has incomplete information. The other two formulas take the red-green axis clearly into account, but they overweight the importance of one shade into whiteness. For this reason they are said to have a preference, since shade is not explicitly quantified with these formulas, comparison of whiteness of different samples is very difficult. In the late sixties and during the seventies a set of formulas were developed that explicitly take whiteness and tint into account. Formulas of this type have the general form:

W= Y + P*(x₀-x) + Q*(y₀-y)

T= m*(x₀-x) + n*(y₀-y)

where (x₀,y₀) are de coordinates of the achromatic point for the reference illuminant. Whiteness numbers are referred to a neutral white (dominant wave- length of 470 nm) and the tint as a deviation from this neutral axis. The evaluation of the tint is based however on a slight preference of reddish over greenish whites i.e. the tint axis is not perpendicular to neutral whiteness axis but it shows a tilt of 15° favoring reddish whites.
Two scales are used for assessing whiteness instrumentally, whiteness according to Ganz and according to CIE; both are quite similar, share the same general form and have following numerical parameters:

         Parameter                   Ganz                       CIE

             P                              1869.3                      800

             Q                             3695.2                     1700

             m                             1014.1                       900

             n                               -714.5                      -650

in general the parameter values are valid for the illuminant daylight D65 only.
Metric is different for both scales, threshold for distinguishing different whiteness is defined in Ganz scale as being 5 points, for CIE whiteness it is about 2.3 to 2.4 points. Threshold for distinguishing different tints lies at 0.5 points.
Numerical values are valid only for correct measuring instruments i.e. instruments that can calculate color coordinates for D65 illuminant or those illuminating the sample with a profile identical to D65. Actually this is not the case under normal conditions (see Calibration section) such that whiteness numbers are in general a little off; through extensive calibration Ganz whiteness and tint can be reproduced quite well by changing slightly numerical values of parameters, the CIE formula is not flexible and tint values loose their sense and utility.

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