In 1976, the CIE defined two new
color spaces to enable us to get more uniform and accurate models. The
first of these two color spaces is the CIE L*u*v* which component are
L*, u* and v*. L* component defines the luminance, and u*, v* define chroma.
CIE L*u*v* color model is very often used in calculation of small colors
or color differences, especially with additive colors. The CIE L*u*v*
color space is defined from CIE 1931
color model.

The quantities of L*, u* and v* will be calculated from the tristimulus
values X, Y and Z using the following equations:

for Y/Y_{n} > 0.008856

for Y/Y_{n} <= 0.008856

where

and

X,
Y, and Z
are the CIE tristimulus values.
Xn, Yn, and Zn are the tristimulus values for the illuminant.
xn, yn and zn are the chromaticity coordinates.

Color differences will be measured as total difference of the L*, u*
and u* values of a sample and the standard using the following equations:

∆L* = L*sample
- L*standard

positive ∆L* means, the sample is lighter
than the standard
negative ∆L* means, the sample is darker than the standard

∆u* = u*sample
- u*standard

positive ∆a* means, the sample is redder
than the standard
negative ∆a* means, the sample is greener than the standard

∆u* = u*sample
- u*standard

positive ∆u* means, the sample is yellower
than the standard
negative ∆u* means, the sample is bluer than the standard

In addition, there are two other delta values
that are related to this scale, ∆C* and ∆H*. The ∆C* is
the difference in chroma between the sample and standard as described
in a polar coordinate system. The ∆H* is the difference in hue angle between
the sample and standard as described in a polar coordinate system.