There are two numarical color specification system,

- CIE xyz system
- CIE uniform 3D color space or CIE L*a*b color space (Mostly used)

**# Draw back of xyz system : **

- They can not interpret hue, chroma and lightness.
- The tristimulus values do not represent co-ordinates in 3 dimensional color space
- A numerical value for the perceived difference in color between similar samples is not represented by differences in their tristimulus values or chromaticity co-ordinates.
- etc

**# CIE L*a*b Color space :**

The basis of all color measurement work is the CIE system of color specification, agreed in 1931. The initials C.I.E stands for “Commission internationale de I’Eclairage,” which is an organization developed to international co-operation and exchange of information among its member countries countries on all matters relating to the art and science of lighting.

In 1976 CIE recommended the L*a*b Color system. The system is intended to be a uniform color space with the following properties;

- A rectangular three dimensional color space (L*a*b) in which all surface colors can be represented.
- The distance between the points representing the colors of two samples is proportional to the visual color difference between them.
- the axes are scaled so that just perceptable color difference is represented by unit distance.
- The L*a*b values can be easily interpreted in terms of hue, chroma and lightness.

L*a*b is a very popular one for color and color specification. The three parameters calculated are L*, a* and b* the value of L* for a given color varies between 0(perfect black) and 100 (perfect white) and gives a measure of the lightness of the color. The value of a* is a measure of red-green character of the color, with +ve values for red shades and -ve values for green. The value of b* gives the yellow-blue character with +ve values for yellow shades and -ve for blues. The details are shown as following figure.

Fig : the mutually perpendicular L*a*and b* axes of the CIE LAB color space.

The values of L*, a* and b* are calculated from the tristimulus values of the color (X,Y and Z) each value being first divided by the corresponding tristimulus value of the appropriate illuminatn (Xn, Yn an Zn). The psychometric lightness L* is calculated from :

A human oserver inveriably characteristics color differences in term of hue, saturation and lightness. The cylindrical coordinates L*, C* and h can be used instead of L*a*b* color space. The calculation of C* and h is based on the trigonometry of a right -angle triangle:

C* = ( a*^{2} + b*^{2} )^{1/2 } and h = arctan(b*/a*)

The value of h is 0 to 360°

When h= 0°, red

h= 45°, orange

h= 90°, yellow

h=135° light green

h=180° green

h= 225°, cyan

h=270°, blue

h= 315°, magenta

h= 360°, red