AN40 or ANLAB

The most important contribution in this field is by Adams (1942). He proposed three methods of plotting CIE data so that Munsell colours form nearly uniform circular locii about a neutral point at given value levels. The last and third is the most important and is the basis of the AN40 or ANLAB equations.

Kis first proposal is known as the chromatic valence or 'chromance' diagram. In this system when illuminant C is used, the tristimulus values X and Z are adjusted so that Xc = Y = Zc. To convert X to Xc and Z to Zc the ratios are used as follows:

,                         

Plots of (Xc - Yc) and (Zc - Yc) for colours can te plotted for various Munsell values.

The colour fifference equations based on the chromatic valence space depend on the differences of the three functions: Vy, Wx and Wz

where Vy is the Munsell value function and

,              

The form of the equation is Euclidean and the constants 0.5, 0.4, Wx and Wz were chosen to give correspondence with Riemannian, Munsell spacing.

His second transformation is called a constant brightness chromaticity diagram. Here the ratio Xc/Yc is plotted against Zc/Yc and the resulting geometric pattern of Munsell colours plotted in the diagram similarly to that of the chromatic valence diagram.

Adams Chromatic Value

Adams third and most important useful transformation is the chromatic value diagram derived from his theory of vision (1923). This transformation involves a non linear projection of the CIE chromaticity diagram and defines three parameters Vx, Vy and Vz.

Vy = Munsell value function

Vx and Vz are determined by setting Y = Xc and

Y =Zc respectively for illuminant C, thus applying the Munsell value function to X and Z as well as Y.

Dorothy Nickerson has prepared tables for reading Vx, Vy and Vz functions from CIE values. The equation derived from the diagram combined with the Munsell Neutral value function is:

The factor of 40 is recommended by Dorothy Nickerson to convert the equation to NBS units and is also recommended by the International Organisation for Standards Technical Committee 38 (Scarborough 1954).

This ISO recommendation now bears the name AN40 or ANLAB and gives the following equation:

where

L = 9.2Vy

a = 40(Vx - Vy)

b = 16(Vy - Vz)