The Color Matching Experiment

The goal of an additive color matching experiment is to superimpose appropriate amounts of the three primaries $P_j\;\;\;(j=1,2,3)$ so that the resulting color $L'$ is perceived the same as a given color $L$. This can be actually carried out by three projectors that project the three primary colors with adjustable intensities on a screen.

This process is symbolically represented by

$$[L]\equiv [L'] = A_1(L) [P_1] + A_2(L) [P_2] + A_3(L) [ P_3]$$

This is not a mathematical equation in the normal sense, as the symbols used here have special meanings:

• Anything inside a pair of brackets (e.g., $[L]$ or $[P_j]$) is a color (an arbitrarily given color or a primary color) of certain energy spectral distribution;
• $A_j(L)$ is a scaler coefficients representing the amount of a primary color $P_j$ needed to match the given color $L$;
• The symbol $+$ represents the actual mixing of the colors by projecting them on the same screen.
• The symbol $\equiv$ means the color on the left-hand side is equivalent to that on the right-hand side in the sense that they are perceived by the human eye as the same color. (But this does not mean that the two energy distributions are necessarily the same, as discussed later.)

As we are usually concerned with the proportions of the color mixing but not the absolute intensities, the color matching process can be normalized by using a reference white color $W$. The amount of primary $P_j$ needed to match $W$, represented by $A_j(W)$, is used to normalize the intensity $A_j(L)$ for matching $L$:

$$T_j(L)=\frac{A_j(L)}{A_j(W)}\;\;\;\;(j=1,2,3)$$

The $T_j(L)$'s are called the tristimulus values.