OptipediaSPIE Press books opened for your reference.

Color Addition

Excerpt from Color Vision and Colorimetry: Theory and Applications, Second Edition

Additive mixing of color takes place when two or more light beams with different colors are superimposed on a screen or directly on the retina of the observing eye. One example is theater stage illumination where several colored light projectors illuminate the same region. Another example is the well-known rotating top with a disc of colors. If all colors of the spectrum are in the disc, a neutral gray color is observed when the top is rotating. A third example is in color television screens, or in computer screens. Extremely small red, green and, blue dots are produced on the screen. The relative intensities of these colors produce a wide range colors for the eye.

The CIE chromaticity diagram is a useful tool to predict the color produced by different color additive mixtures. Assume that two light fields with spectral powers P1(λ) and P2(λ) are mixed. If the tristimulus values are (X1, Y1, Z1) and (X2, Y2, Z2), the total tristimulus values are expressed as

equations 1-3

The chromaticity coordinates for the addition of the two fields are (xT, yT, zT) given by

equation 4


Figure 6.1 Weight wifor a colored light beam with spectral power Pj(λ) (sum of color matching functions).

equations 5-6

Now, when we define the weight wi of the colored light beam i, plotted in Fig. 6.1 as

equations 7-10

Thus, with these definitions, the chromaticity coordinates for the combination of two colored light beams become

equation 11-13

This result can be interpreted as a lever in equilibrium, where each of the two colors with weights w1 and w2 are on each end of the resultant color at the equilibrium point (Fig. 6.2). The conclusion is that any color in the line joining the two added colors can be reproduced with the proper weight of these components. Generalizing this result, we conclude that with three colors—A, B, and C in the chromaticity diagram (Fig. 6.3)—any color inside the triangle can be faithfully reproduced. To find the resultant color a first step is to find the color resulting from the combination of A with B, and then combine that color with color C. Figure 6.4 shows how three colors combine by color addition. Unfortunately, these rules do not apply for the CIELAB uniform color system.

lever in equilibrium

Figure 6.2 A lever in equilibrium, with weights w1 and w2 on each end and resulting color at the equilibrium point.

CIE chromaticity diagram

Figure 6.3 The CIE chromaticity diagram with three colors A, B, and C.

three colors

Figure 6.4 Three colors (red, green and blue) combined by color addition.

D. Malacara, Color Vision and Colorimetry: Theory and Applications, Second Edition, SPIE Press, Bellingham, WA (2011).

View SPIE terms of use.