19.1 Additive color mixing

The combination or additive mixing of two or more light sources is employed in a number of applications. In LED displays, three different types of LEDs, usually emitting in the red, green, and blue, are used. The three colors are mixed so that the observer can experience a wide range of colors. Another useful application of color mixing is the generation of white light by two, three, or more complementary colors. A schematic of additive color mixing and a corresponding experiment are shown in Fig. 19.1.

Next, we determine the chromaticity coordinates of the mixture of three discrete emission bands. Assume that the three emission bands have spectral power densities /’i(k), P2(k), and P3(k) with peak wavelengths of k1, k2, 'k3, respectively. We assume that each emission band is much narrower than any of the three color-matching functions. We further assume that the three light sources have the chromaticity coordinates (x1, y1), (x2, y2), and (x3, y3). Then the tristimulus values are given by

Y = lxy(X)fl(X)dX + JXy(X)Pi(X)dX + JXy(X)P3(X)dX^y(Л.1)p + y(X2)P> + У(X3)P3 (19.2)

Z =f z(X)P1(X)dX+f z(X)P2(X)dX+f z(X)P3(X)dX « z(X1)P1 + z(X2)P2 + z(X3)P3 (19.3) J X J X J X

where P1s P2, and P3 are the optical powers emitted by the three sources. Using the abbreviations

L1 = x (X1) P1 + У (X1) P1 + z (X1) P1 (194)

L2 = x(X2) P2 + У(X2) P2 + z(X2) P2 (195)

L3 = x(X3) P3 + y(X3) P3 + z(X3) P3 (196)

the chromaticity coordinates of the mixed light can be calculated from the tristimulus values to yield

X1 L1 + X2 L 2 + X3 L 3 x = (19.7)

L1 + L2 + L3

y1 L1 + y2 Lt + y3 L3 y = -^-L-1 . (19.8)

L1 + L2 + L3

Thus, the chromaticity coordinate of the multi-component light is a linear combination of the individual chromaticity coordinates weighted by the Li factors.

The principle of color mixing in the chromaticity diagram is shown in Fig. 19.2. The figure shows the mixing of two colors with chromaticity coordinates (x1, y1) and (x2, y2). For the case of two colors, L3 = P3 = 0. The mixed color will be located on the straight line connecting the chromaticity coordinates of the two light sources. Thus any color (including white) located between the two chromaticity points can be created by mixing the two colors.

Figure 19.2 also shows the mixing of three colors, located in the red, green, and blue regions of the chromaticity diagram. The three chromaticity points, connected by a dashed line, are typical points for red, green, and blue LEDs. The area located within the dashed line, called the color gamut, represents all colors that can be created by mixing the three primary colors red, green, and blue. The ability to create a great variety of colors is an important quality for displays. It is desirable that the color gamut provided by the three light sources is as large as possible to create displays able to show brilliant, saturated colors.

The color gamut represents the entire range of colors that can be created from a set of
primary sources. Color gamuts are polygons positioned within the perimeter of the chromaticity diagram. For the case of three primary colors, the color gamut is a triangle, as shown in Fig. 19.2. All colors created by additive mixtures of the vertex points (primary colors) of a gamut, are necessarily located inside the gamut.

Fig. 19.2. Principle of color mixing illustrated with two light sources with chromaticity coor­dinates (Xi,>>|) and (лг2,y-у). The resulting color has the coordi­nates (дг, >>). Also shown is the triangular area of the chromatic­ity diagram (color gamut) acces­sible by additive mixing of a red, green, and blue LED. The locations of the red, green, and blue phosphors of the sRGB dis­play standard (лу = 0.64, yr = 0.33, Xg = 0.30, yg = 0.60, .vb = 0.15, = 0.06) are also shown.

The sRGB standard is similar to the NTSC standard.

The insight now gained on color mixing allows one to understand the location of different LEDs in the chromaticity diagram. The perimeter of the chromaticity diagram in the red spectral region is approximately a straight line, so that red LEDs, despite their thermal broadening, are located directly on the perimeter of the chromaticity diagram. In contrast, the perimeter is strongly curved in the green region, so that green LEDs, due to their spectral broadening, are displaced from the perimeter towards the center of the chromaticity diagram.