# Color Subtraction

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

If a colored light field is observed through a colored filter, some color components will be removed. If the spectral radiance for the light field is P(λ) and the spectral transmittance of the filter is τ(λ), the effective final spectral radiance is the product of P(λ)τ(λ). It follows that if P(λ) and τ(λ) do not have any wavelength range different than zero in common, the final color is black. Therefore, the process of color subtraction has to be done with continuous nonmonochromatic colors. Figure 6.6 shows the spectral characteristics of three filters—cyan, magenta, and yellow—that are used to reproduce color by the subtractive process. Ideally, each colorant transmits two-thirds of the visible spectrum and absorbs one-third. Figure 6.7 illustrates how these three filters combine with this process.

Figure 6.6 Spectral characteristics of three ideal filters that can be used to reproduce color by subtraction. (Click to enlarge.)

Figure 6.7 Three colored filters (cyan, magenta, and yellow) combined by color subtraction.

The subtraction process selectively removes some parts of the visible spectrum. For example, the yellow filter removes the blue color, transmitting the green and red colors. The magenta filter removes green, transmitting the red and blue colors. The cyan filter eliminates red, and transmits blue and green. Thus, by adjusting the transparency of these filters the amounts of red, green, and blue color can be controlled. Mathematically, we may express the relation between these filters using the following set of equations:

cyan = white — red,                    (6.17)

magenta = white — green,           (6.18)

yellow = white — blue.                 (6.19)

With these colors we have what is known as the CMY system. However, these ideal filters do not exist, so a more practical set of cyan, yellow, and magenta filters is illustrated in Fig. 6.8. Ideally, cyan, magenta, and yellow are sufficient to generate a wide range of colors by the subtractive process. For example, equal amounts of these three colors should produce black, but in practice, a dark brown color is generated. For this reason a fourth real black ink is added in many printing processes to obtain a truer color. This is called the CMYK system.

Figure 6.8 Three practical filter transmissions for color subtraction. (Click to enlarge.)

Predicting colors obtained by color subtraction is not as simple as with color addition. As shown in Fig. 6.9, cyan, yellow, and magenta are obtained inside a triangle where the three curved lines are formed. The subtractive color process is used, for example, in color photography where several layers of different colors are superimposed. It is also used by printers where three or four inks are mixed.

Figure 6.9 Colors obtained by subtraction using cyan, magenta and yellow.
Citation:

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

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