Subtractive mixing in coloured filters

As we have just seen, if we pass beams of light through two separate coloured filters and then combine the beams, the resulting "colour mixing" (strictly, colour stimulus mixing) is classed as additive mixing. A different kind of "colour mixing" occurs if we instead overlap the two filters and pass a single beam through them together. Now the effect of the second filter is to remove light that has passed through the first filter, rather than to add to that light, and so the process is generally known as subtractive colour mixing. The resulting beam consists of those wavelengths that are transmitted by both filters, as opposed to either filter in the case of additive mixing (Fig. 5.1.1).

Figure 5.1.1. Additive and subtractive mixing contrasted using ideal yellow and cyan filters. Adding cyan and yellow light gives greenish white light; successively removing light with cyan and yellow filters gives saturated green light.

The result of subtractive mixing of two filters is calculated by multiplying together the percentage of light energy passed on by both filters, for each wavelength of the visible spectrum. (This has led some to prefer the term multiplicative mixing). Thus if 20% of a particular wavelength is passed on by one filter and 50% of the same wavelength is passed on by the other, the subtractive result will be 20% of 50%, or 10%. If any wavelength is completely blocked by one or other filter, then that wavelength will be absent from the result. In the theoretical example of Fig 5.1.1, an ideal yellow filter transmits all light in the red-orange and green bands of the spectrum, but no blue-violet light, while the ideal cyan filter transmits all light in the green and blue-violet bands, but no red-orange light, and so subtractive mixing leaves only the spectral component that the two filters have in common: green.

Take a moment at this point to make sure that you have completely eradicated from your mind the naive idea that green is "made of" yellow and blue. Subtractive mixing doesn't work like that. We get a green mixture from yellow and cyan because these components both are partly (so to speak) "made of" green. If any colour can be said to be "made of" yellow and blue, it's white!

Subtractive mixing and coloured illumination

The colour stimulus resulting from the interaction of a coloured object with a coloured light source is another example of subtractive mixing (Fig. 5.1.2). Here we think of the incident light as having had certain wavelengths removed compared to white light, and we multiply the percentage of each wavelength present with the percentage of that wavelength reflected by the object. How this stimulus is actually perceived, however, will depend on the degree to which the observer's vision adapts to the colour of the light source.

Figure 5.1.2. Cyan coloured ball under yellow light. IMAGE: D. Briggs, Photoshop CS2.

Subtractive mixing in traditional paint media

Subtractive mixing is important to artists using traditional paint media because of its role in the physical mixing and glazing of paints. Subtractive mixing is involved in mixing or glazing of physical colourants because most light will be influenced successively by particles of each component colourant (Figs 6.1.2, 6.1.3). Once again the result of the subtractive interaction is calculated by multiplying the percentages of light passed on by each colourant, wavelength by wavelength throughout the spectrum.

Because of the phenomenon known as metamerism, two colourants may be similar in colour, but have somewhat different spectral reflectance curves, and consequently the exact results of subtractive mixing of real colourants can not be predicted merely from their colour. This uncertainty should not be overstated, however. All common cyan and yellow colourants combined subtractively will make a green; only the precise appearance and spectral composition of that green will depend on the specific colourants used.

Subtractive mixing in digital painting

Subtractive mixing in digital media is emulated by blending layers in Multiply mode, which multiplies the RGB values of a layer with the underlying RGB values. This blending operates on the nonlinear (perceptual) RGB values, but because it is a multiplication, the resulting colour is the same as if it were done on the linear (physical) RGB values. Subtractive mixing is simpler in digital media than in traditional media and in nature, in that there are only three bands of the spectrum to be considered. It gives a realistic representation of what subtractive mixing involving comparably coloured lights and materials might result in, but real-world subtractive mixing could give a somewhat different result because it depends on the actual spectra of the lights and materials involved. Unrealistic effects may result from subtractively mixing very bright and/or very saturated digital colours that are outside the range of real object colours.

Even in a program such as Painter, which cleverly simulates the appearance and physical behaviour of artists' paints, colours nevertheless still mix by ideal subtractive rules (e.g. "Monitor yellow" and "Monitor blue" mix to make black or grey, while paints of similar hues would mix to a dull green).




Modified August 13, 2012. For original (2007) page see here.

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