Cones, Spectrums, and Color
© 22 Jan 2014 Luther Tychonievich
Licensed under Creative Commons: CC BY-NC-ND 3.0
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How the digital age is teaching us some colors don’t exist.


In most people’s eyes are three kinds of cones. There are also rods, but they saturate at such low levels of light that they give no useful information in most cases. So we are left with just the three. Because there are just three cone types, all possible color combinations we might see can be described by three numbers between 0 and 1: (0, 0, 0) would mean none of the cones are reacting at all, (1, 0, 0.5) would mean one kind of cones is reacting as much as it can, one not at all, and one at half-capacity.

Light comes in photons, and each photon has a wavelength. Visible light is approximately between 400nm and 700nm wavelengths, but each cone reacts to different wavelengths differently. There are lots of versions of the graph about their sensitivity; here’s a simplified one (good enough for this post):

400 nm700 nm

From this picture we can take a wavelength of light—say, 497nm—and see how likely each kind of cone is to respond if hit by a photon of that wavelength.

400 nm700 nm497 nm

In this picture (it is worth repeating it is just a simple image for exposition) we have about (0.16, 0.4, 0.24) for what are sometimes called the Short, Medium, and Long wavelength cones (S, M, L). Usually when dealing with color we don’t care much about intensity of light. 497nm light looks the same “‍color‍” no matter how bright it is. So let’s normalize that response so the total excitation is 1, giving us (0.2, 0.5, 0.3).

It is evident from this picture that some (S, M, L) combinations cannot be created by any combination of light waves. For example, there is simply no way to get (0, 1, 0): any photon that excited the middle-wavelength cone also excites either the short or long or both.

It is also the case that the normalized colors provide a linear space: if one wavelength gives normalized eye color (S1, M1, L1) and another (S2, M2, L2) then having a photons of the first and b photons on the second will create color
a + b
(aS1 + bS2, aM1 + bM2, aL1 + bL1). We can thus draw the space of all color perceptions we could experience like so:

Clearly this image does not have every possible color… again, just a diagram.

However, some of the points in this triangle cannot be achieved by any wavelength of light or combinations thereof. In particular, we can draw on the image above a curve representing all pure wavelengths.

The only colors we ever actually see are inside that curve:

But most of us rarely see some of those too, because most computer screens and printing processes just use a triangle from inside that region. Because it is a curve, they’d need every wavelength in the visible spectrum to get them all so instead they just grab 3 inexpensive-to-produce colors and use them. This gives just a triangle out of the set of possible colors.

One of the side effects of this phenomena is that many people have been raised on only the triangle of colors. There are other colors that they almost never see and never hear identified as a color. Of course, before computers and quality color printing only a small number of artists had names for almost any colors, so it’s still probably an improvement. But it is not an unmitigated one.

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