Appendix A: Color Perception

In this appendix, a (simplified) introduction to how the eye perceives color is given. This helps to understand some issues mentioned in the main text, for instance why the sky does not appear violet, why there are 'pure' colors like green that are difficult to produce and 'mixed' colors like yellow that arise much easier.

Spectral vs. RGB colors

When we look at a rainbow, we see how white light is separated into different wavelength by refraction. We see the different wavelengths as different colors, in the spectrum there is a direct corresponence between the two: Light at a wavelength of 400 nm (nanometers) appears violet, at 800 nm red and at 600 nm a yellowish green. So as far as the physical spectrum is concerned, there is no difference in principle between yellow and green - they are just two different wavelengths, but no color is pure or mixed.

However, when we look at a computer monitor, all colors are characterized with an RGB triplet - values of red, green and blue that are mixed to determine a color, and we find that green is a pure color (only the green channel can be active) but yellow requires a mixture of green and blue to appear.

Why the difference - why can RGB values encode wavelengths at all?

Color-sensitivity of the eye

The answer is that what provides color vision are light-sensitive cells called 'cones' in the retina. They come in three types - which for simplicity we can denote 'red', 'green' and 'blue'. The reason is that they have different sensitivities at different wavelengths. For instance, the 'blue' type provides a strong signal when short wavelength light hits it, but hardly any signal when the light is of long wavelength and red. The following illustration shows how the tree types are sensitive to different wavelengths (or spectral colors).

Sensitivity (vertical axis) of the three different cone types to light as a function of wavelength (or color, horizontal axis). For simplicity the cone types are named 'red', 'green' and 'blue' although that is not strictly what they perceive.

So whatever spectrum of light falls into the eye, the retina always delivers a triplet of output values to the brain, namely the relative excitation between 'red', 'green' and 'blue'. Fundamentally, this is why colors can be encoded in RGB (although the precise relationship is a bit more complicated, and there are colors which can not be displayed at all in the RGB scheme).

Pure vs. mixed colors

So, how does that work in practice? Assume we let a beam of yellow spectral light at 570 nm fall into the eye (see narrow yellow bar in the figure).

Different light spectra falling into the eye.

The response of the eye is the strength of the signal times the sensitivity of the cone. The blue cones don't respond much at all, whereas green and red in equal measure. Thus the brain knows that no signal from blue and equal signals from red and green means seeing yellow light.

But what if a mixture of different wavelengths falls into the eye? We just divide the problem, imagine a collection of narrow bands at a given wavelength - for each we multiply with the eye sensitivity and then we add all up to get the output of the red, green and blue channel.

But that means something interesting can happen - consider the wide, yellow signal (also labeled 'yellow'). It still does not produce much blue response as the blue sensitivity curve is very low - and it still produces about equal response in the red and green. What does that mean?

It means that perceived colors aren't physical like spectral colors. The wavelength distribution in both cases is different, but we see the same color because the cones are excited the same way. Imagine a different case - we can have a spectral violet at the edge of the short wavelength regime (note how the red cones respond to that). Or we could have a mixture of blue and red light that gives just the same small response in the red cones - and it would also look the same color.

A mixed color thus can arise from a broad distribution of wavelengths, for instance a spectrum from which violet and blue are partially removed starts looking yellow. A pure color requires a distribution with a peak underneath the maximum sensitivity - we can not get green in any way by exciting red and blue cones, the only possibility is to have a stronger 'green' signal than 'red' and 'blue'.

Why the sky isn't violet

We stated earlier that Rayleigh scattering is strongly wavelength dependent and removes more of the short wavelength part. The spectrum of radiation that makes the sky blue is hence strongest in the violet region (see the line labeled 'sky blue') - so why don't we see a violet sky?

Consider how the line falls into the response functions of the cones - it gives a strong signal in the 'blue', but due to the odd shape also a smaller response in the 'red', and then some in the green. If there were no violet (and hence excitation of 'red' cones), the sky would look blue with a small amount of green, i.e. roughly turquoise. If one adds the red component caused by the violet however, it removes the green signal and creates just the impression of sky blue we see.

But how can 'red' possibly remove 'green'?

That has to do with a complication in how the three signals are processed in the brain. Most combinations mix - for instance one can see a greenish blue or reddish blue, or a bluish green, or a red-violet changing into blue - but one can not see a greenish red or reddish green, the two colors don't blend. That is because they're not summed up but rather veto each other, so seeing a component of 'red' can indeed literally remove a component of 'green'.

There is much more detail about how the eye perceives colors, but that is beyond the scope of this appendix.

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