fundamental primaries Primary Colours

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Question

What are the three primary colours?

(a) red yellow blue
(b) magenta yellow cyan
(c) red green blue
(d) extreme red psychedelic aquamarine extreme purple


Answer

In kindergarten you probably learned that the primary colours are
(a) red yellow blue .

Later on you learned that those are `subtractive' primaries, good when colours are produced by subtracting light, as in printing, or when mixing colours from a paintbox. You further learned that a better set of subtractive primaries is
(b) magenta yellow cyan .

You also learned that there are `additive' primaries, good when colours are produced by adding light, as in TVs and computer monitors,
(c) red green blue .

The magenta-yellow-cyan and red-green-blue primaries are good in the sense that their combinations yield a wide range of colours from only three primaries. However, as seen on the chromaticity diagram on the spectrum Where's purple? page, three primaries can produce only colours within their gamut, leaving many colours, such as disco purple, beyond the pale.

Suppose that you could, by some magic, tickle each of the three types of cone in your eye individually, or in any proportion, at will. Clearly you could produce any possible colour - along with some impossible colours - by tickling your cones in the appropriate combination. As discussed immediately below, the colours that correspond to tickling each cone separately are the cone primaries, or fundamental primaries,
(d) extreme red psychedelic aquamarine extreme purple .
It should be emphasized that the colours you actually perceive are coloured by processing in the brain, and do not depend simply on how much each cone type is tickled. The complicated wiring that converts what you see on your retina to what you get in your brain is traced for example in the lucid text by D. Falk, D. Brill & D. Stork `Seeing the Light' (Wiley, 1986).


The Fundamental Primaries

cone sensitivities Your eye contains long, medium, and short wavelength cones, called L-cones, M-cones, and S-cones. The graph at right shows the sensitivity of each of the three cones, taken from tables at the UCSD Color and Vision database. The Ll and Ml sensitivities are from A. Stockman, D. I. A. MacLeod & N. E. Johnson (1993, J. Opt. Soc. America A, 10, 2491) while the Sl sensitivity is from A. Stockman, L. T. Sharpe & C. C. Fach (1999, Vision Research, 39, 2901). All three sensitivities are based on the Stiles & Burch (1955) 2° colour matching functions.

Just as any colour can be characterized by its CIE X, Y, Z coordinates, so also can any colour be characterized by its L, M, S coordinates. The L coordinate of a spectral distribution Pl of light power is an integral of the power over the sensitivity Ll graphed at right, L   Ll Pl dl . The M and S coordinates are defined similarly.

Stockman et al. normalize the cone sensitivities to one at their peaks, as graphed. With this normalization, an equal energy white spectrum, Pl = constant, of unit luminance corresponds to

Leq = 1.051  ,     Meq = 0.873  ,     Seq = 0.508  .
 (1)
The three numbers in equation (1) are in proportion to the areas under the corresponding sensitivity curves. Unit luminance means  Vl Pl dl = 1, where Vl is the photopic luminosity function. The luminosity function used here is the 2-degree V*(l) from A. Stockman & L. T. Sharpe (2000 Vision Research, 40, 1711) available at the UCSD Color and Vision database.

The LMS sensitivities could be normalized in other ways. For example, the 1931 CIE XYZ functions are normalized so that equal energy white of unit luminance corresponds to Xeq = Yeq = Zeq = 1. One might consider normalizing the LMS primaries similarly, so that equal energy white of unit luminance would correspond to Leq = Meq = Seq = 1. However, the resulting equal energy white point in the lm chromaticity diagram (see immediately below), at leq = meq = 1/3, would be too close to the monochromatic boundary to offer a balanced palette of colours. Stockman et al.'s normalization locates the equal energy white point somewhat more judiciously in the lm chromaticity diagram.

chromaticity diagram in the fundamental primaries Colours in the L, M, S system of fundamental primaries can be defined, without reference to their overall brightness, by their l, m chromaticities (compare the similar definition of the CIE x, y chromaticities)

l L
L + M + S
 ,     m M
L + M + S
 .
(2)
The diagram at left shows the chromaticity diagram plotted in the l-m plane of fundamental chromaticities. Colours in the lm chromaticity diagram combine linearly, as they do in all chromaticity diagrams. Compare this diagram to the xy chromaticity diagram on the spectrum Where's purple? page.

Incidentally, if you are looking at this chromaticity diagram on a Mac and the colours look washed out (too much white), read Charles Poynton's Gamma FQA to find out why. The policy for rendering colours on these pages is set forth on the spectrum Where's purple? page.

The white point in this chromaticity diagram has been taken at equal energy white, equation (1), with lm chromaticity coordinates

leq = 0.432  ,     meq = 0.359  .
 (3)

The three fundamental primaries lie at three corners of the chromaticity diagram. These are the colours I call extreme red, psychedelic aquamarine, and extreme purple, at (lm) = (1, 0), (0, 1), and (0, 0) respectively. Maybe extreme purple should be called extreme violet. But violet whispers pale, while purple shouts vibrant, clearly a sounder choice.

What do the fundamental primary colours look like? All of them lie outside the range of colours that can be produced by ordinary light, so you have to stretch your imagination. Extreme red and extreme purple lie close to crimson red and disco purple, the colours of monochromatic light at the longest (l  700 nm) and shortest (l  425 nm) wavelengths. So perhaps those are not too much of a stretch.

The colour of the green fundamental, at (lm) = (0, 1), is quite another trip. I call it psychedelic aquamarine because it lies well outside the range of physically realizable colours, at least for people with normal three colour vision. The nearest monochromatic colour, obtained by adding white to psychedelic aquamarine, is around 497 nm, about the colour of the water around the reefs of Heron Island in the Great Barrier Reef of Australia, which I had the privelege of visiting in 1995. You should mentally subtract white to imagine psychedelic aquamarine in its vivid primal hue.

In the brainless theory of colour, people who are red colour-blind (protanopic) should see psychedelic aquamarine at the longest wavelengths. In reality, however, the colours people actually perceive depend not only on the relative stimulation of the different cone types, but also on processing by the brain. Next time you meet a protanope, ask him (1% of males are red colour-blind, but only 0.02% of females) what he sees when he sees red.


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Updated 6 June 2001