Please inspect Figure 1.
Figure 1. The World’s Most Misleading Scientific Graph: The CIE 1931 Chromaticity Diagram.
If this diagram gives you a headache, this web log is for you. I will never show it to you again.
If you’re a color-technology professional, or training to become one, this web log is intended to give you a headache.
⁂
Color in One Dimension
“She brakes
She brakes for rainbows
She knows where the rain goes.”
—She Brakes for Rainbows, written by Kate Pierson, Cindy Wilson, Fred Schneider, and Keith Strickland; performed and recorded by The B-52’s, from their album Bouncing Off the Satellites (1986)
Figure 2. Rainbow and friends.
Color Ab Initio
Rainbows have the power to stop traffic and cause accidents, but the human perception of color has more power than that.
Although a rainbow does not display all the colors the human eye can perceive or distinguish, it does reveal something essential about color: it is best understood as a space. In the case of a rainbow, nature offers a single, continuous coordinate for labeling its colors – the frequency (or wavelength) of the light that we see. In other words, a rainbow is an example of a one-dimensional space. Figure 3 is an attempt to show a more scientific version of a rainbow’s appearance, shown labeled by the spectral frequency depicted in the color bar.
Figure 3. Simulated rainbow as permitted by a conventional computer display. (Spectral colors are converted to the sRGB color space with hue-preserving compression; the appearance is an approximation suited to a display with standard dynamic range.)
A rainbow illustrates another important feature of color. We call the array of rainbow hues a “spectrum,” but look closely: that spectrum is far from uniform (Figure 3). Notice how much of it is taken up by the red and violet hues compared to the others.
So despite the convenient physical label — frequency1 — that maps each color of the rainbow to a single number, human perception knows nothing of these numbers. Instead, it cobbles together its own clunky sensing system, one that throws away most of the physical detail present in the spectrum before it ever reaches consciousness.
Imagine yourself in a color laboratory, and your job is to count how many distinct colors you can sense in a rainbow. You set up a prism as a stand-in for the rainbow, and a narrow viewing slit that you can slide along the spectrum to isolate one thin band of color at a time. You move the slit in small steps, each time asking: “In this new position, does this look any different from the last position?” How many positions of the slit do you end up needing to label and count every distinct color you can perceive?2
Under realistic viewing conditions, the answer is not thousands or millions. It’s on the order of a hundred to maybe a couple hundred distinct spectral colors. Beyond that, the steps become too small to notice. For the sake of having a number to hold in our heads, let’s say there are about 150 distinct rainbow colors you could reasonably count in this experiment.
Yet, the set of colors we can see in the world — skin tones, paints, digital displays, sunsets, fabrics, plastics — is vastly richer than these 150 spectral samples. So there must be something more going on in our perception of color than just sampling frequencies along a line.
I’ll return to where all those other colors come from in a moment; for now, continue the experiment and measure the location of the slit at each point that exhibits a just noticeable difference (JND) from its immediate spectral neighbors. Now you have two ways of labeling the spectrum: nature’s coordinate (frequency) and a perceptual coordinate — the physical slit positions where each JND occurs, which you may think of as stepping through the rainbow one distinguishable color at a time.
If you plot each measured slit position against its corresponding frequency, you get a curious curve. It’s not a straight line (Figure 4).3 It bends and stretches in some regions, compresses in others, yielding a shape that has nothing to do with the geometry of the rainbow in the sky. What the graph depicts is our first glimpse of the structure of the perceptual rainbow — as measured via human vision itself.
Figure 4. Color discrimination by a standard observer. Psychophysical data demonstrating that the ability of the human eye to distinguish equal-brightness patches of spectral colors is not uniform with respect to spectral frequency. ΔE2000 quantifies perceptual color differences detected by human subjects as officially codified by the Commission Internationale de l’Éclairage (CIE) in the year 2000.
Figure 5. Color discrimination by a standard observer. The first derivative of the curve depicted in Figure 4.
And if you were the first person to make and understand that graph, your name would be David MacAdam, and you performed those measurements a little more than 80 years ago.
Color in Two Dimensions
Metamers
Note: This is a note block.
Frequency is a more natural unit to label spectral colors, and I will be using that unit uniformly throughout. This decision stands contrary to convention in modern commercial practice and engineering, where wavelength is the preferred unit. This will not be the only occasion I go against convention. ↩︎
In a realistic lab setting, not this hypothetical one, great care would be taken to properly normalize the light intensities and angles of incidence presented to a human subject. ↩︎
ISO/CIE 11664-6:2022 (formerly ISO/CIE 11664-6:2014), “Colorimetry — Part 6: CIEDE2000 colour-difference formula ↩︎