How acutely can we tell two colours apart? A century of answers, and why the most famous one cannot be used the way it has been.
A healthy eye can tell apart the two sodium lines, 589.0 and 589.6 nm, if the light is bright enough (about 100 Td), using two cone filters that are each over 100 nm wide.
König and colleagues shifted a spectral light until it just looked different, using the average error of 50 matches.
MacAdam's single observer made colour matches around 25 points of the CIE diagram.
Stiles measured how bright a brief coloured flash must be to be seen on a coloured field.
A side note from 1885: Nichols reported that 25 parts of red lead in 100,000,000 parts of white powder already tinted the mixture. Section 1.
The just-noticeable change in wavelength has two optima, near 580 nm in the yellow and 490 nm in the blue-green, a pessimum in the green near 540 nm, and rises at both ends.
Set a wavelength step and see where it can be seen: as the step grows, the first places it becomes visible are the two optima.
König's measure was performance, not judgement: 50 matches to each wavelength, scored by their average error.
Section 1.1 · curve: two-subsystem model at 100 Td; its green pessimum falls nearer 520 nm than König's 540 nm · discs on a screen only approximate spectral lights
At Eastman Kodak, David MacAdam had one observer, Perley G. Nutting Jr., adjust colour along lines through 25 reference points at a fixed 48 cd/m², in a 2° field with a dimmer neutral surround.
Each ellipse is the spread of his matches. The ellipses differ hugely in size and shape, so equal distances in the diagram are not equal differences to the eye. Switch to the 1976 diagram: the sizes even out, but no ellipse becomes a circle.
Still, they shaped the CIE 1960 and 1976 diagrams, colour-difference formulas, and estimates of how many colours we can see.
Section 1.2 · MacAdam 1942 ellipses, magnified ×10 · click an ellipse
Stiles explained his increment thresholds with independent, non-opponent "π mechanisms". But late in his career he found the exception: a red flash on a bright red field becomes harder to see when a green flash is added to it.
Move the second flash along the spectrum. Where the index drops below zero, the two flashes push an opponent detector in opposite directions and cancel.
Conditions that favour such opponent detection: large, long or blurred flashes, short wavelengths, intense or congruent fields, and neutral adaptation.
Section 1.3 · Stiles 1967 · model with an L−M opponent detector and an L-cone detector (plus an S-cone detector, a model addition)
Helmholtz wrote colour distance as the sum of Weber-scaled changes in three receptors. Stiles later gave each cone its own Weber fraction, the S cones' much larger, probably because they are sparse.
Even refined, a model of independent cones cannot predict MacAdam's ellipses.
Section 2.1 · Helmholtz 1896, Stiles 1946
Stiles's Weber fractions. a, b, c stand for each receptor's "self-light", today perhaps spontaneous opsin activity.
Re-expressing MacAdam's ellipses as cone signals in 1949, Le Grand saw that their long axes lie largely along tritan lines, lines on which only the S cones change. S thresholds depend on the level of S/(L+M); L/M thresholds are lowest where the L and M signals are similar.
MacLeod and Boynton built this into a diagram: L/(L+M) across, S/(L+M) up, all at equal luminance. Switch to it: every tritan line becomes vertical. Its axes are the two subsystems, not the red–green and yellow–blue of experience.
Section 2.2 · MacAdam's ellipses ×10, each with the tritan line through its centre · click an ellipse
Krauskopf and colleagues (1982) adapted observers to colour flickering along one line through white. Along either MacLeod–Boynton axis, the loss of sensitivity was confined to that axis; along a diagonal, it spread much more widely. They called the axes cardinal.
Compare the two hypotheses. Many tuned channels would let the loss follow any adapting direction. Two channels predict the observed pattern.
Section 2.2 · polar plot: rise in threshold in each direction after adapting
The colours the adapting light flickered between
The two cardinal signals were matched to two retinal routes. The ancient one compares S cones with L+M; the recent one, made possible by the split of L and M pigments, compares L with M.
Separate anatomy fitted the psychophysical independence. By 2000 this was the straightforward, dominant account.
Section 2.2 · Derrington et al. 1984; Dacey & Lee 1994; Martin et al. 1997
Walraven pictured the normal eye as two dichromats in one. The L/M subsystem gives the yellow optimum; the S subsystem gives the blue-green one.
Switch off either subsystem and one optimum disappears. Without S signals, as for tiny targets at the centre of the fovea where S cones are sparse or absent, discrimination fails badly near 460 nm.
Dim the light: the blue-green optimum moves to shorter wavelengths.
Sections 2.3–2.4 · Figure 5a · two-subsystem model
Dim the light or add white and watch the threshold fall. Rates of change of cone ratios cannot explain this.
Section 2.4 · model curves; Tyndall found little change from 100% to 30% purity, then a sharp improvement, where the model improves steadily
Natural surfaces almost never produce the huge S/(L+M) ratios of a 450–460 nm light. The S channel's output is compressive, so a bright, steady spectral blue drives it into saturation, where neighbouring wavelengths give nearly the same response.
Dimming, shortening or diluting the light pulls it back onto the steep part of the curve. The sliders are shared with the previous slide, so this is the same stimulus.
Section 2.4, assumptions 1–5 · Polden & Mollon 1980
Craik showed it for brightness in 1938; it is now one of the firmest findings for colour. Thresholds form a V around the adapting point, and the V moves when adaptation moves.
Move the adapting colour toward the marked test, and the test becomes easier to discriminate. Much of this shift happens after the cones, at a chromatically opponent second site.
Section 3 · Craik 1938; Loomis & Berger 1979 · schematic L/M channel
Mollon and Cavonius tested 1,000 Td yellow half-fields after adapting to monochromatic fields of only 10 Td: too weak to matter much to the cones, but enough to polarise a ratio-extracting second stage.
Two hypotheses make different predictions. Step through the four fields, then reveal what was found.
Section 3 · Mollon & Cavonius 1987
He made long runs of settings at each reference with no instruction to look at the surround. Each ellipse therefore records a local, adapted expansion of colour space, not what he could see everywhere at once.
Stitch those local minima together and you get a space that is far too fine. It cannot be a uniform colour space for a neutral observer, nor a count of discriminable colours.
Section 3.1 · compare the two observers
Two abutting fields may be told apart by a signal at their shared edge, as in photometry. Double-opponent cortical cells could supply such a signal. If so, split-field thresholds say little about how distinct two isolated colours are.
The paper's prediction: thresholds should rise as the fields are pulled apart. Try it: make the difference just visible with the halves touching, then separate them.
Section 3.2 · Le Grand 1970 · the curve is the paper's prediction, not data
Krauskopf and Gegenfurtner (1992) separated the two conditions MacAdam had mixed. Adapted to white, thresholds were lowest at white and rose with distance; a white-adapted observer might distinguish only about 448 equiluminant colours.
Two independent channels allow only circles or upright ellipses. Yet two quadrants held oblique ellipses pointing at the adapting point.
Sections 4–5 · raise the third channel to reproduce the obliques
Sections 5.1–5.3 · model: L/M thresholds at two referents as S changes
A step around the hue circle is easier to see than an equal step toward white. Judd found a hue circle of radius n holds about 4πn steps, not 2πn, so no Euclidean colour space can work.
On an oblique line, both steps use the same two cardinal signals, only combined in a different phase. With independent noise they would be equally visible. Correlated noise in the two channels can mask the purity step.
Section 5.4 · Judd 1969; Danilova & Mollon 2016 · the gap is largest in the upper-left and lower-right quadrants and small near white, which this simple noise model cannot show
One fix is a channel that sets L and S against M, which would signal redness versus greenness and balance on the yellow-blue line. Old recordings hinted at it; in 2024 Godat and colleagues imaged macaque ganglion cells of both noncardinal types.
Human connectomics shows several routes for S signals to reach L or M pathways selectively.
That firm framework has gone.
Section 6 · Godat et al. 2024; Kim & Dacey 2026
Perley G. Nutting Jr. died in South Pasadena, Florida, in 2001.
"We need a worthy successor."
Mollon & Danilova, Section 7
Based on Mollon, J.D. & Danilova, M.V. (2026). The legacy of Perley G. Nutting Jr.: the past and the present of chromatic discrimination. Annu. Rev. Vis. Sci. 12. Demos use simplified models; see the companion explorer for model notes.