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.
Look at a split field of spectral light. Adjust the wavelength of one half until it matches the other. Make 50 matches per wavelength.
Look at a 2° field, divided vertically, in a dimmer 42° neutral surround. Adjust one half along a line through the other half's colour until they match. About 50 matches per reference, 25 references.
Fixate a coloured field. A brief (200 ms) monochromatic flash appears on it, or not. Say whether you saw it, as its intensity is brought to threshold.
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.
König and his colleagues viewed a split field of spectral light. One half held a fixed wavelength; the observer adjusted the other until the halves matched, 50 times at each wavelength. The measure was a performance measure: the average error of those matches.
Their errors were smallest near 580 nm in the yellow and 490 nm in the blue-green, largest in the green near 540 nm, and grew toward both ends.
Section 1.1 · König & Dieterici 1884 · a screen mixes three primaries, so its “wavelengths” only approximate spectral lights, and its field is not 100 Td
Curve: two-subsystem model at 100 Td; its green pessimum falls nearer 520 nm than König's 540 nm. Dots: your average errors, measured on this screen.
At Eastman Kodak, Perley G. Nutting Jr. looked at a 2° field, divided vertically, at 48 cd/m², inside a dimmer (24 cd/m²) neutral field of 42°. One half held a reference colour. He adjusted the other along a line through it in the chromaticity diagram, at constant luminance, until the halves matched.
He made nearly 25,000 matches, in different directions through 25 references. The spread of his settings in each direction gives one radius; MacAdam fitted an ellipse to them.
The ellipses differ hugely in size and shape, so equal distances in the diagram are not equal differences to the eye.
Section 1.2 · MacAdam 1942 · the screen field is drawn larger than 2° and is not at 48 cd/m²
Close-up of the selected ellipse at 3 SD. Centre: the reference colour. Orange ends: ±3 SD along the long axis. Blue ends: ±3 SD along the short axis. All four ends were equally hard for Nutting to tell from the centre.
Ellipses magnified ×10; click one. Switch to 1976 u′v′: the sizes even out, but no ellipse becomes a circle. Yet they shaped the CIE 1960 and 1976 diagrams, colour-difference formulas and counts of discriminable colours.
Stiles's observers detected brief (200 ms) monochromatic flashes on monochromatic fields. Thresholds across flash and field wavelengths defined his independent, non-opponent “π mechanisms”.
Late in his career he added a second, congruent flash. A 640 nm flash on a bright red field became harder to see when a green flash was added: an opponent channel, pushed both ways, cancels.
Section 1.3 · Stiles 1967 · on screen the field and first flash are the display's red primary, not 640 nm, each flash scaled to the same fraction of its own threshold
Model with an L−M opponent detector and an L-cone detector (plus an S-cone detector, a model addition). Opponent detection is favoured by large, long or blurred flashes, short wavelengths, intense or congruent fields, and neutral adaptation.
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
Distance from the centre: threshold after adapting (× unadapted). Inner ring ×2.5, outer ring ×4.0.
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
Each pair is shown as a split field and as a tiny dot about 6 px wide. Look straight at each tiny dot from your normal viewing distance. The pair that differs only in S cones merges into one colour, because the centre of the fovea has almost no S cones. The L/M pair stays two-coloured.
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
A 2° field, divided horizontally. The lower half stays at 455 nm; the observer adjusts the upper half. The illuminance and purity sliders above change both halves together, and the white is identical in each. A screen cannot reach the saturation of real 455 nm light.
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
The adapting field fills the view. The test pair in the middle sits at L/(L+M) 0.76, its halves 0.008 apart. Move the adapting colour toward the test and the pair stands out more; move it away and the halves blend.
Two candidates. An L/M ratio channel, one of the two subsystems, cares only about the balance of L and M signals. A Hering red–green channel, the one behind hue appearance, is balanced for yellow and for blue and pushed off balance by reddish or greenish light.
Mollon and Cavonius adapted observers to a dim (10 Td) single-wavelength field, then measured the threshold for bright (1,000 Td) yellow test fields: how far apart in wavelength the two halves must be before the observer can tell them apart. A field that raises this threshold makes yellows harder to discriminate. A field that dim barely changes the cones, but a ratio stage responds to its L:M balance however dim it is.
Yellow and green are controls: both theories agree. Blue and violet pull the theories in opposite directions.
Section 3 · Mollon & Cavonius 1987
The dim adapting field of the chosen wavelength, with the bright yellow test pair in the middle (a 2° split field). Brightnesses here are only roughly in proportion.
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
Four patches, equiluminant with the white background, appear for 0.4 s. Three are the referent; one differs in a random direction, by 3× the model's threshold for that direction. Click where the odd one was.
Sections 5.1–5.3 · model: L/M thresholds at two referents as S changes
A foveal split field flashed on a neutral adapting field. The halves differ only in L/(L+M), here by 3× the model threshold. Both halves share the same S level, so S cannot tell them apart, yet the S level changes the threshold.
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
Both steps start at the referent, at the chosen direction from white, and have the same length in the diagram (the orange and blue arrows). Under a neutral state of adaptation, most observers find the hue step more visible.
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.