Colour Science & Perception
what the eye settles, and what it cannot
Concept

Display gamut — where it appears

The set of colours a screen can produce, bounded by the triangle its three primaries enclose and by how much light it can emit. It moves with the room, the black level and the age of the backlight, so a stated gamut is a claim about a device in a laboratory.

Named by 31 essays across 7 fields — each of them below, with the objects they name alongside it.

The CIE 1931 chromaticity diagram with its unreachable region marked. The spectral locus encloses every chromaticity a human eye can see. Cells inside the sRGB triangle are drawn in their own colour; the 85 per cent outside it are hatched, because no value this display accepts is the colour belonging there.

Most of this diagram cannot be shown

The chromaticity horseshoe is the canonical illustration of colour science, and nearly every printed copy is filled edge to edge with colours the page cannot produce. The honest version marks them, and the marking covers most of the picture.

matching · Gamut A gamma probe: which grey matches a half-white dither?. The striped block on the left is half white and half black, so it carries half the luminance of white. Stand back until the stripes blur and find the patch that matches it. On an sRGB display the answer is code 188, not 128 — code 128 has only 22 per cent of white's luminance.

The display is an unknown

This site is displayed on the very apparatus it is about, and it knows almost nothing about that apparatus. Two figures here stop assuming and ask instead — a probe for the transfer function and a probe for the gamut.

limits · Limits sRGB, Display P3 and Rec. 2020 compared on the chromaticity diagram. Three nested triangles inside the horseshoe. sRGB covers 74 per cent of the area P3 covers. Rec. 2020's red and green primaries sit on the spectral locus itself, within 0.000 and 0.002 of it, meaning they are monochromatic.

What a gamut costs

Three primaries reach a triangle and the visible region is not a triangle, so something has to give. Widening the primaries helps, has a price in precision and compatibility, and runs into a limit that is geometric rather than technological.

matching · Gamut Dominant wavelength as a construction on the diagram, against equal-energy E. A ray is drawn from the white point through each sample and continued until it leaves the diagram. The sample at (0.28, 0.52) leaves through the spectral locus at 537 nm, at excitation purity 0.43. The sample at (0.36, 0.19) leaves through the line of purples, so it has no dominant wavelength at all and is written 544c nm — the crossing on the opposite side, marked with a c. The hatched region is colour this display cannot show and is not drawn as though it could.

Not every colour has a wavelength

The question every reader arrives with is which wavelength a colour is. For close to a third of the directions on the chromaticity diagram the honest answer is that there is none, and the construction colorimetry offers instead is a statement about a diagram rather than about light.

matching · Gamut Chromaticity-triangle area against CIELAB volume, both relative to sRGB. Two ratios for each space, both against sRGB. The upper bar is the area of the primary triangle on the CIE 1931 diagram; the lower is the volume of the gamut solid in CIELAB, computed by tetrahedral decomposition of the RGB cube at 24 cells per axis. Display P3 is 1.36× sRGB by area and 1.50× by volume; Rec. 2020 is 1.89× sRGB by area and 2.26× by volume. The chromaticity diagram divides luminance out, so its triangle is a projection along the axis the eye is most sensitive to — and a coverage percentage quoted on it is a statement about the shadow.

The triangle is a shadow

A display's gamut is drawn as a triangle on the chromaticity diagram, and coverage is quoted as a percentage of that triangle's area. Chromaticity has luminance divided out, so the triangle is a projection along the axis the eye cares most about — and the ratios computed on the solid are not the ratios computed on its shadow.

limits · Limits What no surface can be more colourful than. The MacAdam limits at 4 lightnesses under D65, each computed by sweeping two-transition reflectances over the whole band and keeping those that land at the target luminance factor. This is a physical bound rather than a gamut: a reflectance above 1 is a surface that emits, so no pigment anybody invents will ever put an object colour outside these curves. The boundary shrinks steeply as the surface lightens, from 0.310 at Y = 0.1 to 0.028 at Y = 0.9 — a very light surface has almost no room to be colourful, and that is physics rather than pigment chemistry. Drawn against it is sRGB at the same luminance factor rather than as a primary triangle, because a triangle is what a display can reach at some luminance and the bound is what a surface can reach at one; matched properly, sRGB covers 36% at Y = 0.1, 40% at Y = 0.3, 40% at Y = 0.6, 21% at Y = 0.9. The faint triangle is the familiar figure, kept only to show how much it misleads.

No surface can be that colourful

There is a hard bound on object colour that no pigment will ever move, and it follows from a reflectance being at most 1. Its boundary is generated by two numbers, it shrinks by a factor of eleven from dark to light — and measured against it properly, sRGB reaches 40% of what a surface could be at mid lightness while Rec. 2020 reaches 106%.

scene · Scene What a press and a display can reach at L* = 50. A slice through both solids at lightness 50, with the press dashed and the display solid. The boundaries cross: the press reaches past sRGB in 15 of 48 directions and falls inside it in 31. That is the shape of every conversion between them — colours are lost in one direction and gained in the other, and the picture cannot show the gained ones, because it is being displayed on the gamut that cannot reach them. Those are hatched.

Neither gamut contains the other

Converting a picture to CMYK is described everywhere as a reduction, as though the press were a smaller version of the screen. Measured as solids, the press reaches eleven per cent of its volume outside sRGB while sRGB reaches fifty-four per cent of its volume outside the press — and in the cyans the press wins by seventy per cent of chroma.

applied · Delivery The solids, by volume. CIELAB volume, all measured by the same cell count with the same extrapolation, and quoted against sRGB because that is the comparison the estimator supports. The four-colour press reaches 49 per cent of the sRGB solid's volume — and contains colours sRGB does not, which is why "half the gamut" is the wrong summary of a ratio of one half.

The fifth ink buys a corner

Orange, green and violet are sold as the answer to a four-colour press's gamut, and each one adds seven to nine per cent of volume. All three together add 23 per cent — almost exactly the sum, with no interaction — and every bit of it lands in the region of the ink that was added, at lightnesses where that ink is dark.

applied · Delivery The tone scale of one display, in four rooms. Code value along the bottom, the lightness it comes out at up the side. The curves are the same display: what changes is the light falling on the screen, which adds a fixed luminance to every pixel. The signal value that means black arrives at L* = 11.7 at 600 lux, against 0.9 in the dark — the lightness of a dark grey card, from a pixel that is switched off.

The screen is not the room

A thousand-to-one display in an ordinary office is a hundred-and-thirty-seven-to-one display, and the signal value that means black comes out at the lightness of a dark grey card. Nothing is wrong with the panel. Light falls on the screen and comes back off it, and the two per cent it returns is added to every pixel — most of all to the ones with nothing else in them.

applied · Delivery The colourfulness the sRGB cube reaches, against the light in the room. The display is the same display throughout and the signal is the same signal. What moves is the adapting luminance, which enters the appearance model and nothing else. The furthest colourfulness the cube reaches falls from 131 to 57, a factor of 2.29. A gamut in CIELAB cannot show this at all, because CIELAB has no light level in it — which is why every gamut percentage in circulation is quoted without one.

The gamut shrinks in the dark

Every gamut number here is a property of a device and of nothing else, which is why the same display has the same gamut in a studio and in a cinema. It does not. Turn the room down four decades and the solid loses a fifth of its reach and two thirds of its volume, with the signal unchanged.

limits · Limits Temporal sensitivity, and where each channel gives out. Modulation frequency in hertz against relative sensitivity. The luminance channel is band-pass, peaking at 8 hertz and running out at 60; an isoluminant modulation is low-pass and runs out at 15, which is 4.0 times sooner. Both cutoffs are at the same criterion of 5 per cent of that channel's own peak, so the ratio between them is a ratio between two measurements rather than between two conventions.

The eye has a shutter

An isoluminant flicker fuses at fifteen hertz and a luminance one at sixty, so a light whose colour changes forty times a second is a steady light of a colour it never emits. And the frequency at which flicker stops being visible is not a property of the eye — it moves twelve and a half hertz for every decade of light.

eye · Cones A 100 hertz drive, and whether anybody sees it. 3 cycles of a 100 hertz drive at 100 per cent modulation. The number beside each is how far above the threshold for seen flicker its loudest harmonic sits: above one and a stationary observer sees the flutter, below it and only something moving does. Fusion is at 60 Hz at 100 cd/m², and moves 12.5 Hz for every decade of light.

A lamp has a waveform

A lamp modulating a thousand times a second is a hundred times past the frequency at which flicker fuses, and it is plainly visible — as a dotted trail, during any glance across the room. The reason is not a new measurement; it is the spatial contrast sensitivity function, arriving from an unfamiliar direction.

light · Light Several sources on one scale. planck, led, narrowband, each normalised to its own peak and drawn on shared axes with the colour each produces beside it. Every one of these is sold as white light and every one is ordinarily described that way; what they have in common is a chromaticity, and very little else.

A screen is a poor lamp

A display's white is a light. Shone on a surface it renders colour worse than a fluorescent tube — and the wider the gamut, the worse it gets, because the narrow primaries that buy a large triangle are exactly the ones that leave holes in the spectrum.

light · Light How much colour a display delivers, against how bright the room is. The appearance solid of the whole code cube, with the room's reflected light added to every code value and the surround ratio computed from the room's own white against the display's. A 300 cd/m² panel delivers most at 200 lux, and the curve falls on both sides: darker costs the surround, brighter costs the black. At the 32 lux the softproofing standards specify, the solid is 89 per cent of its best — which is not a criticism of the standard, since it is written for matching a screen to a print viewing booth rather than for delivering the most colour.

A display in a room is a smaller display

Two results here turn the room's light in opposite directions and neither knows about the other. A room has one light level and does both at once — so there is a brightness at which a display delivers the most colour, it is not at either end, and it scales with the panel.

limits · Limits What a dither mask is worth, read as components, in two dimensions. Five luminance ramps, each quantised to 8 bits with and without a high-passed mask of the same power. The bars are the most visible single sinusoidal component of the error, as a multiple of the contrast that component needs to be seen: above the line at one it is visible. The mask lowers it by 20–22×, on every ramp — which the one-dimensional model on this site says it does not, and that disagreement is the finding.

Every threshold was measured with a grating

An earlier essay here claimed that the model cannot explain why dither works, and named two missing pieces. One of them was real and worth thirteen times the guess; the other was not needed. The piece nobody named was the detector — and reading the same model two ways changes the answer by a factor of fifty.

limits · Limits A fourth primary, swept — every setting an exact match, none of them the same. Four primaries matching three numbers leave one degree of freedom. Along the horizontal axis it is the fourth primary's share of the white's luminance; at each value the other three powers are solved exactly, so every point on this plot is a floating-point-exact match for the reference member — worst residual 1.3e-15 — and no colorimeter can tell them apart. What the population sees runs from 13.7 ΔE00 at the ninety-fifth percentile to 17.3, a factor of 1.26. The best setting is the largest share the arithmetic admits, so what stops it is not colour but the requirement that four powers stay positive.

Four primaries have a choice

Three primaries matching three numbers have one answer. Four have a family of them, every member exact to floating point for the observer they were solved for — and the members are not equally good for anybody else, so a display with a fourth primary has a setting that is robust to who is looking at it and a setting that is not.

matching · Gamut What a fourth primary actually buys. All three displays are floating-point-exact matches for the reference observer, so no colorimeter can tell them apart. The bars are the 95th percentile of what two hundred other eyes report. Held to the same gamut floor of 1.4× sRGB, the four-primary design leaves the population 2.6 times closer together than the three-primary one. That is what the extra emitter is worth, and it is not more colour — the gamut is held fixed while it is measured.

A fourth primary is a design

A display's fourth emitter is sold as more colour. Optimised instead against how far apart two hundred eyes are about its white — with the gamut held fixed so it cannot cheat — it buys agreement, and two and a half times closer together than three primaries reaching the same area, and the wavelengths it chooses are not the ones anybody would pick.

matching · Gamut Which of these paints the display can show, and to how many people. Each row is a real surface under D65, and the bar is the share of 120 observers for whom a non-negative mixture of this display's three primaries reproduces it. The question has no observer-free answer: the paint is a reflectance, the primaries are emission spectra, and whether one matches the other is a fact about somebody's cones. A dot marks the rows the 1931 observer calls displayable. 2 of them are rows some real people cannot see, and 4 more go the other way.

A gamut has a population

Whether a display can reproduce a paint is a fact about somebody's cones, so the boundary of a gamut is not a curve but a band. On a laser projector, ten of twenty-eight boundary surfaces are ones the standard observer calls displayable and some real people cannot see — and the wider the gamut, the wider the band.

matching · Gamut Four devices, and what each of them can do about a change of light. The mean over the census of what each device is left with. A press has no mechanism, so its number is the whole change — a printed sheet does not adapt to the room it is read in. A display can move its white point, which is a gain in its own primaries. A camera applies a gain in whatever basis its filter dyes happen to give it. And the sensor that satisfies the Luther condition exactly is worse than the silicon one — satisfying the condition means its channels are the matching functions, and a per-channel gain on the matching functions is the transform this site calls the oldest mistake still shipping.

Only one of these devices adapts

An eye, a camera, a display and a press all meet the same changes of light, and each has at most one thing it can do about them. The press has nothing at all, so its column is the whole change; and this collection's sensor built to satisfy the Luther condition exactly is the one that adapts worst.

limits · Limits What share of the diagram the sRGB triangle covers, in twelve published coordinate systems. Each row is a chromaticity diagram somebody has printed, and each bar is the fraction of the enclosed visible area that the sRGB triangle covers in it. Every row describes exactly the same observer and exactly the same gamut. The answer runs from 8.5% to 38.4%, a factor of 4.52, because area is not preserved by the projective maps that carry one of these diagrams to another. The familiar "about a third" is a fact about CIE xy.

Two thirds is not a property of the eye

It has been said from the beginning here that about two thirds of the chromaticity diagram cannot be shown on a screen. The figure is right, on the diagram it was measured on, and across twelve published diagrams the same triangle covers anything from 8.5 to 38.4 per cent of the same locus. Counting stimuli instead gives an answer that does not move.

matching · Gamut Three published primary sets, and a fourth chosen for how it adapts. The spectral locus with four triangles inside it. sRGB covers 33.5% of the diagram and leaves an adapted observer 2.36 ΔE00; Display P3 covers 45.4% at 1.22; Rec. 2020 covers 63.3% at 1.09. The fourth triangle is the best adaptation basis available to a display asked to cover 63.5% of the diagram, at 1.02 — and it is a different triangle from Rec. 2020's rather than a smaller one. The largest triangle that fits at all covers 73.9%, which is where the axis of this argument ends.

Primaries chosen for their inverse

Moving a display's white point is a gain on its R, G and B, so a display adapts in the inverse of its own primary matrix — a basis chosen by committees for gamut coverage and phosphor availability. Pose the design problem properly and the answer costs one per cent of the gamut argument and reaches within two per cent of the best basis there is.

applied · Delivery A display's primaries, scored as the adaptation basis they are. Four primary sets ranked by the mean ΔE00 an adapted observer is left with when the white point moves — which for a display is a gain on R, G and B, and so a von Kries adaptation in the inverse of its own primary matrix. sRGB leaves 2.36, as much as scaling XYZ directly and therefore as much as having no cone basis at all. Rec. 2020 leaves 1.09, better than every published adaptation transform fitted to corresponding-colour data. Nobody chose that: it is what wanting a wider gamut does to a primary's spectral selectivity.

The gamut race chose the basis

Twenty years of arguing about how much of the diagram a display should cover has produced primaries whose inverse is a better adaptation basis than any transform ever fitted to corresponding-colour data. On the invariant count of what those displays can actually show, the same twenty years produced nothing at all.

matching · Gamut What this collection's grid does to its own observer audit. Two bars per light: the mean departure of the observer computed on this collection's five-nanometre grid, and the same computation on a quarter-nanometre one. For five of the six lights the two agree to two decimal places, which is what a well-sampled spectrum looks like. For the laser projector the coarse answer is exactly zero and the fine one is 1.80 — the largest in the table. On a five-nanometre grid a three-line spectrum with lines at 465, 532 and 638 nanometres is a one-line spectrum, and a single wavelength is a stimulus every observer agrees about to the last bit. The two departures do not compound here; the first conceals the second.

One wavelength is everyone's colour

A stimulus with a single wavelength in it produces the same relative cone excitations for every observer, exactly, whatever their age or field size. A display made of three such stimuli is where observers disagree most. Both statements are consequences of the same algebra, and the second is why laser projection has an observer problem.

matching · Gamut The three cone absorptances at two settings of the pigment peaks. Solid and dashed are the same construction at the two ends of two standard deviations, and the L/M polymorphism on top. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 8.9 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The peaks move the flanks

Shifting a cone's peak wavelength by three nanometres changes its sensitivity at its own maximum by almost nothing and on its flanks by several per cent, because a maximum is flat and a flank is steep. Every display primary sits on a flank, which is why a pigment polymorphism is worth 3.60 ΔE₀₀ under a laser projector.

eye · Cones The same white, matched at six primary widths. At every width the three primaries are solved to match D65 exactly for the reference member; the bands are what the population sees. A broad primary integrates the observer differences over a band and averages them away; a narrow one samples them at a point and passes them straight through. From 40 nm to 2 the ninety-fifth percentile rises from 11.3 to 17.9 ΔE00, monotonically, and the technology has been moving from left to right for thirty years.

A narrow primary buys a disagreement

The observer audit decomposes what a display costs a population. Narrowing the primaries raises the pigment-peak departure monotonically, moving one raises or lowers the macular departure, and the two respond to different design variables — so a wide gamut and an observer-robust display are bought with the same money.

matching · Gamut Two primaries mixed, and the line a reader assumes they take. The additive mixture of two sRGB primaries, walked in twenty steps, plotted in the a and b of CIELAB. The filled points are where the light actually goes, which is exactly straight in tristimulus values because that is Grassmann's second law. The open points are the straight line between the two readings. They part company by 26.7 ΔE₀₀ at their furthest, at 60 per cent of the way along, and the half-and-half mixture misses the midpoint by 21.1.

The mixture line bows

Grassmann's second law says an additive mixture is exactly linear in tristimulus values, and tested here it is exact to floating point. Nothing downstream of the three numbers preserves it. The physical half-and-half mixture of two colours sits a median of 5.5 colour differences from the midpoint of their two readings and up to thirty; on a green and a blue display primary it is twenty-one, which is a quarter of the distance between them.

matching · Gamut The same colour, delivered from two documents. A ramp of chroma, mapped into a press's gamut under the perceptual intent from two source solids: the whole of sRGB, and the same solid with its chroma limited, which is what a document containing only muted colours amounts to. Under a colorimetric intent the two answers are identical to the floating-point floor. Under the perceptual one they are 0.69 apart at the mean and 2.64 at the worst, on colours the destination could hold either way.

An intent is not a function of the colour

A rendering intent is chosen per job and applied per pixel, which suggests it is a function of the colour. The colorimetric ones are, exactly — the same colour from two documents comes out identical to the floating-point floor. The perceptual one is not — it compresses the whole source solid into the destination, so the same colour delivered from a wide document and from a muted one lands 2.6 colour differences apart, on colours the destination could hold either way.

applied · Delivery Four mixtures of display primaries, bowing by different amounts in two units. The half-and-half mixture of each pair of sRGB primaries, measured from the midpoint of the two readings as a share of the pair's own separation. The upper bar is ΔE₀₀ and the lower is the appearance model's J′a′b′. In ΔE₀₀ green and blue bows most, at 25 per cent; in the model it is red and blue, at 20, and blue and yellow falls from 22 to 12. The right-hand column gives the model's distance with its power correction, which is smaller than the Euclidean one for every pair here.

Which mixture bows most depends on the ruler

The physical half-and-half mixture of two lights misses the midpoint of their two readings in any unit a person is shown, and the share it misses by is about the same in ΔE₀₀ and in the appearance model's own space — 12.8 and 14.6 per cent at the median. Which mixtures miss most is not. The rank correlation between the two units is 0.57, a display's blue and yellow is the worst pair in one and the mildest in the other, and the smaller number usually quoted for the appearance model is its power correction rather than a straighter line.

matching · Gamut Which appearances a surface can have, lightness by lightness. The same lattice of lightness, chroma and hue a specification is written in, 10488 points, inverted under daylight with the observer adapted to it. Each row is one lightness, split into three shares: appearances a reflecting surface can have, appearances that are a light but that no surface can return, and appearances with no light under them at all. Over the whole lattice the first is 66 per cent, the second 23 and the third 11. At J 90 a surface can have 38 per cent of the row.

A third of the appearance box is no surface

An appearance specification is written as a lightness, a chroma and a hue, and the model's inverse turns any such triple into three numbers. A tenth of the space turns into something that is not a light at all. A further quarter turns into a light no reflecting surface can return, because a surface cannot give back more than all the light at any wavelength. So a third of the space a paint, a print or a dye is specified in cannot be made from paint, print or dye, and at lightness 90 nearly two thirds cannot.

brain · Appearance How much of a display's gamut each observer names differently. Each of 60 observers names every colour of the displayable gamut that the panel can make — 823 of them — and the histogram is how much of that gamut each observer names differently from the standard observer. On an OLED panel the median observer renames 8.1 per cent and the furthest 13.1 per cent. Nobody agrees with the standard observer about all of it.

A name moves with the reader

Three earlier essays have moved a colour's name by changing the distance function, the room and the space. All three held the observer fixed. Handed the same light from the same display, sixty observers rename between 3.5 and 13.1 per cent of the gamut against the standard observer, a quarter of its colours have a dissenter in twenty, and the narrower the display's primaries the worse it gets.

brain · Appearance What a gamut charges a gradient, against what the relaxation's noise is. For each gradient, how much longer the best path that stays inside sRGB is than the free shortest path, as a percentage of the free one. The shaded band is the relaxation's own noise, measured by relaxing the same free path from two different starting points: 0.42 per cent at its worst. Every excess is inside it. So holding a gradient inside a display's gamut costs nothing measurable in the metric's own units, on any of these pairs — including the ones whose free path is outside at most of its points.

A gamut charges a gradient nothing

On red to green the shortest path happened to stay inside sRGB where the straight line did not, and that was called a coincidence of mechanism. Made into a measurement it is not a coincidence: constraining a path to stay inside the gamut costs less of the metric's own length than the relaxation's own noise, on every gradient tested — including the ones whose free shortest path is outside at fifteen of its twenty-one steps. The gamut's boundary and the metric's cheap region point the same way, and the price of the constraint is nothing.

matching · Gamut

Named alongside it

The objects these essays reach for when they reach for this one.

PrimariesGamutSpecificationChromaticityStandard observerIndividual variationObserver metamerismColour managementLuminanceNarrow band displaysObject-colour solidWhite point

All concepts