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

Display primaries — where it appears

The three lights a display mixes to make every colour it shows, stated as chromaticities. They fix the triangle of colours the display can reach, and a primary on the spectral locus, as BT.2020's are, reaches colours a broadband primary cannot.

Named by 13 essays across 3 fields — each of them below, with the objects they name alongside it.

A primary's tolerance is a shape, and part of it is unreachable. The CIE chromaticity diagram with the spectral locus drawn, and three closed regions marking where each primary of a display designed for its own inverse can sit while the adaptation cost stays within 1 per cent of its best. None of them is round: the widest runs 15.1 times further one way than another, so a single tolerance figure for a primary is the average of a shape the shape never takes. 47 of the 144 boundary directions leave the region a real primary can occupy, which is a second constraint the objective knows nothing about — the cost does not rise there, and the primary cannot go there.

A tolerance is a region

How far a display's red primary can move before its adaptation behaviour costs anything is not a distance. It is a closed region on the chromaticity diagram, fifteen times longer one way than another, and about half of it lies outside the area a real primary can occupy — where the objective does not rise and the primary cannot go.

applied · Delivery Moving the red primary in lowers the reds' move and raises one red-purple's. Five base colours' moves at the edge of a display with BT.2020's blue and green primaries and a red primary moved along the spectral locus from 630 to 605 nm. The red at lightness 25 and hue 30 falls from ×1.64 to ×1.25; the red-purple at hue 345 falls with it; the red-purple at lightness 25 and hue 315 rises from ×1.61 to ×1.68 and is the display's largest move from 625 nm in; the yellow-green holds at ×0.54. Hollow circles at 615 nm are the same bases on Display P3, whose red primary is a 615 nm line. At 630 nm the largest move is the red's, ×1.64.

A display's red takes the reds' move and leaves the pair

At BT.2020's edge ΔEITP moved a dark red's balance between lightness and chroma furthest of any colour, ×1.64 from a dim display to a bright one, and the reason offered was BT.2020's red primary, a line far out at 630 nanometres. Moving that primary in along the spectral locus confirms it: the reds fall faster than any other hue, to ×1.40 at 615 nanometres and ×1.25 at 605, and Display P3, whose red is a 615 nm line to three ten-thousandths, gives the reds the same. The top of the range goes to a red-purple, which rises as the red moves in because BT.2020 had pushed it past its own peak. And the forced-choice pair the experiment needs is the same two colours on every display.

difference · Metric How sharp each corner of two displays is, in CIELAB and in ΔE₀₀. For the three primaries and three secondaries of sRGB and BT.2020, the move per unit of margin that a perfect corner of each one's tangent shape makes in CIELAB and carried into ΔE₀₀ by its full local matrix. The blue is ×3.35 and ×3.17 in CIELAB, against the press's blue at ×1.25; in ΔE₀₀ it is ×1.42 and ×1.26. ΔE₀₀ brings every corner of both displays under ×1.9.

A display's blue is sharp where the rotation is not

ΔE₀₀'s rotation term shears chroma into hue near a CIELAB hue of 275 degrees, and at a press's blue corner it had nothing to act on because the corner was blunt. The prediction was that a display's blue — an additive primary — would be a sharp corner, and that there the rotation would change how far a safety margin moves it by more than a tenth. The first half holds: sRGB's blue moves 3.35 times a CIELAB margin and BT.2020's 3.17, against the press's 1.25, and insetting the curved gamut directly confirms it to the second decimal. The second half fails, twice. A display's blue sits at 306 degrees, thirty past the rotation's centre, where the term grips a quarter as hard; and ΔE₀₀ blunts the corner to 1.42 by compressing its chroma sevenfold. Along the edge from blue to cyan the hue does pass through 275 and the grip reaches −0.87 — where the edge is nearly a face. Nowhere near either display's blue does the rotation move a prediction by four hundredths.

matching · Gamut What ΔE₀₀'s chroma length alone does to each corner of two displays. For the six corners of sRGB and BT.2020, the move per unit of margin their tangent shapes predict in CIELAB, with ΔE₀₀'s chroma length alone, and with its lengths along lightness, chroma and hue together. The chroma length alone brings every corner but the yellow under ×1.35; it leaves the yellow at ×1.78 and ×1.80, and the full metric at ×1.75 and ×1.78.

The yellow is sharp where the tolerance unit does not compress

A safety margin moves each corner of a display's gamut inward by a multiple of itself that depends on the corner's shape. In CIELAB, sRGB's blue is its sharpest corner and its yellow among its bluntest; carried into ΔE₀₀, the order turns over, and the yellow becomes the sharpest corner of both sRGB and BT.2020. The prediction was that the yellow keeps its sharpness because its faces run along lightness, where ΔE₀₀'s weighting is largest at the yellow's L* of 97. Taking ΔE₀₀ apart length by length says otherwise. Its lightness weighting changes the yellow's move by nothing. Its chroma compression — the term that opens every other corner — does, on its own, bring every other corner of both displays under 1.35 times a margin, and leaves the yellow at 1.78. Of the yellow's three directions only one runs along chroma; at the other corners two or three do, and a metric that compresses chroma pulls those together and flattens the corner between them.

matching · Gamut How sharp each corner of two displays is, in three units. For the six corners of sRGB and BT.2020, the move per unit of margin that a perfect corner of each one's tangent shape makes in CIELAB, in ΔE₀₀ and in CAM16-UCS at the display's white, 64 cd/m² and an average surround. CAM16-UCS keeps the yellow the sharpest corner of both displays, at ×1.66 and ×1.66, and blunts the blue — the sharpest corner of sRGB in CIELAB — to ×1.17 and ×1.10, the bluntest of all twelve.

An appearance model flattens the blue by its hue

A safety margin moves a corner of a display's gamut inward by a multiple of itself set by the corner's shape, and the unit the margin is written in decides the shape. In ΔE₀₀ the yellow is the sharpest corner of an sRGB and a BT.2020 display, because its sharpness lies across hue where ΔE₀₀'s chroma compression cannot reach it. CAM16-UCS compresses colourfulness less steeply, and the prediction was that it would leave the blue sharper than the yellow. It leaves the yellow sharpest, at 1.66 times a margin on both displays, and flattens the blue to 1.17 and 1.10 — the bluntest corner of all twelve. Its colourfulness does what the prediction said: on its own it would sharpen the blue past the yellow. Its hue scale undoes that. At a display's blue one degree of CIELAB hue is three and a half degrees of the appearance model's, and a unit that counts hue that finely there spreads the blue's directions apart until the corner is nearly a face.

matching · Gamut How sharp each corner of two displays is, in four units. For the six corners of sRGB and BT.2020, the move per unit of margin that each corner's tangent shape predicts in CIELAB, ΔE₀₀, CAM16-UCS and ΔEITP, the last with the white at 320 cd/m². ΔEITP keeps the blue the sharpest corner of both displays, at ×3.12 and ×3.24, where CAM16-UCS makes it the bluntest at ×1.17 and ×1.10. At the green, cyan, magenta and yellow the three tolerance units agree within a quarter.

A quantiser keeps the blue a spike

A gamut margin moves a display's corners inward by multiples set by the unit it is written in. ΔE₀₀ and CAM16-UCS both blunt an sRGB or BT.2020 display's blue, CAM16-UCS to nearly a face, and the prediction was that ΔEITP — the difference built on ICtCp for high-dynamic-range television — would blunt it too. It does the opposite. With the white at 320 cd/m² the blue is ΔEITP's sharpest corner on both displays, moving 3.12 and 3.24 times a margin, about as far as in CIELAB; at the green, cyan, magenta and yellow the three tolerance units agree within a quarter, and at the blue they span a factor of three. ΔEITP's lengths alone would blunt the blue as ΔE₀₀ does. What keeps it sharp is the perceptual quantiser: ICtCp's chroma rows sum to nought, so under a response that compresses like a logarithm, dimming the blue primary is a step in intensity and nothing else. Replace the quantiser by a linear response and the blue falls to 2.15; by a logarithm, it rises to 3.39. A brighter display sharpens it further.

matching · Gamut The blue corner in four units, as the blue primary moves towards the violet. For displays with red and green primaries at 630 and 530 nm and a monochromatic blue primary from 440 to 490 nm, the blue corner's move per unit of margin in CIELAB, ΔE₀₀, CAM16-UCS and ΔEITP. ΔEITP's blue is sharpest at 485 nm, ×4.37, and falls to ×1.23 at 440; CIELAB's runs the other way, from ×1.92 at 480 nm to ×11.8 at 440, and ΔE₀₀ follows it; CAM16-UCS stays near a face.

A violet primary is no spike to the quantiser

ΔEITP makes a display's blue its sharpest corner, about three times a margin, and the account of why predicted that a shorter-wavelength blue would be sharper still — past four times by 450 nm. Moving a monochromatic blue primary from 490 nm to 440 does the opposite. ΔEITP's blue corner is sharpest at 485 nm, ×4.37, and falls at every step to ×1.23 at 440, where CIELAB's runs the other way, from ×1.92 at 480 to ×11.8, and ΔE₀₀ follows CIELAB. The spike needs the two primaries that can be added to the blue to move it in nearly the same direction. Adding red always raises the blue's L signal by the larger fraction. Adding green does so only while the blue carries enough M signal of its own; a violet primary carries almost none, so adding green raises its M by the larger fraction and the two steps split, from 37 degrees apart to 111. No cone response rescues it — a logarithm blunts the violet further — and a brighter display dulls it while sharpening the longer blues.

matching · Gamut A longer green makes every blue sharper and keeps the spike at 485. For displays with a red primary at 630 nm, a monochromatic green at 505 to 555 nm and a blue from 440 to 490, ΔEITP's blue corner's move per unit of margin, the white at D65 and 320 cd/m². Every curve peaks at the 485 nm blue, from ×2.39 with a 505 nm green to ×8.19 with a 555 nm green; the violet end moves far less, ×1.18 to ×1.57.

The green primary decides how sharp the blue is

ΔEITP makes a display's blue its sharpest corner when the blue sits near 485 nm and nearly a face when it sits at 440, and the turn between them is where adding green stops raising the blue's L signal by the larger fraction. The prediction was that the turn follows the green — near 445 nm with a 545 nm green, near 470 with a 515 nm one. It follows the green, by less than half as much at the short end: 461 nm with a 515 nm green, 446 with a 545 nm one, and with a 555 nm green there is no turn left in the range at all. What the prediction did not ask is larger. The green sets how sharp the blue can be: with the blue at 485 nm the corner moves 2.4 times a margin against a 505 nm green and 8.2 times against a 555 nm one, while the sharpest blue stays at 485 nm for every green. The red primary, moved from 615 to 690 nm, leaves the turn where it was to a hundredth of a nanometre. The appearance model follows the green far more gently, under half of ΔEITP's move at every green.

matching · Gamut A broad green sharpens the blue corner; a broad blue dulls it. For displays with a red at 630 nm, a green at 530 and a blue swept from 440 to 490, each primary a Gaussian spectrum of a stated width, the blue corner's ΔEITP move per unit of margin, white at D65 and 320 cd/m². At the 485 nm blue: ×4.37 with three single wavelengths, ×4.51 with a twenty-nanometre green, ×5.05 with a forty-nanometre green, and ×3.94 with a twenty-nanometre blue.

A broad green sharpens the blue; a broad blue dulls it

ΔEITP makes a display's blue corner sharp or blunt according to its primaries, and the census of single-wavelength primaries found the green deciding how sharp — the 485 nm blue's corner moving 4.37 times a margin against a 530 nm green and 8.19 against a 555 nm one. Real primaries have widths, and the prediction was that a broad green acts as a longer green, raising the spike and moving the turn towards the violet, while a broad blue barely matters. The first half holds: a green forty nanometres wide at 530 nm sharpens the 485 nm corner to 5.05 and moves the turn from 453.7 nm to 451.2, as a single-wavelength green at 535.8 nm would, though its dominant wavelength has moved only to 533. The second half does not: a blue twenty nanometres wide moves the turn by a nanometre but dulls the corner by a tenth, to 3.94. The two widths pull the corner opposite ways, and a display whose green and blue are both broad lands near where its line primaries were. The red, at forty nanometres, still changes nothing that matters.

matching · Gamut A long tail sharpens the blue; a short one barely touches it. With the green's core twenty nanometres wide at 530 nm and a share of its power moved into a tail twenty-five nanometres long, the 485 nm blue corner's move per unit of margin in ΔEITP. A third of the power on the long side takes the corner from ×4.51 to ×5.70, past the symmetric forty-nanometre green's ×5.05; the same share on the short side leaves it at ×4.39.

A green's long tail sharpens the blue; its short tail does not

A quantum-dot green falls steeply on one side and trails on the other, and the prediction was that a tail on its long side, holding a third of its power, would make ΔEITP's blue corner treat the green as a line past 538 nm, further than a symmetric forty-nanometre green's 535.8, because all its spread is on the L side. It does: 540.7 nm, the 485 nm corner rising from ×4.51 to ×5.70. The control is the larger finding. The same tail on the short side costs the green far more purity — 0.77 against the long tail's 0.95 — and moves its equivalent line by under a nanometre and a half. The corner reads the green's ratio of L to M signal, to within a third of a nanometre for every long tail, and not its purity, its centroid or its dominant wavelength; a short tail lowers that ratio less than its colour suggests and brings S signal that pushes the corner back.

matching · Gamut A brighter display sharpens every green's blue by much the same share. The 485 nm blue corner's ΔEITP move per unit of margin against the green primary, on displays balanced to D65 at 100, 320, 1,000, 4,000 and 10,000 cd/m². From 100 to 10,000 cd/m² the corner rises from ×2.36 to ×2.51 with a 505 nm green and from ×7.78 to ×9.12 with a 555 nm one: five curves of one shape, stacked.

Brightness and the green sharpen the blue almost independently

ΔEITP's blue corner is sharper the longer a display's green, and sharper the brighter the display. The prediction was that the two compound — that the 555 nm green's lead over the 505 nm one, 3.42 times at 320 cd/m², would pass four by 4,000, because a brighter display narrows every angle and the long green's was narrowest — and that the turn, where adding green starts raising the blue's L by the larger fraction, would not move with the peak at all. Both halves fail. The lead grows by a twentieth, to 3.60 at 4,000 and 3.63 at 10,000; across thirty-five displays the corner is a green factor times a brightness factor to within 4.5%. And the turn moves at every step, two to six nanometres towards the violet from 100 to 10,000 cd/m², crossing the blue at which green raises L and M equally near 1,000. The quantiser weighs a fractional rise in L against one in M by their encoded levels, and brightness evens the scales.

matching · Gamut The turn is set by the level the blue arrives at. For displays with a red line at 630 nm, a green at 505 to 545 nm and the census's blues, balanced to D65: the turn — the blue at which adding green moves ICtCp's red–green axis from M-ward to L-ward — against the level the blue is delivered at, whatever peak and drive deliver it. With the 530 nm green it runs from 451.6 nm at 10,000 cd/m² to 457.3 at 10; a dimmer blue turns at a longer wavelength for every green.

A tone-mapped blue turns where it lands

In ΔEITP a display's blue corner, and the turn at which adding green to it changes which side of ICtCp's red–green axis it moves the colour to, both shift with the display's peak, because the quantiser reads absolute levels. A high-dynamic-range picture graded on a bright master and shown on a dimmer panel is tone-mapped, its blues delivered below the levels they were graded at. The prediction was that a blue at a tenth of full drive on a 1,000 cd/m² panel turns where a 100 cd/m² panel's full blue does, and that the corner's move differs, because the dimmed blue no longer sits at a vertex. The turn agrees within a hundredth of a nanometre. So does the corner, within half a per cent: the steps both are read from are directions at one absolute signal, whatever drive delivered it. The tone map's whole effect on the blue is where it puts the blue. Through ITU-R BT.2390's curve, a master's bright blues are gathered near a dim display's peak and share one turn there — two nanometres from where the master turned them — while blues under the curve's knee keep their turns exactly.

matching · Gamut Per channel, a tone curve turns a sky's blue towards cyan. A blue of the 530 nm green's display mixed with a share of green, graded at full blue drive on a 1,000 cd/m² master and shown on displays of 100 and 300 cd/m² through BT.2390's curve applied to each channel or to the largest with all three scaled together: the change in the mixture's ICtCp hue from the master's. Per channel on the 100 cd/m² display the hue turns 23.4° towards the green at a tenth of green; scaled, it moves under three degrees at every share.

A tone curve per channel turns a sky towards cyan

A pure blue tone-mapped from a bright master to a dim display turns, in ΔEITP, wherever its delivered level puts it, and any tone curve that delivers it to the same level gives it the same turn. A picture's blue is not pure. The prediction for a blue mixed with a little green was that a tone curve applied to each channel separately raises the green's share by about half — the blue channel compressed above the curve's knee, the dimmer green left near it — turning the mixture's hue several degrees towards cyan and its turn a nanometre or more from where a curve that scales all three channels together puts it. The turn does move, by 1.6 to 3 nanometres on a 100 cd/m² display and up to 6.5 on a 300. But the share is not raised by half: through BT.2390 to a 100 cd/m² display, a blue graded with a tenth of green arrives with its green at 69 per cent of its blue, nearly seven times as much, and its ICtCp hue turns 23 degrees towards the green. The scaled curve keeps every mixture's hue within three degrees and its turn within half a nanometre of the pure blue's.

matching · Gamut

Named alongside it

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

ΔEGamutPQ, the perceptual quantiserHigh dynamic rangeModelling assumptionToleranceCone fundamentalsNarrow band displaysCIECAM16CIELABConvexityDominant wavelength

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