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

Hue — where it appears

Where a colour sits round the circle from red through yellow, green and blue and back, as distinct from how light or how saturated it is. A gamut's reach varies enormously with it, so what a rendering intent costs is a question about hue before it is a question about anything else.

Named by 26 essays across 5 fields — each of them below, with the objects they name alongside it.

A clipped channel turns the hue of what is left. CIELAB hue shift against exposure for one saturated stimulus, measured against the same stimulus rendered without clipping. Nothing moves until the first channel reaches the ceiling at 0.25 stops; after that the recorded hue rotates by as much as 67 degrees, with nothing in the scene having changed colour.

A blown highlight turns

An exposure that clips nothing changes no hue at all. Once one channel reaches the ceiling the recorded hue rotates by as much as sixty-seven degrees, with nothing in the scene having changed colour — and every response a converter can make to that is an invention.

imaging · Capture A gradient of one hue, mapped into a press's gamut 3 ways. Chroma asked for along the bottom, chroma delivered up the side, for a ramp at lightness 55 and hue angle 25°. A colorimetric intent follows the diagonal until the press runs out and is flat afterwards — the flat part is a gradient arriving as a single colour. The perceptual intent is under the diagonal from the start, which is the price of never going flat.

A budget drawn through one hue

The three-stage error budget this collection publishes for a colour-management chain is computed over twenty-four colours of a single hue at a single lightness. The quantity that actually varies with hue — how many distinguishable colours a rendering intent destroys — runs from nothing at all to more than a third, and the hue the budget uses is near the bottom of that range.

applied · Delivery Where a sample's colour goes as the aperture closes. The a and b of three translucent materials as the measuring aperture narrows from forty millimetres to one. Each track starts at the open circle, which is the colour the model says the sample has, and ends at the filled one. The axes cross at the neutral point. pale marble passes through neutral at a radius of 5.32 millimetres and comes out on the other side; candle wax passes through neutral at a radius of 7.07 millimetres and comes out on the other side; skin passes through neutral at a radius of 0.76 millimetres and comes out on the other side. Nothing about the sample changed: the aperture is a filter with a colour of its own, and the colour is decided by how the sample scatters rather than by what it absorbs.

The hue the hole decides

A piece of pale marble measured through a wide aperture is faintly yellow. Measured through a narrow one it is faintly blue, and between the two there is an aperture at which it is exactly neutral. Nothing about the stone changes; the aperture is a filter with a colour, and what decides that colour is the size of the particles rather than the pigment between them.

scene · Scene Thirty-six rooms as a viewer adapted to each would see them. Each cell is one room at a satin finish: wall colour down, lamp across. The large number is the share of the faces' chroma a viewer adapted to the room's own light loses, read through CIECAM16; the small number under it is what the room's light loses against the lamp's white. The viewer loses between 12.8 and 30.9 per cent, always more than the light, and the rows differ far more than the columns: a deep red room loses about twice what a green one does under every lamp.

What an adapted viewer loses is set by the wall

A satin finish takes about a tenth of a room's colour, measured on the room's light against its lamp's white. Read through an appearance model by a viewer adapted to the room, the same thirty-six rooms lose between 12.8 and 30.9 per cent — 1.4 to 2.4 times as much — and the wall colour decides the multiplier: a deep red room loses twice what a green one does, under every lamp. A test on the bare wall predicts it. Add a little of the lamp's white to the wall's own colour and ask the model what that costs: the answer orders the thirty-six multipliers at 0.95.

scene · Scene How far each model turns a display colour's hue as white is added. The twenty-four most saturated colours an sRGB display makes, one every 15° of HSV hue across, each mixed with the display's white at the same luminance down to a fifth of its purity. Up, how far that mixture's hue angle turns in CIECAM16, CIELAB and Oklab. From red to a fifth of its purity CIECAM16 turns −9.4° and Oklab −10.2°; CIELAB −18.1°. From the display's blue, Oklab turns +16.3°, CIECAM16 +3.6° and CIELAB −8.9°.

White turns a hue, and the models part at blue

Mix a saturated light with white and its hue changes as well as its saturation — the Abney effect, and the reason lines of constant perceived hue curve in a chromaticity diagram. Asked what adding white does to the twenty-four most saturated colours a display makes, CIECAM16, CIELAB and Oklab all turn the hue. About reds they agree: CIECAM16 turns within a degree of Oklab, whose hue was fitted to observers' constant-hue judgements. About the display's blue they do not: Oklab turns sixteen degrees, CIECAM16 four, and CIELAB nine the other way.

brain · Appearance Which way a tint turns a pigment's hue, made in paint and made in light. For eight pigments tinted nineteen parts white to one of colour, the Oklab hue turn from the pure pigment: of the tint made in paint (upper bar) and of the additive mixture with white at the same luminance (lower bar). For seven of the eight the two point in opposite directions. The orange turns +13.5° in paint and −13.9° in light.

A tint in paint turns the other way

A pale colour can be made two ways: by stirring white pigment into a coloured one, or by adding white light to it — which is what a halftone on white paper and a display both do. At the same luminance the two tints are not the same colour. For seven of eight pigments they turn the hue in opposite directions, an orange by +13.5 degrees in paint and −13.9 in light, and the paint tint is the more colourful of the two every time. The cause is in the reflectance: diluting a pigment moves its absorption edge, and adding light does not.

brain · Appearance Three uniform spaces, three answers: red to blue. The gradient from above, in the a and b plane: CIELAB's straight line, and the shortest paths under ΔE₀₀'s local metric, under CAM16-UCS's and under Oklab's, whose shortest path is its own straight line carried back into CIELAB. They bow from CIELAB's line by 14.4, 42.5 and 42.6 units. ΔE₀₀'s and CAM16-UCS's paths run 28.3 apart at their furthest, Oklab's runs 29.0 from ΔE₀₀'s and 5.6 from CAM16-UCS's, and the space furthest from the other two here is ΔE₀₀.

A third space breaks the tie only once

ΔE₀₀ and CAM16-UCS disagree about which colours lie between two colours. Oklab was the obvious tie-breaker, and it breaks the tie on one gradient of five: on red to blue its path runs within six CIELAB units of CAM16-UCS's and twenty-nine from ΔE₀₀'s. On red to green and cyan to magenta it keeps to CIELAB's straight line while both others bow, and on blue to yellow it bows further than either. Each of the three spaces is the odd one out somewhere. Asking also exposed a CAM16-UCS path that had never converged.

matching · Gamut A halftone tint, between the two ideals and nearer one of them. For each pigment, how far the hue turns when it is tinted to the same lightness three ways: mixed with white pigment, mixed with white light, and printed as a halftone at a Yule–Nielsen factor of two. Right is towards a longer wavelength. 7 of the eight pigments' two ideals turn the hue opposite ways. The halftone mark sits between them at every pigment and between 26 and 44 per cent of the way from the light ideal to the paint one — so it keeps the additive tint's direction and loses about a third of its size.

Printing does not change the sign

A tint mixed in paint and a tint mixed in light turn seven of eight pigments' hues opposite ways. A halftone sits between the two because light entering the paper between dots emerges under a dot, and the question was where. At the optical gain a coated sheet is fitted at, a halftone has travelled between 26 and 44 per cent of the way from the light ideal to the paint one — the same fraction for every ink — and only one pigment in eight changes direction.

brain · Appearance An orange ink's tints on three papers: which way the hue turns. The hue of each tint of an orange ink, from the solid to a tenth coverage, against the solid on the same paper, in degrees of Oklab hue: on a coated sheet, an unbrightened uncoated sheet and a newsprint. Solid lines are read against daylight's white, as an instrument reads them; dashed lines against the paper's own white, as a reader adapted to the page. At a tenth coverage, read against daylight, the coated sheet's tint has turned -8.7 degrees and the newsprint's 21.8; read against each paper's white, -8.7 and -1.1.

Newsprint turns a tint with its colour, not its gain

A halftone tint turns its hue the way a mixture of light does, by less, because optical dot gain carries it part of the way towards a paint tint. The straight line through a coated sheet's gain predicted that an uncoated sheet's larger gain would carry the orange past the crossing at a factor of 3.2, so that the same ink would turn opposite ways on two papers. It does turn opposite ways — on newsprint the orange's pale tints swing 13 degrees one way where a coated sheet's swing 8 the other. But the gain is not what does it. The road towards paint bends and stops at 60 to 70 per cent of the way, the orange needs a factor of 5.4 to cross, and newsprint's reversal comes almost entirely from the paper being yellow. Read against the paper's own white, as a reader looking at the page is adapted, it goes away.

brain · Appearance The share of its colour each display hue loses to a quarter of its luminance in white. The twenty-four most saturated colours of an sRGB display, one every fifteen degrees of HSV hue, each scaled to a luminance of 20 and given white of a quarter that luminance: the share of its colourfulness lost, in CIECAM16, CIELAB and Oklab. All three put the fastest loss at an orange and the slowest at a blue. At the orange end they are close — CIECAM16 27 per cent, CIELAB 28 per cent, Oklab 21 per cent — and at the blue end CIECAM16's 1.7 per cent is a quarter of the others'.

White drains the blue last in every model

CIECAM16 says a dab of white costs a deep red wall four times the colour it costs a dark blue one, and the experiment proposed to test it asked whether observers lose colour in that hue order. Held at equal luminance and given equal doses of white, twenty-four display hues are ordered alike by CIECAM16, CIELAB and Oklab — an orange loses fastest and a blue slowest in all three. So the order cannot tell the models apart. What does is how much slower the blue is: CIECAM16 has it losing a sixteenth of what the orange loses, CIELAB and Oklab about a quarter. That ratio is the number an observer study has to measure.

brain · Appearance How much of the turn a reader sees, adapted part of the way to newsprint. The hue turn of a fifth-coverage tint against its solid ink on newsprint, for five pigments, as the reader's adaptation moves from daylight's white to the paper's. Open circles mark where each tint stops turning the opposite way from the same tint on a coated sheet: orange at 0.97, red at 0.89, magenta at 0.98, cyan at 0.90, green at 0.93. Half-way, the orange still turns 7.3 degrees.

A reader sees the reversal until almost adapted

An orange halftone tint on newsprint turns its hue one way and the same tint on coated paper turns it the other, and the reversal is the newsprint's yellow. An instrument sees it in full; a reader fully adapted to the paper does not see it at all. A real reader is somewhere between, adapted to a mixture of the paper and whatever surrounds it. Half-adapted, the reader still sees more than half of the instrument's turn, and the reversal lasts until the reader is adapted nine-tenths or more of the way to the paper. On a paler uncoated sheet it is gone by just past half-way. A coated sheet does not care.

brain · Appearance A pale orange tint's turn on a brightened sheet, against the reader's adaptation. The hue turn of a fifth-coverage orange tint against its solid on brightened office paper in daylight, as the reader's adaptation moves from daylight's white to the sheet's, beside a sheet of the same colour that does not fluoresce, a white sheet with the same dot gain, a heavily brightened sheet, newsprint and a coated sheet. Unadapted the brightened sheet turns it -41.5 degrees, the coated sheet -8.0 and newsprint 12.7. Fully adapted, the non-glowing sheet of the same colour comes down to -3.2, beside the white sheet's -3.4; the brightened sheet stops at -10.0.

Adapting to a brightened sheet leaves the glow

A pale tint on newsprint turns its hue one way and on coated paper the other, and a reader fully adapted to the paper sees newsprint's reversal vanish, because it was only the paper's colour. On a sheet with an optical brightener the tint turns the coated way and five times as far — 41.5 degrees for a fifth-coverage orange. A reader adapted to the sheet removes most of that, as expected, but not all: ten degrees stay. The sheet's colour adapts away like newsprint's. The brightener's glow does not, because the ink puts it out under the solid and leaves it under the tint, and an added light is not something adapting to a white can divide out.

brain · Appearance How far white turns each display colour's hue, in CIECAM16 and with its cone space changed. The twenty-four most saturated sRGB colours, each mixed with white of the same luminance down to a fifth of its purity, and the turn of its hue angle in Oklab, in CIECAM16, in CIECAM16 with its compression done in the Hunt–Pointer–Estévez space rather than CAT16's, and in CIECAM02's front end. At the display's blue Oklab turns 16.3 degrees and CIECAM16 3.6; compressed in Hunt–Pointer–Estévez it turns 15.6, and CIECAM02 16.1. Over all twenty-four the two lie 3.2 and 3.2 degrees from Oklab, root mean square, against CIECAM16's 5.3.

The blue's hue turn was lost with a matrix

Add white to a saturated blue and its hue turns — sixteen degrees by the constant-hue data Oklab was fitted to, four by CIECAM16. The obvious suspect was the model's compressive response, acting on a very large blue signal. It is not: removing the compression's saturation moves no hue by half a degree, and a cube root instead of its exponent moves the blue by one. What decides it is the cone space the compression happens in. Computed in Hunt–Pointer–Estévez, the space CIECAM02 compressed in, the same model turns the blue 15.6 degrees; CIECAM02's own front end turns it 16.1. CIECAM16 merged CIECAM02's two spaces into one sharpened for adaptation, and that one gives a display's blue almost as much long-wave signal as white has.

brain · Appearance How far below nought the two-matrix model's smallest signal goes, along the locus. For every spectral light from 380 to 700 nm, the smallest of its three Hunt–Pointer–Estévez signals after CIECAM16's adaptation, divided by the light's luminance, adapted to the display white and to illuminant A, drawn down to −2. Adapted to the display white the smallest signal dips below nought only past 560 nm, and by at most 0.0037; adapted to A it is below nought from 380 to 474 nm and reaches −6.7 of its luminance at the violet end.

Two matrices fail under a warm white

Compressing in Hunt–Pointer–Estévez after adapting in CIECAM16's own space restores the blue's Abney turn, and the reason CIECAM16 stopped using two spaces was that converting between them sends some colours to negative signals. Where it does depends on the white. Adapted to a daylight display's white, only spectral lights past 560 nm fail, in their short-wave signal, by thousandths of their luminance, and nothing on sRGB's boundary fails at all. Adapted to a tungsten white, every spectral light from 380 to 474 nm fails in its long-wave signal, some by several times their luminance, and so do points on every display's boundary; there the display blue's restored turn becomes a swing of fifty degrees.

brain · Appearance Where each display's boundary and the spectrum fail, as the adapting white warms. For radiators from 6500 K down to 2700 K, the temperatures at which the two-matrix front end sends some point of each display's boundary, or some spectral light, negative: shaded where it fails. sRGB and Display P3 first fail at 2871 K, just above illuminant A; BT.2020 at 3626 K. P3 and BT.2020 also fail at their red corners under whites cooler than 5700 K, and no spectral light fails between 5700 and 4700 K. The dashed line is the 3500 K the prediction named.

Two matrices hold to almost tungsten, and the blue turns long before

An appearance model that adapts in CIECAM16's space and compresses in Hunt–Pointer–Estévez gets the blue's hue turn right under daylight and sends the display's blue to a negative signal under illuminant A. The prediction was that the failure reaches sRGB's blue near 3500 K, a warm-white LED, and that the blue's turn holds its daylight value down to about 4000 K. Walked down the radiator and daylight loci, sRGB's boundary holds to 2872 K — fifteen kelvin short of illuminant A — while BT.2020's fails at 3626. There is a neutral window, 4700 to 5700 K, where no colour at all goes negative. But the blue's turn does not wait for the failure: it is five degrees above its daylight value by 4500 K and nearly three times it before anything breaks, because it follows the blue's long-wave signal down towards nought.

brain · Appearance The blue corner and its edges, in both units. For six colours between the press's cyan and magenta — the blue corner, four edges beside it and the blue corner with half black — the move per unit of margin a perfect corner of each one's tangent shape makes in CIELAB, the move a four-unit margin makes on the finely sampled press, the same shape carried into ΔE₀₀, and the move a two-ΔE₀₀ margin makes. In CIELAB every one is already blunt, under 1.3; in ΔE₀₀ every one is within a tenth of a flat face.

The blue corner has nothing to twist

A safety margin's cost at each corner of a coated press is predicted by the corner's own shape, read off its ink recipe and carried into whatever unit the margin is stated in — for nine corners, none of them blue. At a hue near 275 degrees ΔE₀₀ has a rotation term that couples chroma and hue, and the prediction was that leaving it out would miss the press's blue corner by more than a tenth of the margin. At the blue corner the term is strong: ΔE₀₀'s local matrix correlates a chroma step with a hue step by three quarters. And it changes the prediction by three hundredths. The blue corner and its edges are already blunt in CIELAB — none moves more than 1.3 times a margin — and a corner that is nearly a face has nothing for a shear to twist.

matching · Gamut What adaptation cannot remove from an orange tint, with and without a thin dot edge. For a reader fully adapted to brightened office paper, the orange tint's hue turn against its solid beyond what a non-fluorescent sheet of the same colour leaves, at coverages from five to sixty per cent, with a uniform ink film and with rims of three, six and twelve micrometres. The residue is largest at the palest tint for every rim, and every wider rim raises it: at a fifth coverage from 6.8° to 7.9°.

A thin dot edge lets the glow back in

A pale tint printed on brightened paper keeps part of its hue turn however fully a reader adapts to the sheet — ten degrees for a fifth-coverage orange where a non-fluorescent sheet of the same colour leaves three — because the ink's vehicle puts out the brightener's glow under the solid and the tint's bare paper keeps it. That census gave every dot a uniform film. A real dot thins at its edge, a thin film lets ultraviolet through, and at the pale end of a ramp most of a dot is edge. The prediction was that the edge would restore the glow under the tint's dots, shrink the residue by a third at a fifth coverage and move the worst of it to the mid-tones. The edge does restore the glow — nine times as much under a small dot with a twelve-micrometre rim. And the residue grows: 6.8 degrees to 7.9 at a fifth coverage, 7.2 to 9.0 at a twentieth. The residue is the tint glowing where the solid does not, and more glow under the tint's dots is more of the difference. The palest tint keeps the most, with or without an edge.

brain · Appearance 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 What adaptation cannot remove from an orange ramp, screen by screen. For an orange ramp on brightened office paper, the hue turn against the solid that a reader fully adapted to the sheet still sees beyond what the sheet's colour accounts for, on conventional screens of 100, 150, 200 and 300 lines and on stochastic screens of 10, 20 and 35 µm dots, every dot with a six-micrometre rim. The 150-line screen falls from 8.1° to 5.7° along the ramp; the 20 µm stochastic screen stays near 9.0°; the 10 µm one rises, from 10.4° to 11.4°. The axis starts at 4.5°.

Stochastic dots hold the glow at every tint

On brightened paper a halftone tint keeps a hue turn that a reader fully adapted to the sheet cannot remove, because the paper's glow survives under the ink where the solid puts it out, and a dot's thin edge lets more of it back. A dot's size at a given coverage is set by the screen. Across conventional rulings from 100 to 300 lines the residue rises at every coverage for every pigment, a finer screen making every dot more edge. A stochastic screen of twenty-micrometre dots holds it flat — the orange within a quarter of a degree from five per cent to sixty, starting where a 300-line screen starts — as predicted. What the prediction did not say is where the switch costs: not the pale tints, by under a degree, but the mid-tones, by three or four, because a conventional screen's mid-tone dots are large and mostly full film. On ten-micrometre dots, all edge, the ramp turns over and the mid-tone keeps more than the pale tint. At any one coverage the residue is set by the dot's diameter alone, whichever screen printed it.

brain · Appearance What merging the spots gives back along an orange ramp. For an orange ramp on brightened office paper, the turn a reader fully adapted to the sheet still sees beyond the sheet's colour, on a stochastic screen of twenty-micrometre square spots kept separate and merged where they touch, beside the round-dot stochastic screen and a 150-line screen. Merged and separate agree until the spots begin to touch near thirty per cent; at sixty per cent the merged screen keeps 6.9° against the separate spots' 8.6°. The axis starts at 4.5°.

Merged spots give the mid-tones half the glow back

On brightened paper a halftone tint keeps a hue turn a reader adapted to the sheet cannot remove, and a stochastic screen's small dots, being mostly thin edge, keep it high along the whole ramp — three times the 150-line screen's cost in the mid-tones. That census kept every dot separate. A real stochastic screen's spots touch and merge, and a shared edge between two spots is no edge of the ink. The prediction was that a merged screen would follow the separate-dot curve to about thirty per cent and then fall towards the conventional screens, giving back half the mid-tone cost by sixty. It does, almost exactly. Square spots twenty micrometres on a side, switched on in a dispersed order, stay apart up to a fifth coverage and start touching near thirty per cent; by sixty, nine in ten touch, the rim has fallen from 84 per cent of the ink to 50, and the merged screen keeps the orange's residue at 6.9 degrees against the separate spots' 8.6 and the 150-line screen's 5.7 — giving back 58 per cent of the cost. Every pigment gets back the same share, 55 to 58 per cent, because the share is set by the geometry of the ink, not by its colour.

brain · Appearance One ink overshoots on the light sheet and falls short on the premium. Every pigment printed at the strength that cancels its ten-per-cent residue on the office sheet, its coverage matched to each sheet's own five-per-cent target: the residue a reader adapted to each sheet still sees, signed. On the office sheet it is near nought; on the light sheet seven of eight pigments' residues have turned past nought the other way, and on the premium sheet all eight keep the full-strength ink's sign, by under 1.8 degrees.

One light ink serves three papers within two degrees

On brightened office paper a pale tint keeps a hue turn even for a reader fully adapted to the sheet, and each pigment has one light-ink strength — the pigment diluted and printed over more of the paper — at which that residue vanishes. The prediction for a printer with several stocks was that the cancelling strength falls as the brightener loading rises, and that the office sheet's ink leaves a premium sheet's pale tints within two degrees and a lightly brightened sheet's within one. The strength does fall, at every step and for every pigment — by a fifth for the orange and the yellow, by under one per cent for the green. The office ink keeps the premium sheet within 1.8 degrees, as predicted, but the light sheet only within 1.8 too: it overshoots there, turning seven of eight pigments' residues past nought the other way, and falls short on the premium sheet for all eight. Either way it removes more than four fifths of what the full-strength ink leaves.

brain · Appearance The fresh sheet's ink holds until half the brightener is gone. On the premium sheet as its brightener bleaches, the worst residue any of eight pigments leaves from five to twenty per cent: printed at full strength, with the fresh premium sheet's light inks, and with the office sheet's. The fresh premium inks stay under two degrees to half bleached (25%: 1.75°, 50%: 1.80°, 75%: 2.35°); the office inks, 1.80° on the fresh sheet, stay under one and a half once any of the brightener has bleached.

An ink for a fading sheet is set for its middle age

A light ink cancels a pale tint's residual hue turn on brightened paper at a strength that falls along a straight line in the sheet's glow, and a brightener bleaches with use, so a sheet's glow falls over its life. The prediction was that as the premium sheet's brightener bleaches, every pigment's cancelling strength rises back along that line, and that the fresh sheet's ink stays within two degrees until half the brightener is gone. Both hold. Bleached by a quarter, a half and three quarters, the premium sheet asks for strengths within 0.015 of the census line at its glow, always on or just below it; the fresh premium ink errs by 1.75, 1.80 and 2.35 degrees at worst. But the office sheet's ink, set for a glow the premium sheet passes through on its way down, keeps the bleaching sheet within 1.4 degrees at every stage after the first. An ink set for the sheet's middle age outlasts one set for its first day.

brain · Appearance The census line is a chord across a curve. For four pigments, the cancelling strength less the census line's at each sheet's glow — the light, office and premium sheets and the three bleached and yellowed premium sheets — in order of glow. The light and premium sheets sit above their own line and the office sheet under it, the orange by −0.0161, deeper than any bleached sheet: the line through the three census sheets is a chord across a sagging curve, and the bleached sheets sag beneath it as the office sheet does.

A yellowing base leaves the ink where the glow put it

A light ink cancels a pale tint's residual hue turn on brightened paper at one strength for each pigment, and as a premium sheet's brightener bleaches that strength rises back along the straight line in glow through three census sheets — a shade under it, by up to 0.013. Real photo-ageing yellows the base paper as well, and the prediction was that a base yellowed in step lifts the strengths onto the line within 0.01 and that the office sheet's ink still holds every residue within one and a half degrees. The ink holds, at 1.38°, 1.13° and 1.38°. The strengths do not lift: no pigment's moves by more than 0.0023, and its gap under the line by more than 0.0006. The yellowing raises the sheet's b* by 0.31 at most while the bleaching raises it by five. And the gap was never the base's: the office sheet itself sits 0.016 under the line, deeper than any bleached sheet. The line is a chord across a sagging curve.

brain · Appearance Every stock's ink lies on the premium stock's curve. Five pigments' cancelling strengths at a ten-per-cent target against the sheet's glow: the premium stock at eleven brightener loadings from a tenth of its own to all of it, the light, office and premium census sheets, and the premium stock bleached until its glow equals the office's and the light's. Every census sheet lies on the premium stock's curve, and the bleached premium sheets on the census sheets — the orange at 0.5581 and 0.6461 against 0.5578 and 0.6456.

The glow alone sets the light ink

A light ink cancels a pale tint's residual hue turn on brightened paper at one strength for each pigment, and that strength falls with the share of the sheet's luminance that is glow — along a curve, not the straight line through three census stocks, which runs as much as 0.016 above it. The prediction was that the strength is one curve in the glow whatever the stock: that a premium sheet bleached until its glow equals the office sheet's, or the light sheet's, needs that sheet's ink within 0.003 for every pigment. It needs it within 0.0007, though the two papers differ in base, in whiteness and in how much of the brightener their ink shields. Traced across eleven loadings of the premium stock, the curve runs through every census sheet within 0.003, sags under every chord, and falls five to nine times as steeply on a dim sheet as on a bright one for the orange, red and violet.

brain · Appearance A longer glow moves the cool inks; a shorter one moves them all. For each pigment on the premium stock at the office sheet's loading, the change in its cancelling strength at a ten-per-cent target when the brightener's emission moves from 435 nm to 450 and to 420, the same photons absorbed and emitted. At 450 nm the blue moves by +0.176 and the violet by −0.058, the orange by +0.0011; at 420 nm the orange by +0.038 and the violet by +0.077.

The glow's colour sets the blue ink and spares the orange

A light ink printed on brightened paper turns in hue, because the paper's glow passes through the ink's open area differently from the ink's own film, and a cancelling strength undoes the turn. Every sheet so far glowed with one brightener, and its ink was set by the glow's amount alone. The prediction was that a brightener emitting fifteen nanometres longer, nearer the blue and violet inks' hues, moves their strengths by more than a hundredth and the orange's and red's by under a fifth of that. It does: the blue's strength rises from 0.81 to 0.98, because a glow at the blue's own hue barely turns a blue tint, the violet's falls by 0.06, and the orange moves by a thousandth though the glow's share of the sheet's luminance nearly doubles. A brightener emitting fifteen nanometres shorter moves every ink, the orange by 0.04, and no curve in the glow's luminance reads any of them.

brain · Appearance The glow's pull reads every ink its luminance cannot. For each pigment, the largest miss over the thirty sheets, each left out, of lines in the glow's share of luminance, the share and the chromaticity y, the pull's Oklab a and b, and the pull with its squares and product. The last misses by at most 0.0139; the share alone by up to 0.249, the blue's.

The glow's pull on the white sets every ink

A light ink on brightened paper is diluted to cancel the hue turn the paper's glow gives its tints, and on sheets that all glow with one brightener its strength is a single curve in the glow's share of luminance. Move the brightener's emission and that curve fails by up to 0.21. The prediction was that two numbers — the share and the glow's chromaticity — read every ink within a hundredth. Across thirty sheets, eight of them a grid of emission peaks from 420 to 455 nm, they miss by up to 0.07, and the share alone misses the blue by a quarter. The two numbers that work are the glow's pull: how far, in Oklab, it moves the paper's own reflection to the white an adapted reader sees. Read with their squares, they set every ink within 0.014 — and the warm inks need least strength just short of where that pull is strongest.

brain · Appearance

Named alongside it

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

Chromatic adaptationHalftoneFluorescenceOptical brightenersCIECAM16OklabPaper whiteCIELABColour appearanceModelling assumptionChromaAdditive mixture

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