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

Every essay — page 5

Page 5 of 54, continuing through the fields in the same order.

What light is What the eye does Matching and measuring Difference and uniformity What the brain does What a scene does What a camera does Where the model breaks What it takes to deliver it

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What the brain does

Constancy, adaptation and simultaneous contrast — the reasons a patch of known radiance still has no determined appearance.

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.

6 figures 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.

6 figures 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.

5 figures 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.

6 figures 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.

6 figures CIECAM16's colourfulness loss by hue, with each suspect removed. The share of colourfulness each of the twenty-four most saturated sRGB colours loses when white of 25 per cent of its luminance is added, all at the same luminance, in CIECAM16 as published, with its eccentricity factor held at one, and with its cone-signal denominator replaced by its achromatic signal; CIELAB chroma for reference. The blue at 240 degrees loses 1.7 per cent as published and 1.6 with the hue factor removed, and 5.4 with the denominator replaced — the curve then lies close to CIELAB's.

The blue resists through the model's denominator

CIECAM16 says a saturated blue is nearly impervious to added white: at equal luminance and an equal dose it loses a sixteenth of what an orange loses, where CIELAB and Oklab say a quarter. The model has two obvious places for that to come from — a hue factor fitted to make colourfulness equal across hues, and the sum of cone signals it divides its opponent signals by. Setting the hue factor to one changes nothing. Replacing the sum with the model's own achromatic signal makes the blue lose 0.233 of the orange's loss, beside CIELAB's 0.221 and Oklab's 0.223. The disagreement is one denominator.

5 figures 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.

5 figures 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.

6 figures 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.

6 figures 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.

5 figures 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.

6 figures 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.

5 figures