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

Optical dot gain — where it appears

The darkening of a halftone beyond its printed dot area, caused by light entering the paper between the dots and scattering under the ink before it comes back out. It is modelled by a Yule–Nielsen factor, and it carries a tint's colour part of the way from a mixture of light towards a paint.

Named by 6 essays across one field — each of them below, with the objects they name alongside it.

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 Clustered spots along an orange ramp. For an orange ramp on brightened office paper, the turn a reader fully adapted to the sheet still sees beyond its colour, on stochastic screens of twenty-micrometre spots switched on singly and in clusters of two, three and four, beside 150- and 300-line screens. At five per cent clusters of four leave 8.14° against the single spots' 8.94° and the 150-line screen's 8.12°; at sixty per cent, 6.00° against 6.90° and 5.67°. The axis starts at 5°.

Squares of four print a pale tint like a 150-line screen

On brightened office paper a stochastic screen's twenty-micrometre spots are mostly rim while they stay apart, and the rim lets the paper's glow through, so the palest tints carry the screen's whole cost in hue a fully adapted reader still sees. Merging gives back half of it in the mid-tones, where the spots touch, and nothing in the pale tints, where they do not. A second-order screen switches its spots on in clusters from the first tint, and the prediction was that clusters of four would take the orange's pale-tint residue down by about a degree, to within half a degree of a 300-line screen, while the sixty-per-cent tints stayed where the merged first-order screen leaves them. Squares of four do better in the pale tints than predicted and differ where predicted to agree. At five per cent they take the orange from 8.94 degrees to 8.14 — 0.02 above a 150-line screen and 0.81 below a 300-line one — and every pigment lands within a tenth of a degree of the 150-line screen. At sixty per cent they keep the orange 0.9 degrees below the first-order screen, where pairs and Ls come back to within a quarter. From ten per cent on, the 150-line screen pulls ahead.

brain · Appearance Growing clumps follow the 150-line screen along the ramp. For an orange ramp on brightened office paper, the turn a reader fully adapted to the sheet still sees beyond its colour, on single stochastic spots merged where they touch, on squares of four, on thirteen clumps grown from those squares as the tint darkens, and on a 150-line screen. The growing clumps start as the squares, 8.14°, and follow the 150-line screen from there: 7.22° against 7.09° at thirty per cent, 5.65° against 5.67° at sixty. The axis starts at 5°.

A growing clump prints like the screen with as many dots

On brightened office paper a halftone's ink lets the paper's glow through at its thin rim, and the share of the ink that is rim decides how much hue a fully adapted reader still sees turned. A stochastic screen of squares of four prints the palest tint like a 150-line screen and falls behind it from ten per cent, because its clusters multiply where a conventional dot grows. A hybrid grows each cluster as the tint darkens, the number of clumps held, and the prediction was that it keeps the squares' pale tint, reaches within a tenth of a degree of the 150-line screen by thirty per cent, and stays slightly above it through the mid-tones. With thirteen clumps on the census's tile it follows the 150-line screen within two tenths of a degree at every coverage, within a twentieth at twenty per cent, and dips just below it at sixty. The reason is a count. Thirteen clumps on a tile 640 micrometres across are as many dots per area as a 143-line screen; twenty-six follow the 200-line screen and fifty-two the 300-line. A clump's irregular place on the tile does not matter to the glow; how many clumps share the ink does.

brain · Appearance Most of the residue is not at the rim. At each coverage of the orange ramp, the residue a single clump on the tile leaves — the least rim the tile can hold — beside thirteen clumps'. The single clump keeps 92 per cent of the thirteen clumps' residue at five per cent and 94 at sixty: the rest of the turn is the tint's bare paper glowing beside ink that does not.

The rim was never most of the glow

On brightened paper a halftone tint keeps a hue turn a reader fully adapted to the sheet cannot remove, and five essays have chased the part of it that lives at the ink's thin rim — merging spots, clustering them, growing them — down to a rule: the clump count sets the residue, and only coarser patterns lower it. The proposal was a screen coarse in the pale tints and finer as the tint darkens, and the prediction that six clumps on the tile beat the 150-line screen by more than half a degree below twenty per cent. They beat it by 0.11 to 0.17. Scheduled six, thirteen and twenty-six clumps save a third of a degree at ten per cent and give back a fifth at sixty. The reason is the floor. One clump on the tile — the coarsest pattern it can hold, nearly all its rim gone — still leaves 7.48 degrees of an orange's 8.14 at five per cent and 5.30 of 5.65 at sixty. What screening can move is the rim's tenth; the other nine tenths is bare paper glowing beside ink that does not.

brain · Appearance A lighter ink swings the residue through nought. For a five-per-cent tint on brightened office paper, printed instead with the same pigment diluted to a share of its strength over more of the paper — matched in colour on a non-fluorescent sheet — the hue turn a reader fully adapted to the sheet still sees, signed, against the dilution. The orange's -7.2° at full strength passes nought near 0.54 and reaches 10.3° at a quarter.

A light ink can cancel the glow at one strength

A pale tint on brightened paper keeps a hue turn a reader fully adapted to the sheet cannot remove, and nine tenths of it survives every screen, because it is the tint's bare paper glowing beside ink that puts the glow out. A light ink — the same pigment diluted, printed over more of the paper — was the proposed lever, and the prediction that a quarter-strength ink lowers a five-per-cent orange's residue by a third. It does not lower it; it reverses it, from −7.2 degrees to +10.2. Somewhere between, the residue passes through nought, and for every one of eight pigments there is a strength that cancels it: 0.41 for the red, 0.54 for the orange, 0.80 for the blue and the cyan at a five-per-cent tint. The cancelling strength moves by under a tenth from five per cent to forty, so one ink per pigment keeps every pale tint within a degree and a quarter to twenty per cent, where full-strength ink leaves up to nine. The lever is real; it has a setting, and the light inks printers carry are diluted past it.

brain · Appearance

Named alongside it

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

HalftoneChromatic adaptationOklabOptical brightenersSubstrateAdditive mixtureColour appearanceHuePigmentFluorescenceKubelka munkPaper white

All concepts