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

Substrate — where it appears

The sheet under the ink, which multiplies every colour printed on it and fixes the lightest one available. Its own colour and its own brightener are the two things a printing specification most often leaves unstated and most often disagrees about.

Named by 15 essays across 6 fields — each of them below, with the objects they name alongside it.

Two mechanisms, one ramp, and the patch that separates them. A cyan ramp printed by a press with 10 per cent mechanical gain and a Yule–Nielsen exponent of 2.4. Fitting a mechanical gain at n = 1.0 gives 23 per cent and fitting one at n = 2.4 gives 10 per cent; both reproduce the ramp to under 0.66 of a lightness unit, and the curves lie on top of one another. The two-ink overprint below was in neither fit, and there they are ΔE00 = 3.20 apart.

A dot is larger than it was asked to be

Two quite different things make a printed midtone darker than its coverage says — ink spreading under pressure, and light scattering sideways inside the paper. Both bend the tone curve the same way and neither touches its ends, so the measurement every press is characterised by cannot say which happened. A patch that nobody measures can.

applied · Delivery The process inks as reflectance. Each ink is a sum of Gaussian absorbance bands with stated centres, widths and peak densities, and the reflectance shown is the substrate's times the square of the ink's transmittance, because light crosses the film going down and coming back. The first band of each ink is what it is for; the rest are what is wrong with it. Magenta's unwanted absorption in the blue-violet reaches an optical density of 0.46 against 0.95 for the band it exists to have — 48 per cent of its own strength, absorbing exactly where a saturated blue needs light to survive.

The paper is the white point

A printed colour is reported against the sheet it sits on rather than against the light in the room, and the choice is a switch in every colour engine. Flipped one way, the same separation on coated stock and on newsprint is a 3.04 colour difference; flipped the other, it is 0.13 — and the two answers are about different questions.

applied · Delivery The colour of a beam, against the angle it leaves at. A conformal converter — an even layer laid straight onto the die — makes light leaving at θ cross 1/cos θ times as much of it, so it is more completely converted and the beam is warmer at its edge. From the axis to 75° the correlated colour temperature falls by 556 K and the whole difference is ΔE00 16.4. The flat line is the same emitters under a dome, whose path length is the same in every direction by construction: no angular colour at all, exactly, which is what a remote converter is sold for.

A lamp has a direction

A white LED is a blue die under a converter, and light leaving at an angle has travelled further through the converter than light leaving straight up. So the mixture is different in every direction, the beam is bluer in the middle than at its edge, and the number on the box is one direction's worth of a device that has no single colour.

light · Light What a halftone measures, against what it looks like. A 50 per cent screen, measured by an aperture that averages the patch and seen by an eye that blurs it first and compresses afterwards. At a coarse ruling the two disagree by ΔE00 11.1, and the patch looks 14.3 lightness units darker than it measures — the average of a concave function is below the function of the average, which is Jensen's inequality and not an illusion. The gap falls under a unit above 30 cycles per degree. That is a viewing distance, and the correction a press applies for dot gain has no distance in it anywhere.

Measured with an aperture, seen with an eye

A spectrophotometer averages a halftone patch and reports one reflectance. An eye blurs it first and compresses afterwards, and the average of a concave function is below the function of the average — so a resolvable screen looks darker than it measures, by fourteen lightness units at a coarse ruling and by nothing at a fine one. The correction a press applies is the same size and has no viewing distance in it.

applied · Delivery Media-relative colorimetry is a von Kries adaptation in the worst basis there is. Changing the paper is a change of the light reaching the reader, and the rule colour management uses for it — divide the tristimulus values by the substrate's — is a gain applied in XYZ. That is the one transform the table here describes as the oldest mistake still shipping. On the three stocks a press actually uses the penalty is real and small, because a sheet of paper-mill white is the smoothest change of light in the census. On blue it is 10.2 times the residual the same rule would leave in a cone basis.

Dividing by the paper

Media-relative colorimetry divides tristimulus values by the substrate's, which is a von Kries adaptation applied in XYZ — the one basis the table here describes as the oldest mistake still shipping. On a paper-mill white it costs a few hundredths of a unit. On a tinted sheet it costs ten times what the same rule costs in a cone basis.

applied · Delivery A sample with two reflectance curves, and neither below one. The apparent reflectance of an optically brightened sample, measured under D65 and A. It exceeds 1 — the shaded band — which no reflector can do: more light leaves at these wavelengths than arrives at them, because the sample absorbs in the violet and re-emits in the blue. And the two curves differ, so the sample has no single reflectance to store. The effect drawn here is a floor: most of the excitation band lies below 380 nm, outside the range computed here.

A surface that is not a multiplication

Every argument here about what light does to a surface begins by multiplying two spectra together. A surface with a brightener in it takes light at one wavelength and returns it at another, so it is a full operator rather than a diagonal one — and it does not have a reflectance at all.

scene · Scene 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 a proof on an unbrightened sheet cannot reach. The paper white of a heavily brightened stock beside the paper white of an unbrightened one, both under an ultraviolet-included instrument. They are ΔE00 9.8 apart and 10.3 of that is in the blue-yellow axis. A proofing system on the unbrightened sheet can print towards the brightened one only by adding ink, which makes the paper darker rather than bluer; it cannot add light at 435 nanometres because it has no brightener and its own lamp is the one in the room. This is why a soft proof and a hard proof of the same job disagree about the white, and why the disagreement is in one direction.

A proof cannot glow

A proof is a different sheet of paper pretending to be the production one, and the pretence works by adding ink until the two agree. It cannot work for a brightened stock, because the direction the proof has to travel is towards more blue at the same lightness and every ink a proofer owns moves it towards less light instead.

applied · Delivery The best possible 3×3, and the patches it makes worse. Each row is one patch printed on a brightened sheet, measured under both conditions. The pale bar is how far apart the two measurements are; the dark bar is what is left after the best least-squares 3×3 over the whole set has been applied. It leaves 23 per cent of the mean, and — the part a mean hides — it makes 4 patches worse than doing nothing. The solids are the ones it damages: the ink blocks the ultraviolet, so a solid barely disagrees between the two conditions and the correction has no business touching it. A matrix has no way to apply itself only where the paper is showing.

A tolerance cannot cross a condition

If two measurement conditions disagree by seven units, the obvious repair is a correction matrix fitted between them. The best least-squares 3×3 over seventeen printed patches leaves 23 per cent of the disagreement and makes five patches worse than doing nothing — because the term it is trying to remove is proportional to how much paper is showing, and no linear map on three numbers can express that.

difference · Metric Each departure over forty-two surfaces rather than one. The same six departures measured over a family of forty-two analytic reflectances — an absorption band of stated centre, width and depth — with the smallest, the median, the ninety-fifth percentile and the largest marked. Every one of them spans more than a factor of three, and the ranking between them is not stable across the family: what decides a departure's size is which sample it is asked about, because a departure is a pairing and the sample is one of the two factors. Quoting any single number for what an observer's age is worth is quoting a choice of example.

A brand colour for a population

A brand colour is chosen once, specified in a number, and seen by everybody. The observer audit says two candidate colours with identical specifications can carry observer spreads differing by an order of magnitude, and that the spread is computable from an ink's spectrum at the moment the ink is chosen.

applied · Delivery 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 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 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

Named alongside it

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

HalftoneChromatic adaptationProcess inksSpecificationColour managementQuality controlAssertionHuePaper whiteReflectanceWhite pointAdaptation

All concepts