Newsprint turns a tint with its colour, not its gain

Printing does not change the sign placed a halftone tint between two ideals that turn most pigments’ hues in opposite directions. A tint in paint turns the other way had found them: a tint made by stirring in white pigment moves its absorption edge, and a tint made by adding white light does not, so an orange diluted in paint turns towards yellow and an orange diluted in light turns towards red. A halftone is mostly the second, because its dots and its paper are averaged by area — but paper scatters light sideways under the dots, and that optical gain carries a halftone part of the way towards the first.

On a coated sheet, whose Yule–Nielsen factor stops at about two, every pigment’s halftone travelled between a quarter and a half of the way, along what looked like a straight line. Only the violet crossed. The essay ended by extending the line. An uncoated sheet is fitted at factors of 2.5 to 5 and newsprint higher, and on the straight line the yellow would cross at 2.4, the orange at 3.2 and the cyan at 3.4 — “the same ink, the same coverage, and opposite hue shifts on two papers.”

The opposite shifts happen. The reason is not the one the straight line gave.

The paper turns the tint #

The journey from the additive tint towards the paint tint bends past a factor of two and stops, at infinite optical gain, between 60 and 70 per cent of the way. The orange crosses at 5.4 rather than 3.2, the cyan at 11.5 rather than 3.4, and the red, the blue and the green cannot cross on any white sheet at all. On newsprint the warm inks’ pale tints still turn the other way from a coated sheet’s — and that reversal is the paper’s yellow colour, not its gain. Read against the paper’s own white, it disappears.

• At a factor of eight each pigment has gone less than half as far as its straight line predicts. The limit of infinite gain is the geometric mean of ink and paper, which lies 60 to 70 per cent of the way to the paint tint.
• The yellow crosses at 2.68, the violet at 1.74, the orange at 5.43 and the cyan at 11.5; the magenta would need a factor beyond twenty; the red, the blue and the green would need to travel further than any gain takes them.
• At a fifth coverage, an orange tint on a coated sheet turns −8.0 degrees against its solid and on newsprint +12.7. The red and the magenta reverse too.
• Newsprint’s gain on a white sheet turns the orange −0.6 degrees; newsprint’s colour at a coated sheet’s gain turns it +13.3. The colour carries the reversal, and the gain keeps the coated sign.
• Adapted to the paper’s white, newsprint’s tints turn within 1.2 degrees of what its gain alone does, for all eight pigments. A reader looking at a newspaper does not see an orange that turns the wrong way.

An orange ink on three papers #

The figure is the measurement the earlier essay asked for. One orange ink, printed on three papers at coverages from solid down to a tenth, and the hue of each tint compared with the hue of the solid on the same paper. The papers are a coated sheet, flat at a reflectance of 0.9 and fitted at a Yule–Nielsen factor of 1.8; an unbrightened uncoated sheet at 3; and a newsprint at 5.

The two uncoated sheets differ from the coated one in two ways at once. They scatter more, which is what their higher factors say. And they are yellow: without an optical brightener, paper made from mechanical pulp absorbs in the blue, so the uncoated sheet falls from 0.84 to about 0.72 at the short end of the spectrum and the newsprint from 0.62 to about 0.45. The earlier essay’s straight line was about the first difference. The question was always going to be which of the two a real paper’s tints answer to.

Read against daylight’s white, as a spectrophotometer reports it, the three papers’ curves in the figure above part as coverage falls. On the coated sheet the orange’s tints turn steadily towards red, reaching −8.7 degrees at a tenth coverage. On the uncoated sheet they turn the other way from the start, by under two degrees down to a third coverage and then steeply. On the newsprint they turn the other way from the start and reach +21.8 degrees. Same ink, same coverages, opposite shifts: the prediction’s observable consequence, exactly.

The road bends #

The prediction’s mechanism was that a larger Yule–Nielsen factor carries a halftone further along the road from the additive tint to the paint tint, in proportion to the factor above one. The earlier essay measured the road only as far as a coated sheet goes, where it looked straight.

Past a factor of two every journey bends over. At a factor of eight each pigment has gone less than half as far as the straight line through its first stretch predicted, and the curves are levelling towards a ceiling. The orange’s journey, drawn thick, is at 36 per cent at 2.5, 44 at 3.5 and 50 at 5; its straight line would have been at 44, 73 and 116.

The ceiling has an exact meaning. The Yule–Nielsen relation — which a halftone is not a mixture set beside Demichel’s area rule — raises the ink’s and the paper’s reflectances to the power 1/n, averages them by area and raises the result back to n, and as n grows without limit that becomes the geometric mean of the two — the paper’s reflectance to the power of the uncovered area times the ink’s to the power of the covered area. That is not a paint tint. It is what light does when it passes through a partial layer of ink rather than beside it: a filter’s mixture, which multiplies transmittances instead of averaging reflectances, and it sits between the additive ideal and the paint one — for these eight pigments, between 60 and 70 per cent of the way to the paint tint.

So the gain buys a size, as the earlier essay said, and the size has a maximum that no paper exceeds. However much a sheet scatters, a halftone on it is at most a filter.

Who can cross #

A pigment’s halftone reverses its hue turn when its journey reaches the point on the road where the turn passes through nought. That point is fixed by the two ideals, and whether a halftone can reach it is fixed by the ceiling.

Five pigments can cross on some white sheet and three cannot. The violet needs 28 per cent of the road and crosses at a factor of 1.74, inside a coated sheet’s range. The yellow needs 45 and crosses at 2.68. The orange needs 51 and crosses at 5.43, at newsprint’s end of the range rather than at 3.2. The cyan needs 64 of a possible 69 and crosses at 11.5; the magenta needs 62 of a possible 65 and has not crossed by twenty. The red needs 72, the blue 96, and the green more than the whole road — its two ideals turn the same way — and all three have ceilings below what they need.

The rule the earlier essay offered a press operator survives in a sharper form. If an ink’s additive hue turn is less than its own ceiling’s share of the distance between its two ideals — between three fifths and two thirds for these inks — some paper can reverse it; if it is more, none can. Where the straight line put the cyan and the orange a little beyond a coated sheet, the ceiling puts the cyan beyond any sheet made and the orange at newsprint’s far end.

Newsprint reverses anyway #

That makes the reversal in the three papers’ curves a puzzle. Newsprint’s factor of 5 is short of what the cyan needs and barely at the orange’s crossing, yet the orange, the red and the magenta all turn the other way on newsprint, and at a fifth coverage the orange’s reversal is 21 degrees wide.

A real paper differs from the coated sheet in its colour as well as its gain, and the model separates them exactly. The ink is a transmittance, so a tint on a coloured paper is the paper’s reflectance times the same tint on a white one; putting newsprint’s factor on a white sheet gives its gain alone, and putting newsprint’s reflectance at a coated sheet’s factor gives its colour alone.

The colour does it. For the orange, newsprint’s gain on a white sheet turns a fifth-coverage tint −0.6 degrees — still the coated sign, just smaller — and newsprint’s colour at a coated sheet’s gain turns it +13.3, nearly all of the +12.7 the real newsprint shows. The red: −3.0 from the gain, +27.2 from the colour, +17.9 together. The magenta: −0.3, +33.8, +21.4. In every case the gain keeps the coated sign and the colour carries the reversal.

The mechanism is the plainest in the essay. A pale tint on newsprint is mostly newsprint, and newsprint is yellow. As coverage falls, the tint’s colour slides from the ink’s towards the paper’s, and the paper’s yellow lies on the paint side of the orange’s hue — towards yellow — so the tint turns that way whatever the gain is doing. The cyan, whose paint tint turns it away from yellow, is dragged the other way: +8.4 on a coated sheet and −23.4 on newsprint, reversed by the same yellow for the opposite reason.

A reader does not see it #

A spectrophotometer reads every tint against daylight’s white. A reader holding a newspaper does not. The paper is the white point set out the two ways of reporting a print — against an absolute white, or relative to the paper — and the second is how a visual system adapted to the page sees it: the paper looks white, and every colour on it is judged against the paper.

Adapted to newsprint’s white, every tint turns within 1.2 degrees of what newsprint’s gain alone would do. The adaptation takes the paper’s colour out and leaves its gain, almost exactly, because a tint on a coloured paper is the paper’s reflectance times a tint on a white one and an adaptation to the paper divides the paper out — dividing by the paper is where that equivalence between the ICC default and an adaptation was measured. The orange on newsprint, read that way, turns −0.6 degrees, the coated sign; the red −2.9; the magenta −0.3. The one pigment whose reading against the paper still differs in sign from the coated sheet is the yellow, at +0.9 against −1.3, and that is the gain: the yellow’s crossing, at 2.68, is below newsprint’s factor, so it is the one genuine reversal the gain produces.

So the prediction was right twice and wrong once. The same ink turns opposite ways on the two papers, measured by an instrument. The gain does not do it. And a reader adapted to the page does not see it, except for a yellow whose turn is under two degrees either way.

What a press room can take from it #

A tint’s hue on uncoated stock is mostly a statement about the stock. A measured reversal on newsprint is real in absolute terms and will show in any comparison against a coated proof viewed side by side — where the eye is adapted to neither paper, or to the proof’s — but it is not a property of the ink, and profiling the ink against it is profiling the paper.

Compare tints relative to the paper. Read media-relative, an uncoated sheet’s tints are the coated sheet’s tints with a larger gain, which is a small and predictable change: a turn in the same direction, by less. A dot is larger than it was asked to be is where the gain was separated from the mechanical spread of the dot; this essay adds that, relative to the paper, the gain’s effect on hue is bounded, at most two thirds of the way to a paint tint.

And expect the ceiling to hold. No uncoated stock reverses the red, the blue or the green. If a measured tint of one of those inks turns the paint way relative to its paper, something other than optical gain is at work — a brightener, a varnish, or ink sitting in the paper rather than on it.

How the tints were computed #

The eight pigments and the flat white of 0.9 are those of the earlier halftone essay. A pigment’s reflectance on that white is read as a transmittance squared, $0.9\,T^2$, so that on a paper of reflectance $P$ the solid is $P\,T^2$ and a tint at coverage $a$ through factor $n$ is $P\,[(1-a) + a\,T^{2/n}]^{n}$. That form makes a coloured paper’s tint the paper times a white paper’s tint, which is what allows gain and colour to be varied separately.

Hue angles are Oklab under D65 and the 1931 observer. Against daylight, the XYZ of each tint is converted directly; against the paper, it is first adapted from the paper’s white to D65’s by the Bradford transform. The journey and its crossings use the earlier essay’s luminance-matched comparison — each halftone at the coverage whose luminance equals the paint tint’s at 95 per cent white — extended to factors of 20, and the ceiling is the geometric mean W^(1−a)·R^a at the matching coverage. The paper comparisons hold coverage fixed rather than luminance, because a press prints a coverage.

What this leaves out #

The papers are three shapes, not three measurements. An unbrightened uncoated sheet and a newsprint were modelled as falling reflectances with the stated levels, and a measured sheet would differ in detail. The finding that the colour carries the reversal depends only on the papers being yellow, which unbrightened mechanical pulp is.

Most uncoated office and book papers are brightened. The brightener is being used up and some paper is brighter than white describe what a fluorescent brightener does, and its effect runs the other way from the yellow modelled here: a brightened sheet returns extra blue, so its tints would be pulled away from yellow in absolute terms. Newsprint is rarely brightened, which is why it carries this effect most cleanly.

The adaptation is complete. A reader is never fully adapted to a page, and in a room with other white surfaces the adaptation to a newspaper’s yellow is partial; how much of the absolute reversal survives then is a question of the degree of adaptation, which this model sets to one.

Still open: whether a partly adapted reader sees half of it #

A reader looking at a newspaper on a white table, under a lamp, is adapted to something between the paper and the table. The absolute reading and the paper-relative reading are the two ends of that range, and they bracket the orange’s fifth-coverage tint between +12.7 and −0.6 degrees.

The prediction is that the reversal a reader sees scales with how much of the visual field the paper fills, so that a newspaper held close is seen as the paper-relative reading says and a clipping pinned to a white wall is seen nearer the absolute one. The computation is this one with a partial adaptation — a degree of adaptation from nought to one, as appearance models carry — and the observation that tests it is a pale orange tint on newsprint placed beside a coated print of the same tint, first on a white ground and then on a sheet of the same newsprint, with the hue matched each time.

Two differences in one sample #

The habit is about separating what a sample differs in before attributing its behaviour to one of them.

An uncoated sheet differs from a coated one in how much it scatters and in what colour it is, and the prediction reasoned about the first because the first was the variable the earlier computation had swept. The observable consequence arrived as predicted, which is the dangerous case: a prediction that comes true for the wrong reason looks exactly like one that comes true for the right one until the two causes are pulled apart. Here they could be pulled apart exactly, because a tint on a coloured paper factors into the paper and a tint on a white one.

The failure mode is to credit an outcome to the variable that was being studied. When a sample changes two things at once, the check is to change them one at a time, and the second check is to ask which of the two a reader’s eye discounts. Here the eye discounts the one that did the work.