A reader sees the reversal until almost adapted

Newsprint turns a tint with its colour, not its gain found a halftone tint of orange ink at a fifth coverage turning its hue by 12.7 degrees one way on newsprint, where the same tint on a coated sheet turns eight degrees the other way. It took the newsprint apart and found that the reversal came from the paper’s colour — a yellow that falls away in the blue — rather than from its heavy optical gain. And it made one more reading: adapted to the paper’s own white, as a reader looking at the page might be, the orange tint on newsprint turns by −0.6 degrees, the coated way. The reversal an instrument reads is not one a fully adapted reader sees.

The two readings bracket every real reader, and the essay’s closing section said so. A reader holding a newspaper on a white table is adapted to something between the paper and the table, and the share depends on how much of the view the paper fills — “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 it named was a partial adaptation, a degree running from nought to one, and the question it left was where between the two readings a real reader’s turn falls.

A turn that fades, not one that flips #

A reader adapted half-way from daylight to newsprint’s white still sees the orange tint turn 7.3 of the instrument’s 12.7 degrees, the red 9.3 of 17.9 and the magenta 9.5 of 21.4. The warm tints keep turning the opposite way from the same tints on coated paper until the reader is adapted 89 to 98 per cent of the way to the paper, and the cyan and green until 90 and 93. On an unbrightened uncoated sheet, paler and less yellow, the reversal ends between 54 and 88 per cent. On a coated sheet, whose white is daylight’s, adaptation changes nothing.

• The reversal is not seen or unseen; it fades with adaptation, steadily for the warm pigments.
• On newsprint it lasts almost to the end. A reader has to be adapted nearly completely to the paper not to see it.
• The paper’s colour sets the threshold. The paler the sheet, the less adaptation it takes to cancel what its colour does.
• An experiment on readers now has a number to find: not whether the reversal is seen, but how adapted a reader holding a newspaper is.

Adapted to a mixture #

A reader’s adaptation is modelled the way the collection’s appearance essays model a room with more than one light: the white the reader is adapted to is a mixture. At a degree of adaptation D it is D of the paper’s white and 1 − D of daylight’s, the two scaled to the same luminance and mixed in the cone-like space the Bradford transform uses. At D = 0 the reader is adapted to daylight alone and reads the page as the instrument does; at D = 1 to the paper alone. The tint’s turn is then computed exactly as before — the hue of the tint at a fifth coverage minus the hue of the solid ink on the same paper, in Oklab after adapting — at every D from nought to one.

A room with two lights has no white is the collection’s standing reminder that a mixed adaptation is a model, not a measurement: there is no stimulus whose appearance says which mixture a viewer is adapted to. That is exactly why the result has to be stated across D rather than at one value of it.

Every curve runs from the instrument’s value at the left to the fully adapted value at the right, and every one crosses zero only near the right edge. The orange falls from 12.7 degrees through 10.3 at a quarter, 7.3 at a half and 3.8 at three quarters, to 1.3 at nine-tenths and −0.6 at one. The red and magenta start higher and fall faster, but they are still turning by nine degrees half-way. The cyan and green, which turn the other way on newsprint — against the coated sheet’s positive turns — rise from −22 and −11 degrees towards zero on the same shape.

The open circles are where each tint stops turning opposite to its coated counterpart: the red at 0.89, the cyan at 0.90, the green at 0.93, the orange at 0.97, the magenta at 0.98. The yellow, blue and violet tints never reverse on newsprint in the first place, and have no circle.

Most of the turn survives most of the adaptation #

Read as a share of what the instrument reads, the newsprint curves fall steadily and reach nought only at the far end. Half-adapted, the orange keeps 58 per cent of its turn, the red 52 and the magenta 44. That is the first part of the answer to the proposal: the reversal a reader sees does scale with adaptation, but it does not scale down to nothing in proportion. A newspaper that fills a third of the view, if that means a third of the adaptation, leaves a reader seeing four-fifths of the instrument’s reversal.

The uncoated sheet’s curves cross zero a little past the middle and end pointing the coated way, at six to eight tenths of the instrument’s turn in the other direction. An uncoated sheet is paler than newsprint — its reflectance falls in the blue from 0.84 to 0.72, against newsprint’s 0.62 to 0.45 — and its colour does less, so a reader has to be adapted less to cancel it. Once past that point, the reader sees the tint turn the way it turns on a coated sheet: the paper’s gain, which the earlier essay separated from its colour, pulls it the paint way, and nothing is left of the paper’s colour to pull it back.

On the uncoated sheet the same five curves cross zero near the middle. The orange starts at 4.4 degrees the paint way and ends at 3.5 the coated way; the red runs from 6.9 to −4.2; the cyan from −5.3 to 4.4. Their instrument readings are a third of newsprint’s, because the sheet’s colour is a third as strong. Their fully adapted readings go further the coated way than newsprint’s do, because what is left once the colour is adapted away is the paper’s optical gain, and printing does not change the sign found gain moving a halftone from the light ideal towards the paint one — the uncoated sheet has less of it than newsprint, so less pull the paint way, and its adapted tints stay nearer the coated sheet’s. On this sheet a reader’s adaptation decides the sign, and the likeliest readers — a book held in the hand, a letter on a desk — sit near the middle, on either side of it.

The threshold is the paper’s colour #

On newsprint every reversing pigment needs the reader adapted more than 89 per cent of the way. On the uncoated sheet the orange needs 59, the red 64, the cyan 54, the green 77 and the magenta 88. The magenta is the slow one on both papers, and the reason is in where its reflectance sits: a magenta reflects at both ends of the spectrum, so a yellow paper that falls in the blue changes the magenta tint’s blue end more than any other pigment’s, and it takes the most adaptation to undo.

The coated sheet is not on the figure because it has no threshold. Its reflectance is flat, its white is daylight’s white, and a reader adapted to any mixture of the two is adapted to the same thing. Every pigment’s turn on coated paper is the same at every degree of adaptation, to a part in a trillion. So the whole phenomenon is the paper’s colour interacting with a reader’s partial adaptation to it: a neutral sheet cannot produce it, and a coloured sheet produces it in proportion to how far the reader is from having adapted it away.

What the tints look like to three readers #

All three readers see the solid ink in nearly the same place, and they part at the pale end. A tint of orange ink on newsprint is mostly paper, and the paler the tint, the more it is the paper’s colour a reader is looking at. To a reader adapted to daylight, the paper is yellow, and the pale tints run off towards yellow — a turn of the hue towards the yellow the paint way turns an orange, and away from the direction a coated sheet’s tints take. To a reader fully adapted to the paper, the paper is neutral and the tints run straight towards the neutral point, their hue barely changing. Half-adapted, half-way between.

This makes plain why the turn depends so smoothly on adaptation. The turn is the angle between the solid and the pale end as seen from the neutral point, and adaptation moves the pale end by an amount proportional to how much of the paper’s colour the reader still sees.

What the experiment would now measure #

The earlier essay proposed an observation: a pale orange tint on newsprint 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. It was framed as a test of whether readers see the reversal at all.

The computation turns it into a measurement of adaptation. On the white ground a reader is adapted mostly to the white, and the model predicts the tint on newsprint turns seven to twelve degrees the paint way; on a sheet of newsprint the reader is adapted mostly to the paper, and the prediction falls towards nothing. The hue a reader matches in each arrangement, read against this curve, gives the degree of adaptation directly. If readers on the newsprint ground still see a turn of four degrees, they are adapted about three quarters of the way; if they see none, more than nine tenths.

That number is the one the rest of the collection’s print essays need. Printing does not change the sign found a coated sheet’s halftone turning a hue the opposite way from a paint tint, and the newsprint essay found an uncoated sheet reversing it again. Whether a reader of a newspaper sees the newsprint reversal is not a question about ink or paper at all; it is a question about how completely a reader adapts to a page, and every prediction about newsprint colour carries it.

What it means for a print buyer #

A proof on coated paper tells a buyer little about what newsprint readers see. A brand colour is an ink argued that a brand’s colour is specified as an ink and proved on a stock; here the stock decides the direction a pale tint of that ink turns for most readers, not only its solid colour. The coated proof’s tints turn the coated way whatever the reader’s adaptation; the newsprint’s tints turn the other way for any reader not almost fully adapted to the page. A buyer approving an orange by its coated proof is approving a hue turn that most newspaper readers will see reversed, by up to twelve degrees in the pale tints, where a tint in paint turns the other way first priced how noticeable such turns are.

And a paler sheet is more forgiving. On the uncoated sheet a reader adapted just past half-way already sees the coated turn. The same ink, run on a whiter stock, gives a turn that most readers will not see as a reversal at all — which says the choice of paper is a colour decision for the pale tints, not only for the solids.

How the adaptation was modelled #

The papers, inks and halftone model are those of the newsprint essay: a coated sheet flat at 0.9 at a Yule–Nielsen factor of 1.8; an unbrightened uncoated sheet at 0.84, falling to about 0.72 in the blue, at 3; a newsprint at 0.62, falling to about 0.45, at 5; eight inks as transmittances whose reflectance on a white of 0.9 is 0.9 times the transmittance squared. Colours are integrated under D65. A reader adapted by D has as its white the mixture, in Bradford’s cone-like space, of D times the paper’s white and 1 − D times D65’s, both scaled to a luminance of 100; each colour is adapted from that white to D65 by the Bradford transform and read in Oklab. The turn is the difference of Oklab hue angle between a fifth-coverage tint and the solid, wrapped to within 180 degrees; the threshold is found by bisection as the D at which the newsprint or uncoated turn changes sign away from the coated sheet’s.

What this leaves out #

The degree of adaptation is not predicted here. Mapping the share of a view a paper fills onto D is exactly what the proposed experiment would measure; the essay reports the turn across every D rather than guessing that mapping.

The mixture is linear in a cone space. Real partial adaptation may mix differently — CAT16 applies its degree of adaptation to the cone gains rather than to the white itself, which is close to but not the same as mixing whites — and the thresholds would move slightly under a different rule. They would not move from the newsprint’s nine-tenths to anything near a half.

And the reader sees the whole tint. A halftone at reading distance is a mean — a halftone is a luminance object found that at any ruling a press runs, only the eye’s luminance channel can resolve the screen at all, so the colour a reader sees is the dots’ average. At the distance a proof is examined with a loupe it is dots and paper, and the adaptation that matters is then to the paper between the dots.

Still open: whether a brightened sheet reverses the other way #

A paper with optical brighteners is bluer than daylight under a lamp with ultraviolet in it: its reflectance rises in the blue, where newsprint’s falls. A brighter white still looks white found a reader’s adaptation absorbing most of a brightened sheet’s blueness at the paper itself; what it does to the tints printed on it is the other half of that question. By the logic here, a tint on such a sheet should turn the opposite way from a tint on newsprint — pulled towards the paper’s blue rather than its yellow — and a reader not adapted to the brightened white would see the orange turn further the coated way than it does on the coated sheet.

The calculation is this one on a brightened sheet, with the brightener’s emission under D65 added to the paper’s reflectance as the collection’s whiteness essays model it, and the turn read across D. The prediction is that the orange and red turn more strongly the coated way on the brightened sheet at small D and converge on the coated sheet’s turn at D = 1, so that the brightener exaggerates the coated sheet’s turn for a reader who does not adapt to it. If that is right, the three papers — newsprint, coated, brightened — turn the same pale tint three different amounts for an unadapted reader and nearly one amount for a fully adapted one.

A bracket is a question, not an answer #

The habit is about treating two readings that bracket a quantity as the ends of a curve to be computed rather than as two answers to choose between.

The earlier essay had the instrument’s reading and the fully adapted reader’s, and they disagreed about whether the reversal existed. Neither was the reader’s reading. Computed across the bracket, the answer was neither yes nor no but a curve, and the curve’s shape — nearly all of the turn surviving until nearly all of the adaptation — was not predictable from its ends. A straight line between the two readings would have put the threshold near the middle; the actual threshold is near the far end.

The failure mode is to settle a bracketed question by arguing for one end. Here the argument for the paper-relative reading was good — readers do adapt to what they look at — and it would still have misreported what almost every real reader sees.