Adapting to a brightened sheet leaves the glow

Newsprint turns a tint with its colour, not its gain found a pale orange tint on newsprint turning its hue 12.7 degrees one way from its solid ink, while the same tint on a coated sheet turns 8 degrees the other way. The reversal was the paper’s yellow: a tint is mostly paper, and newsprint’s paper pulls it towards yellow. A reader sees the reversal until almost adapted then put a reader between an instrument, which reads against daylight’s white, and a reader fully adapted to the page, for whom the paper is white. The reversal faded as the reader adapted and was gone only when adaptation was nine tenths of the way to the paper; a coated sheet, whose white is daylight’s, did not care.

That essay ended on the third paper a reader meets every day. Office paper, most book paper and much coated stock carries an optical brightener, a fluorescent dye that absorbs ultraviolet and emits blue, so that under a lamp with ultraviolet in it the sheet returns more blue light than falls on it. Some paper is brighter than white is the collection’s account of why such a sample has no reflectance curve. Its colour leans the opposite way from newsprint’s, so a tint on it should turn the other way from a tint on newsprint — pulled towards the paper’s blue — and further the coated way than the coated sheet. The prediction was that the brightened sheet would exaggerate the coated sheet’s turn for a reader who did not adapt to it and converge on it for one who did, so that the three papers turn a pale tint three different amounts unadapted and nearly one amount fully adapted.

The colour adapts away and the glow stays #

Unadapted, a fifth-coverage orange tint on brightened office paper turns 41.5 degrees the coated way — five times the coated sheet’s 8.0 and opposite to newsprint’s 12.7. A sheet of exactly the same colour that does not fluoresce turns it 33.5, and a reader fully adapted to that sheet sees 3.2, within a degree and a half of a white sheet with the same dot gain for all eight pigments. A reader fully adapted to the brightened sheet itself still sees 10.0 degrees. The part that does not adapt away is the brightener’s: 6.8 degrees on the orange, 8.9 on the red, and more on a more heavily brightened sheet.

• Unadapted, the prediction holds: the brightened sheet turns warm tints the coated way and far further than the coated sheet does.
• Adapted, it half holds. The sheet’s colour adapts away exactly as newsprint’s does. The brightener’s share does not.
• The glow survives adaptation because it is added, not multiplied. Ink puts the glow out where it covers the paper, so the solid has almost none and the tint most of it; adapting to a white rescales light, and cannot remove light that one patch has and the other lacks.
• Under a lamp with no ultraviolet the whole effect vanishes: the same print’s orange tint turns 1.7 degrees.

What a brightened sheet returns #

The sheets are the ones some paper is brighter than white built: a paper base, cream because the lignin left in it absorbs towards the blue, with a two-band fluorophore that absorbs between about 320 and 400 nanometres and emits in a band near 435. Lit by daylight reconstructed down to 300 nanometres, office paper — a brightener loading of 0.8 — reflects a cream curve and emits a blue band on top of it, and the sum rises past a perfect white diffuser in the violet, to a radiance factor of 1.15. The emitted light is 0.6 per cent of the sheet’s luminance, because the eye is not very sensitive at 435 nanometres; it is most of the sheet’s blueness. Normalised to the same luminance as daylight, the sheet’s white has a Z of 125.6 against daylight’s 108.9.

A tint on such a sheet is paper with ink over part of it, and the ink changes both halves of what the paper returns. The reflected half is filtered by the ink as on any paper, through the same halftone model — Yule and Nielsen’s spread of light under the dots with the factor of an uncoated sheet. The emitted half is different. An ink’s vehicle, the resin the pigment sits in, absorbs strongly in the near ultraviolet, so paper under ink receives little excitation: weighted by what the brightener would have absorbed, 13.5 per cent of it gets through. A covered area glows at about a seventh of the rate of a bare one, and what it emits is filtered by the pigment on the way out. The glow of a tint therefore comes almost entirely from the paper its dots leave bare.

Three papers, three directions #

For a reader not adapted to the paper, the three papers turn the same pale orange three ways: newsprint 12.7 degrees one way, the coated sheet 8.0 the other, the brightened sheet 41.5 the coated way. The red does the same — 17.9, −6.1 and −42.0. A heavily brightened sheet, with a loading of 2, turns the orange 56.8 degrees. The pale tint’s colour is dominated by the paper, the paper here is strongly blue, and so the tint’s hue is pulled far round towards blue from its solid’s orange.

As the reader adapts, all of it comes down, and not to the same place. A quarter of the way the orange turns 33.2 degrees, half-way 24.9, three quarters 17.2, and fully adapted 10.0. The coated sheet stays at 8.0 throughout. So at full adaptation the brightened sheet does nearly converge on the coated sheet’s turn for the orange, as predicted; for the red it stops at 13.1 against the coated sheet’s 6.1, and the three papers at full adaptation still span 9.4 degrees on the orange and 10.2 on the red — five times less than unadapted, not one amount.

The figure’s two controls are what separate the reasons. A sheet dyed to the brightened sheet’s exact colour, without fluorescing, turns the orange 33.5 degrees unadapted; fully adapted, 3.2. A white sheet with the same dot gain turns it 3.4 at every degree of adaptation, since its white is daylight’s. The dyed sheet ends on the white sheet, as newsprint’s reversal ended when the reader adapted to its yellow. The brightened sheet ends 6.8 degrees beyond it.

Where the tints lie #

Unadapted, the orange’s tints swing through a wide arc. The solid sits at a hue angle of 49.6 degrees in Oklab, and as coverage falls the tints move towards the paper — which, read against daylight’s white, sits out in the blue — so their hue falls with them: 29.3 degrees at 40 per cent, 8.2 at a fifth, −20.5 at a tenth, where the palest tint reads pink rather than orange. The turn is the angle between the solid and the pale end, seen from the origin.

Fully adapted to a same-coloured sheet that does not glow, the paper sits at the origin and the tints run almost straight in to it, the way tints on a white sheet do. That is the whole of what adaptation does: it moves the paper to neutral, and since every tint is paper multiplied by ink, it moves every tint by the same proportion in each cone signal. A room with two lights has no white is the collection’s account of what goes wrong when light is added rather than multiplied, and it goes wrong here in the same way.

Fully adapted to the brightened sheet, the tints still lean. The paper sits at the origin, because the reader adapted to it, and the solid at 51.3 degrees, almost where it was. The tints do not run straight in: at 40 per cent they sit at 43.1 degrees, at a fifth 41.3, at a tenth 40.4, where on the non-glowing sheet they sit at 48.9, 47.7 and 47.0. The adaptation removed the paper’s blue in proportion to each patch’s light, and a pale tint’s light carries a different proportion of blue glow from the paper’s white — more than its reflected light alone would, because the dots spread and darken the reflected light beyond their area while the glow is lost only in proportion to it.

What adaptation removes and what it cannot #

The sheet’s colour leaves at most a degree and a half at full adaptation, on every pigment. For six of eight it leaves under 0.6 degrees; the blue, whose solid is far from neutral and whose turn is the largest to begin with, is the worst at 1.4. That residue is the adaptation transform’s own imperfection — Bradford’s cone space is not the eye’s, and a tint’s spectrum is not the paper’s — and it is the same size newsprint’s residue was.

The glow leaves −6.8 degrees on the orange and −8.9 on the red, −1.6 on the magenta and the violet and −1.1 on the yellow; on the cyan, green and blue, +2.1, +3.3 and +1.0. Every residue has the sign of the unadapted turn: each pale tint is pulled round towards the glow’s blue from whichever side its solid lies, as it should be for a light that the pale tint has and the solid lacks.

The mechanism is arithmetic. Chromatic adaptation is modelled — and, as far as anyone has measured, works — as a gain on each kind of cone, set by the white. A paper’s colour enters every tint as a factor: the tint’s light is the paper’s light times what the ink lets through. A gain on each cone divides that factor out, nearly exactly for any smooth spectrum, which is why newsprint’s reversal and the dyed sheet’s both vanish. A brightener’s glow enters as a term: the tint’s light is its reflected light plus the glow from its bare paper, and the solid’s is its reflected light plus almost nothing. No gain applied to both can remove a term that one of them has and the other does not.

More brightener, more of it #

The glow’s residue grows with the brightener’s loading, for every pigment. On the orange it is 4.2 degrees on a lightly brightened sheet, 6.8 on office paper and 9.5 on a heavily brightened sheet; on the red, 5.6, 8.9 and 12.0; on the green 2.1, 3.3 and 4.5 the other way. The growth is less than proportional to the loading, because a brightener’s absorption saturates — the collection’s model takes it through Beer’s law, and a loading of 2 absorbs far less than twice what 0.8 does.

This is a property a paper specification could state. The whiteness a mill quotes is a measurement of the glow, and whiteness is mostly the lamp found most of that scale depends on the ultraviolet the instrument supplies. The residue here depends on the same ultraviolet and the same loading, so a sheet sold on its whiteness is a sheet on which pale tints turn by an amount a reader’s adaptation cannot absorb.

Without the ultraviolet #

Under a lamp with no ultraviolet the brightener does nothing, and the sheet is its cream base. An unadapted reader sees the orange tint turn 1.7 degrees and the red 1.6, against 41.5 and 42.0 in daylight; the cyan 2.4 against 26.7. Adapted to the cream base, the orange turns 3.4, which is the white sheet’s value: the base’s cream adapts away like any other paper colour.

The lamp that stopped emitting ultraviolet described the change that made this the common case indoors: a blue-pumped white LED emits nothing below about 420 nanometres, and between about 2005 and 2020 it replaced almost every lamp that did. The same printed page therefore turns its pale tints by forty degrees at a window and by two under the ceiling light, and the reader adapted to either sees ten degrees and three. The ultraviolet is half the product found a fluorescent sample’s departure from the reflectance model proportional to the lamp’s ultraviolet; the turn here is one visible consequence of that departure, and it follows the lamp the same way.

What this means for a proof #

A proof on brightened paper viewed under a light booth’s D50 with its ultraviolet, and a proof viewed under a UV-free LED, disagree about pale tints by more than any adaptation can reconcile. For a colour-critical pale tint — a brand’s tint of its orange, say, on office paper — the difference between the two viewings is about forty degrees of hue for an unadapted glance and seven for a reader who has settled in, and neither viewing is wrong.

Adapting to the page is not a cure for a brightened sheet as it is for newsprint. A reader handed a newspaper adapts to its yellow and the pale tints come right; a reader handed brightened office paper adapts to its blue and the pale warm tints are still off by seven to nine degrees. The only cure is the lamp, and a lamp without ultraviolet removes the brightener’s reason for being there.

How the tints were computed #

The sheets are shortwave stocks: a base reflectance falling towards the blue, and a fluorophore with absorption centred at 358 nanometres and emission at 435, a quantum yield of 0.85 and absorption saturating in the loading. Under CIE daylight reconstructed from its basis down to 300 nanometres, each sheet’s reflected and emitted radiance factors are computed in photons and sliced to the visible grid. A tint of coverage a is the reflected radiance factor times the Yule–Nielsen tint with factor 3, plus the emitted radiance factor times (1 − a) + a × 0.135 × t, where 0.135 is the ink vehicle’s ultraviolet transmittance weighted by what the fluorophore absorbs and t the pigment’s single-pass transmittance, the square root of its reflectance over a 0.9 white. Hues are read as the essay on partial adaptation read them: CIE 1931 tristimulus values under D65, adapted by Bradford’s transform from a white D of the way from daylight’s to the sheet’s, in Oklab. The dyed sheet uses the brightened sheet’s total radiance factor as a reflectance, and the base uses the paper base alone, both through the same halftone model.

What this leaves out #

The ink’s ultraviolet absorbance is one stated number for every ink, a typical value for an ink vehicle. A real ink with a vehicle that passes more ultraviolet would leave more glow under its dots and less residue; the pigment itself may absorb there too, in which case less. The residue’s size depends on it and its sign does not.

The halftone is an area average. Light scattered sideways in the paper before it re-emerges — the dot gain the Yule–Nielsen factor carries for the reflected part — also carries excitation sideways, so some glow arises under the dots from ultraviolet that entered beside them. That would shrink the gap between tint and solid and the residue with it; how much is a question about the paper’s scattering length at 360 nanometres, which is not modelled.

Adaptation is a von Kries gain in Bradford’s space and nothing more. Real adaptation to a sheet under a lamp also involves the sheet’s brightness and its surround, and whether an observer adapts to a fluorescent white as to a reflecting white of the same chromaticity is itself an open question; the argument here needs only that adaptation is multiplicative.

Still open: whether a partial ink film restores the glow it filters #

The residue comes from the ink putting out the glow under the solid, which makes a tint’s glow proportional to its bare paper. A real halftone’s dots are not uniform films: their edges are thinner than their centres, and at the pale end of a tint ramp most of a dot is edge. A thin film lets more ultraviolet through.

The calculation is this one with each dot’s film thickness falling off towards its edge, the ultraviolet transmittance computed through the local thickness and the glow under each part of the dot added up. The prediction is that the residue at a fifth coverage falls by about a third — the pale end is where dots are smallest and most edge — while the solid, a continuous film, keeps none, so that the turn left after adaptation grows towards the middle of the ramp rather than being largest at the palest tints. If it does, the proof a designer should look at is a mid-tone, not the palest tint.

A factor adapts away and a term does not #

The habit is about the algebraic form a disturbance enters in before assuming what will correct it.

Newsprint’s reversal and the brightened sheet’s turn look like the same kind of thing — a coloured paper pulling a pale tint’s hue towards itself — and the first was cured completely by adapting to the paper. The obvious expectation was that the second would be too, and most of it was. What was left was the part that entered differently: the paper’s colour multiplies every patch on the page, and the glow is added to each patch in proportion to the paper it leaves bare.

The failure mode is to judge whether a correction can work by the size or the direction of what it corrects, rather than by its form. A gain can undo a factor of any size. It cannot undo a term, however small, that differs between the things being compared.