A proof cannot glow

The whole business of proofing rests on one substitution. The production job will be printed on a stock nobody has yet, and a proof is a different object from the start; the proof is printed now, on a different stock, on a different device, and the two are made to agree by a profile that knows what both can do.

The substitution works because ink is subtractive and a proofing sheet is chosen to be at least as bright and at least as neutral as any production stock. Wherever the production sheet is darker or more coloured, the proofer adds ink and catches up.

There is one direction it cannot travel, and a brightened stock sits in it.

The claim #

A proofing system can make a sheet darker and can make it more coloured, and it cannot make it bluer at the same lightness. A brightened production stock’s paper white is exactly that, so the proof is out of gamut at the one point every other colour on the sheet is measured against.

• The two paper whites are ΔE00 9.77 apart, with b* at −9.4 on the brightened sheet and +0.9 on the proofing one — a swing of 10.3 in a single axis.
• Ink cannot go that way. Every colourant a proofer has subtracts, so the reachable set from an unbrightened white runs downwards in lightness; the target is at the same lightness and further towards blue.
• A display cannot either, for a different reason: its white is its maximum by construction, so a paper white at 90 per cent of the diffuser’s luminance and a strong blue cast has to be rendered by scaling everything else down.
• So a soft proof and a hard proof of the same job disagree about the white, and the disagreement has a fixed direction: the hard proof is always the yellower of the two.
• And the number moves with the lamp. Under an ultraviolet-excluded measurement the same two sheets are barely a unit apart, so whether the problem exists at all depends on which of four measurement conditions the workflow is using.

Why ink cannot go that way #

The reachable set from a white sheet is the set of colours obtainable by putting colourant on it, and it has a shape worth stating precisely: it is bounded above in lightness by the sheet itself.

Every ink absorbs. A tint of cyan on a white sheet removes long-wavelength light, which lowers Y and moves the chromaticity towards blue-green; a tint of magenta removes middle wavelengths; a tint of a violet or blue toner — which is exactly what a printer reaches for when asked to make a sheet look less yellow — removes long wavelengths and lowers Y again. Every route to a bluer white goes through a darker one.

That is not an accident of the ink set. It is what subtractive means. To raise b* towards blue without losing lightness the sheet has to return more short-wave light than arrives, which is what a brightener does and what no colourant can do.

The proofer’s actual options are therefore two, and both are compromises. It can match the chromaticity and lose lightness, giving a proof whose white is the right colour and visibly duller than the job. Or it can match the lightness and miss the chromaticity, giving a proof that is the right brightness and yellower.

What paper-white simulation does #

Colour management has a name for the attempt, and it is worth being exact about what the name covers.

An absolute colorimetric rendering reproduces the source’s colours in absolute terms, which means it does not remap the source’s white to the destination’s — so the production sheet’s paper white gets printed as a colour on the proofing sheet, using ink, and everything else is printed relative to that — which is dividing by the paper with the divisor made explicit. This is what “paper white simulation” or “media white simulation” means in a proofing workflow.

It half works, and the half that works is the useful half. The chromaticity of the production white is reachable — a very light tint of a blue toner gets there — so the proof shows the correct hue of white. What it cannot preserve is the lightness, because reaching that chromaticity cost ink, and ink cost light.

The consequence is a proof that is uniformly darker than the job. Every colour on it, not just the white, because everything is printed relative to a simulated white that is itself down a percentage. For an ordinary production stock the amount is a fraction of a per cent and nobody notices. For a heavily brightened one it is the difference between a paper white at b* −9.4 and one an unbrightened sheet plus toner can hold, and the toner is doing real work.

The alternative in the standards is a substrate-corrected aim: rather than simulating the paper, the specification’s target values are recomputed for the substrate actually in use, so the press aims at different numbers on a brightened sheet than on a plain one. That is the printing industry’s answer and it is a good one, because it stops pretending the substitution is exact and makes the substrate an explicit parameter.

Why a display cannot do it either #

A soft proof moves the problem rather than solving it, and the way it moves is instructive.

A display’s white is its maximum by construction. Whatever the panel can emit at full drive is what “white” means on it, and there is nothing above. So rendering a paper white means choosing a code value for it, and any code value below maximum makes the paper grey.

The usual arrangement gives the paper white the display’s white — which is to say the display simulates the sheet by being the sheet, and every colour is rendered relative to it. That reproduces relationships correctly and reproduces the paper’s own colour not at all: on screen the paper is neutral by definition, and the whole of what a brightened stock’s blue cast contributes is gone.

A soft proof with paper-white simulation turned on does the other thing: it renders the paper at a code value below white, tinted, and everything else below that. It is correct and it looks wrong, because a display in a room is a smaller display and the eye is adapted to the display’s own white — so a simulated paper white reads as a dirty grey rather than as a sheet of paper.

So the hard proof is too yellow and the soft proof is either too neutral or too grey, and neither failure is a defect in the system. Both are the same missing capability appearing in the two media’s different currencies.

Why the substitution works everywhere else #

It is worth being explicit about why proofing works at all, because the exception only makes sense against the rule.

A proofing substrate is chosen to be a superset of every production substrate it will stand in for: at least as light, at least as neutral, at least as smooth. Given that, reproducing a production stock is a projection onto a smaller set, and projections onto smaller sets are the easy direction — wherever the production sheet is darker, add ink; wherever it is more coloured, add a different ink.

Every part of the machinery assumes that containment. A profile’s gamut mapping assumes the destination can reach what it is asked for or can be told what to do instead; a validation report assumes a distance is a distance to something reachable; an operator assumes that a proof that misses is a proof that needs adjusting.

A brightened stock breaks the containment in exactly one direction and leaves everything else intact, which is the worst way to break it. The profile builds. The proof prints. The numbers validate. What comes out is a plausible answer to an impossible request, and nothing in the pipeline is in a position to say so — because a distance to something unreachable reads exactly like a distance to something reachable.

The general repair is a containment check rather than a better mapping: ask whether the target lies inside the reachable set before asking how close the match is. That is a cheap test and almost no colour workflow performs it.

What was computed, and how #

The two sheets are a heavily brightened stock and an unbrightened one of the same base, both measured under the ultraviolet-included condition and each normalised to that condition’s perfect diffuser. The colour difference between their paper whites is CIEDE2000 on the resulting CIELAB values.

The radiance factor of the brightened sheet is reported with the band over which it exceeds one — 415 to 460 nanometres, peaking at 1.15 under D50 and 1.24 under D65 — because that band is the thing no colourant can produce and stating where it is makes the claim checkable rather than rhetorical.

The assertion is that the two sheets are further apart than any print tolerance, at ΔE00 above 4, with the b* component reported separately. Reporting the axis matters: a difference of ten spread over three axes would be a different problem, one a proofer could split between them. Ten in one axis, and that axis the one ink cannot travel along, is the whole argument.

The claim about a display is not computed here — it is a statement about what a display’s white means, and it needs no arithmetic beyond the observation that a code value has a maximum.

The workflow consequences, in order of how often they bite #

A proof approved and a job rejected. The proof was made on unbrightened stock, the job runs on a brightened one, and the pressroom’s own measurements agree with the specification while the sheet visibly does not match the proof. Every measurement in that dispute is correct.

Two proofs of the same job that disagree. One proofer’s substrate is brightened and another’s is not, and the two whites differ by more than the tolerance the job is being judged to.

A specification that cannot be met on the stock it names, which is a stronger version of the trouble a profile is a table already causes. The aim values were established on one substrate and the job is on another; without a substrate correction the press is being asked to hit numbers that the paper’s own colour has already displaced.

And a soft proof that everybody stops using. Paper-white simulation is switched on, the screen looks dirty, and it gets switched off — after which the soft proof is a picture of the job on an ideal white sheet, which is the one thing the job will certainly not be.

What the compromise costs, computed #

The claim that a light blue tint reaches the chromaticity and costs lightness is the correct shape and this collection has not computed how much lightness. It can be bounded without knowing anything about a particular ink set, because the bound follows from what a colourant is.

Take the best colourant that could exist for the job. To move b* negative it must lower Y relative to Z, and it does that most cheaply by absorbing only where z̄ is zero — above about 560 nanometres — so that Z is untouched and every photon removed is one the blue-yellow axis does not miss.

Start from a paper white at a luminance factor of 0.90 with b* at +0.9, which is L* 96.0. Reaching b* −9.4 with Z held exactly requires the cube root of the luminance factor to fall by 0.0515, which takes the luminance factor to 0.764 and the lightness to 90.0.

So the cheapest possible route to that chromaticity costs 5.97 lightness units and 15 per cent of the sheet’s luminance, and no ink can do better, because the bound assumes a colourant that absorbs nothing the eye’s short-wave channel can see.

Two things make a real toner worse than that.

It cannot confine its absorption above 560 nanometres. Any real blue or violet colourant absorbs some short-wave light as well, which lowers Z, which means Y has to fall further still to reach the same difference.

And the target’s a* is positive. A colourant absorbing only long wavelengths drives a* negative — it removes X faster than Y, because x̄’s main lobe is where the absorption is — so the ideal colourant reaches the right b* by way of a green cast, while the brightened sheet the proof is chasing is at a* near +3. Correcting that means absorbing short-wave light after all, and paying for it twice.

Six lightness units is six times a print tolerance, so the match the chromaticity option is not a mild compromise that a careful operator could absorb. It is a different failure of the same size as the one it was chosen to avoid, which is what makes the two options a genuine dilemma rather than a trade-off with a sensible middle.

The heavily brightened sheet under an unspecified lamp is the worst case a proof can be signed off in, and it is worth drawing as a split.

The two headline numbers are one measurement #

The gap is quoted twice — as ΔE₀₀ 9.77 and as 10.3 units in a single axis — and the second is not additional evidence for the first.

Two colours differing only in b*, at −9.4 and +0.9, are 8.77 ΔE₀₀ apart at any lightness, and 8.57 if both carry a* of +3. CIEDE2000 compresses the 10.3-unit axis swing to about 8.8, because the pair straddles the neutral axis where the chroma and hue terms both apply.

So the b* axis accounts for roughly nine tenths of the reported 9.77, and everything else — the lightness difference between the two sheets, the a* difference — supplies the remaining unit. That is a stronger statement of the essay’s own point than the two numbers side by side make: it is not that most of the difference is in the blue-yellow axis, it is that almost none of it is anywhere else, and the axis in question is the one direction ink cannot travel.

The unbrightened sheet under the same unspecified lamp is the comparison that isolates the brightener from the condition.

The radiance factor is a property of the lamp as well #

The excess is reported as peaking at 1.15 under D50 and 1.24 under D65, and the two are worth dividing, because the ratio is not the ratio of the lamps’ ultraviolet.

Normalised so that both lamps agree at 560 nanometres, D65 carries 2.13 times D50’s power below 380. The excess above one, though, rises only from 0.15 to 0.24 — a factor of 1.60.

The missing factor is the denominator. A radiance factor is measured against a perfect diffuser under the same lamp, and at 430 nanometres D65 makes that diffuser 1.50 times brighter than D50 does. Dividing 2.13 by 1.50 gives 1.42 against an observed 1.60, and the remaining thirteen per cent is the excitation sitting towards the short end of the ultraviolet, where D65’s advantage is larger still — 2.5 at 330 nanometres against 1.9 at 370.

Which means the radiance factor is not a property of the sheet at all, in the way a reflectance is. It is a ratio between what the sheet does with one lamp’s ultraviolet and what a white tile does with that lamp’s blue, and both halves move when the lamp does. The proof is chasing a target whose value depends on the light it is quoted under, on top of depending on the light it is viewed under — which is the same difficulty the essay’s closing figure reports as the paper white moving over ten units by place, arriving one level down in the arithmetic.

Where the model stops #

The proofing sheet here has no brightener at all, and a good deal of proofing stock is mildly brightened precisely to close this gap. That helps and it introduces the reverse problem: a proof whose own white depends on the ultraviolet in the room it is judged in.

Nothing here models a toner. The claim that a light blue tint reaches the chromaticity and costs lightness is the correct shape and this collection has not computed how much lightness, which would need the proofing device’s own ink set rather than a press’s.

And the observer is absent. Everything above is colorimetry: two measurements and a distance. Whether a viewer notices a paper white nine units off depends on what else is in the field, and a proof and a job side by side in a booth is the case where they notice most.

Who found it, and when #

The printing industry met this in the 1990s and 2000s as brightened stocks became standard, and the response is written into ISO 12647-2’s later revisions: substrate-corrected aim values, so that the specification adapts to the paper rather than the paper being blamed for missing the specification.

Paper-white simulation as an ICC rendering option is older than the problem it is usually invoked for, and its original purpose was proofing one press on another rather than proofing a brightened stock on a plain one. That it half solves this is a coincidence of the arithmetic.

The measurement-condition question was settled in 2009 and the workflow question was not settled by it. Naming which of four conditions a number came from tells two parties that they disagree; it does not give the proofer a way to reach a colour that is outside what ink can do.

The generalisation #

The pattern is a substitution that is exact in one direction and assumed to be exact in both.

Proofing works because a proofing substrate is a superset: brighter, more neutral, capable of everything the production substrate can do and more. The substitution is a projection onto a smaller set, and projections onto smaller sets are easy.

Fluorescence makes the production substrate leave the set. It is no longer a subset of what the proofer can reach — it is outside in one specific direction — and every piece of machinery built on the subset assumption produces something plausible and wrong rather than failing loudly. The profile still builds; the proof still prints; the numbers still validate.

The check worth building into any such system is not on the numbers but on the containment. Ask whether the target is inside the reachable set before asking how close the match is, because a distance to something unreachable is a number that reads exactly like a distance to something reachable.

Where the ladder goes next #

If the sheet is outside the reachable set, the natural question is which set — and the answer is broader than any press’s. A brightened sheet is outside the set of colours a reflecting surface can be at all, which is a bound nothing about ink or gamuts can move.

The other direction is time. The gap between the two sheets is the brightener’s contribution, and the brightener is being used up — so a job that matched its proof on the day it printed will drift towards the proof over the following months, and the drift has a half-life.