The paper is the white point

A printing standard specifies the colour of a solid ink to within a couple of ΔE00. It does this knowing perfectly well that the same ink printed on a coated sheet and on newsprint will measure ten units apart, because the number being specified is not the one an instrument reads.

It is the one an instrument reads divided by the paper.

The claim #

Object colour has two white points available and they answer different questions. Against the illuminant, a sheet of paper is a slightly grey, slightly coloured object like any other. Against the sheet, the paper is white by definition and every colour on it is reported as it would look on a sheet that was.

The first is called absolute colorimetry and the second media-relative, and the difference between them is the largest single source of confusion in colour management, because they are the same numbers under two normalisations and nothing in a measurement says which is in use.

Three substrates #

The model here carries three, each a stated reflectance rather than a measurement of a named stock: a level and a tilt across the band, chosen to land where the corresponding printing conditions do.

The absolute column of the magenta solid spans nearly eight lightness units across the three stocks. The media-relative column spans 0.8, and its a* varies by a third of a unit.

That is the whole mechanism. A press lays the same ink film in all three cases; what differs is the sheet it lies on, and dividing the sheet out removes almost all of it.

Two more views separate the part of each curve that belongs to the sheet from the part that belongs to the film.

What was computed, and how #

The demonstration is a single separation carried across two stocks.

Take 40 per cent cyan over 30 per cent magenta — an ordinary pale blue-grey, the kind of tint that fills the background of half the printed matter in the world. Compute its reflectance on coated stock and on newsprint through the same halftone model, and compare the two.

Reported absolutely, against the D50 illuminant: ΔE00 = 3.04. Reported media-relatively, each against its own substrate: ΔE00 = 0.13.

A factor of twenty-three, from a switch in the reporting convention, with no change to any ink, any coverage or any measurement.

The paper itself, coated against newsprint, is ΔE00 = 10.79 apart. Nobody is confused about that: newsprint is visibly greyer and yellower than a magazine cover, and no reporting convention hides it. What the convention decides is whether that difference is attributed to the paper or spread over every colour printed on it.

Which one is right #

Neither, and the pair of questions they answer is worth stating carefully, because a great deal of argument about proofing is two people answering different ones.

Media-relative asks: did the press lay down the ink correctly? It divides out the substrate, so it is the right question for process control, for comparing two runs on different paper lots, and for a standard that has to be met by shops using different stocks. Almost every printing specification is written this way, which is why an ISO aim value can be quoted at all.

Absolute asks: what colour will the sheet be? It keeps the substrate in, so it is the right question for a proof — a proof that is going to be signed as representing a newspaper page has to look like newsprint, which means reproducing the paper as the beige it is rather than as white.

The switch matters most at exactly the moment the two questions are confused: a proof made on a bright white inkjet stock in media-relative mode is a promise about the ink and says nothing about the sheet, and it will be held up against the printed job by somebody who was asking the other question.

The part media-relative cannot rescue #

Dividing by the substrate is a normalisation, not a repair, and it fails in two places that matter.

The ceiling is real. The lightest colour on newsprint is the newsprint, at L* 80.3, and no convention makes a highlight brighter than the paper it is printed on. A picture with important detail in the top ten lightness units has nowhere to put it, and media-relative reporting conceals that by rescaling the top of the range to 100.

The paper’s colour is not a constant multiplier. A substrate with a tilt across the band multiplies the blue end differently from the red, so a colour built from an ink that lives in the blue is not scaled the same way as one that lives in the red. That is why the media-relative magenta column above is not exactly identical between stocks — the residual 0.8 lightness units and 0.3 in a* is the part of the substrate that is a shape rather than a level.

And nothing here covers a fluorescent sheet. Most real printing stock contains optical brighteners, which absorb ultraviolet and emit in the blue, and a fluorescent sample has no reflectance curve at all — its apparent reflectance depends on how much ultraviolet the light contains. Two shops measuring the same brightened sheet under instruments with different ultraviolet content will disagree about the white point everything else is being reported against, and both will be right about what they measured. That is a whole failure mode below this essay, and it is the reason instrument standards specify a filter.

Four tints, two shops, one specification #

The practical form of the argument is a table. Four separations, printed on coated stock and on newsprint, reported both ways:

Absolutely, the two shops have produced four pairs of visibly different colours and no specification could hold both to the same number. Media-relatively, the worst disagreement over the set is 0.97 — inside the tolerance a paint contract would use.

The column also has a slope in it. Sorting the four tints by how much ink is on the sheet, and reading the absolute difference as a share of the paper’s own 10.79:

A tint’s absolute difference between two stocks is the paper’s difference, discounted by how much of the paper the ink has covered. A light tint is nine tenths of the way to being a measurement of the sheet; a heavy one is half. Nothing about that is a separate effect — it is the same multiplication seen through varying amounts of ink — but it says which parts of a page the choice of stock actually decides.

And the parts it decides are the parts a page is mostly made of. Body text sits on bare paper; a background tint is fifty or sixty per cent ink; a photograph’s highlights and skin tones are light. The heavy coverage where the substrate matters least is the smallest area on almost every printed sheet, which is why a job that proofs acceptably on the wrong paper still looks wrong: the disagreement is concentrated in the tints and the whites, which is where the eye takes its reference.

That is the whole reason the convention exists. It lets one document specify what both shops must do, on stocks that differ by ten ΔE00, without asking either of them to compensate for the other’s paper. What it costs is that the document then says nothing at all about what the reader will see, which is left to the choice of stock — a decision made by the buyer, usually on price.

What the sheet does to the gamut #

The substrate is the ceiling of the solid, so it sets the size of the whole thing:

Newsprint reaches 64 per cent of the coated volume — and the black end barely moves, because a full ink film absorbs almost everything whatever it is sitting on. The loss is at the top and it is a loss of lightness range, which then costs chroma everywhere, because a colour cannot be more saturated than the light available to it.

And the three rows are one row, which is worth extracting because it says how nearly a substrate is a pure scaling.

The lightness range each sheet allows is its paper minus its black — 92.33, 88.88 and 78.69 — and dividing each volume by the cube of its own range gives 0.5143, 0.5179 and 0.5285. Constant to 2.7 per cent across stocks whose volumes differ by 57 per cent.

$$V \;\approx\; 0.52\,\bigl(L^*_{\text{paper}} - L^*_{\text{black}}\bigr)^{3}$$

So a substrate scales the solid in all three dimensions at once, and by the same factor in each. That is not obvious in advance: the paper is a ceiling on lightness and there is no a priori reason for it to cost chroma in proportion. It does because chroma is bought by absorbing part of the light the sheet returns, so a sheet returning less light has less to spend in every direction, and the residual 2.7 per cent is the whole of what the substrate does that a single number cannot describe.

That residual is the same quantity as the 0.8 lightness units left in the media-relative magenta column, arriving as a volume rather than as a colour: the part of a paper that is a shape rather than a level is worth a few per cent, and everything else about it is a scale factor. Which is the strongest available defence of the media-relative convention, and also the exact size of what it throws away.

A paper choice is a gamut decision, made before any colour management is applied and usually without reference to it.

It is also a larger one than most of the decisions that do get made with reference to it. Newsprint against coated stock is a factor of 1.57 in volume; the difference between sRGB and Display P3, which an industry sells on, is 1.50 in CIELAB volume. The sheet a job is printed on moves the gamut by more than a generation of display standard, and it is chosen by a buyer weighing postage against paper cost, generally before anybody has opened a colour engine. The cube law above is what makes that comparison possible at all: without it, a paper is a lightness and a display standard is a set of primaries, and the two have no common unit.

Where this model stops #

The three substrates are constructed. A level and a linear tilt is enough to carry the argument and is not a measurement of a named paper; real stocks have structure, especially at the blue end where the brighteners are.

Backing matters and is not modelled. A sheet is measured over a black backing or a white one, and a thin sheet reads differently between them by more than the difference between two ink lots. The specifications say which, and shops get it wrong routinely.

Ink penetration is not modelled. An uncoated sheet absorbs ink into its fibres, so the film is thinner and less of it sits on top; that is a real difference between substrates that this model attributes entirely to the paper’s reflectance.

And no adaptation is applied here. The media-relative numbers divide by the substrate’s XYZ componentwise, which is a von Kries transform in the wrong space and is precisely what the ICC specification prescribes. A proper chromatic adaptation is a different arithmetic and gives slightly different answers, which is a known infelicity of the format rather than an oversight of this essay.

The sheet and the lamp are two normalisations, not one #

A last confusion worth separating, because the two divisions look alike and compose in a way that surprises people.

A printed colour is integrated against a light and then divided by a substrate, and the two are independent operations on different objects. Changing the lamp changes what every reflectance produces; changing the sheet changes what everything is reported against. A media-relative measurement is therefore still an illuminant-dependent quantity — dividing by the paper does not make the light go away, because the paper is not a neutral filter and the ink is not a neutral filter, and a ratio of two spectra integrated separately is not the integral of their ratio.

The practical consequence is that a media-relative aim value is quoted for a stated illuminant, and D50 is in the specification for exactly that reason. Two shops agreeing on media-relative numbers measured under different lights have agreed about nothing.

The generalisation #

Every reported colour is a ratio, and the denominator is a choice that the number does not carry.

The eye does this too, and does it better. Constancy is the default: a sheet of newsprint under a tungsten lamp looks white, a sheet of white paper in shadow looks white, and the visual system is dividing by an estimate of the illuminant in something like the way a colour engine divides by the substrate. The parallel is close enough to be useful and it breaks in the same place — an estimate of the denominator can be wrong, and when it is, everything downstream inherits the error with no indication that anything happened.

The practical form of the rule is short. Whenever a colour is quoted, the white point is half the quotation. A ΔE00 between two measurements taken against different denominators is not a colour difference at all; it is an arithmetic accident, and it is the most common way for a colour argument to be conducted for an hour before anybody notices.

What a specification says #

It is worth reading the shape of a real specification against all this, because the conventions are unusually explicit.

ISO 12647-2 gives aim values for solids and for tone value increase, and gives them for several substrate classes, because the same ink on a different class is a different measurement. The paper itself is specified separately, by class, with its own aim values and tolerances. The two are quoted against different white points and the standard says so.

The structure is not an accident of committee. It separates what the press is responsible for from what the buyer chose, and it is the same separation this essay’s arithmetic performs: the press is judged media-relatively, and the sheet is judged as an object.

Who found it, and when #

The distinction is old in the trade and recent in the arithmetic.

Printers have always known that a job proofed on one paper and run on another will not match, and the practice of proofing on the production stock predates any colorimetry at all. What the ICC did in 1993 was to make the choice explicit and storable: a profile carries a media white point tag, and the rendering intents include both a media-relative and an absolute colorimetric option, which differ in exactly the normalisation described here.

Making it explicit had a consequence nobody quite intended, which is that the switch is now available to people who do not know what it does. Absolute colorimetric rendering produces a tinted white on a proof, which looks like a fault; media-relative produces a proof that will not match the press if the stocks differ, which looks like nothing at all until the job runs.

The one that looks like a fault is the one that is telling the truth, which is a shape this site meets often enough to be worth naming.

Where the ladder goes next #

This rung sits on the halftone, because the substrate is a multiplier on every one of the Neugebauer primaries, and on the illuminant, which is the other half of every object-colour measurement.

Beside it, a profile is a table holds the numbers this essay is about the normalisation of — and the media white point is one of the tags in the file.

Above, the proof is a different object takes the absolute intent seriously and finds that reproducing the paper as a colour is necessary and still not sufficient, because the proof is being looked at in a different room from the print.