A soft proof is exact for one reader

Every stage of a delivery chain has something a colour engineer chose: a profile with a node count, a rendering intent, a viewing condition. A second conversion is not a repeat closed on the one stage that has none. The chain ends at a reader, and the reader has no profile, because the colour management that delivers the print was done for the standard observer and the reader is somebody else.

Exact for one, a colour difference or more for the rest #

A soft proof matched exactly for the standard observer is several colour differences wrong for a substantial part of any population, and more wrong the narrower the display’s primaries.

• On an OLED panel the median observer sees screen and print 2.05 colour differences apart, median over thirty printed patches, and the ninety-fifth percentile observer 5.45.
• On a wide-gamut LCD the figures are 1.81 and 4.80; on a laser projector 3.09 and 7.47.
• The most fragile patch is unprinted paper: 11.1 at the ninety-fifth percentile on the OLED and 16.7 on the laser projector — the white every proof is judged against.
• In the chain’s own unit the reader’s ninety-fifth percentile is 4.58, against 0.42 for the profile and 1.50 for the rendering intent, and 5.05 for the whole chain.

The match, made exact #

The match is constructed, not fitted, because the point is to remove every error except the one being measured.

Each display is modelled as three Gaussian emitters with stated centres and widths. Each printed patch is a spectral reflectance from a four-colour press model, lit by D50. For each patch the three emitter drives are solved so that the display’s light produces exactly the same three cone responses, for the reference observer, as the print does. That is three linear equations in three unknowns, with one solution, and the solved display matches the print for the reference observer to 1.7 × 10⁻¹³ colour differences — the arithmetic’s own rounding.

A proof that could not be matched at all, because it would need a negative drive, is left out rather than approximated. On the OLED panel and the laser projector every patch can be matched. On the wide-gamut LCD six of the thirty cannot, and a proof of a colour the screen cannot make is not a proof.

Two hundred readers #

The population is two hundred observers whose lens density, macular pigment density, cone optical density and pigment peak wavelengths are drawn from the distributions the literature reports. A gamut has a population and a brand colour for a population used it before, and every member adapts to D50 by their own route before a colour difference is taken.

Each member sees two stimuli: the display’s light and the print’s. For the reference observer the two are identical. For every other member they differ, because the display’s light is concentrated in three bands and the print’s is spread across the spectrum, and a member whose cones sit a few nanometres away from the reference’s integrates the two differently. This is observer metamerism in its most extreme form, because a three-band emitter and a broadband reflector are about as spectrally different as two stimuli with the same colour can be.

The patches that fail #

The medians hide which colours fail and by how much, and the ordering is not the one a proofing workflow is built around.

On the OLED panel the most fragile patch is unprinted paper, at 11.1 colour differences for the ninety-fifth percentile reader and 6.0 for the median one. Next come a light stone grey at 9.1, solid cyan with forty per cent magenta and yellow at 9.0, solid cyan at 8.6 and the three-ink overprint at 8.3. The most robust are the yellows: yellow with forty per cent cyan at 1.7, solid yellow at 1.8, yellow with a little magenta at 2.0.

The pattern has a reason. A broad, flat spectrum is the hardest thing for three narrow emitters to imitate for everybody at once, because the display has to build it from three bands with nothing in between, and every observer weights the gaps differently. Paper is the broadest and flattest spectrum in the set, and near-neutrals are close behind. A saturated yellow reflects a long smooth plateau from the green to the red, which three emitters can straddle similarly for every observer. So the whites and greys a proof is judged by — the paper simulation, the grey balance — are exactly where a soft proof is least trustworthy.

The robust end of the list says as much as the fragile end. Solid yellow reflects little below about 500 nanometres and most of the light above, and a display builds it almost entirely from its green and red emitters. Below 500 nanometres is where readers differ most: it is where the lens and the macular pigment absorb, and where the short-wavelength cones take their signal. What protects a yellow is that neither medium puts much light where readers’ eyes differ most, while paper puts a full share of its light there and the display has to answer it with one narrow blue band.

On the laser projector the ordering holds and every number grows: paper at 16.7, stone at 12.4, a fifty per cent black tint at 11.8. The most robust patch, a red overprint, is at 2.9. No patch on a laser proof is under a colour difference for the ninety-fifth percentile reader.

Narrower primaries, larger mismatch #

The three displays differ in several ways at once. A controlled comparison changes only one of them.

With the three emitters held at 465, 532 and 638 nanometres and their widths narrowed together, the ninety-fifth percentile reader’s mismatch rises from 3.6 at forty nanometres to 4.2 at thirty, 5.4 at twenty, 6.7 at twelve, 7.3 at six and 7.5 at two. The median reader’s rises from 1.5 to 3.1. The rise flattens below about ten nanometres, because once an emitter is much narrower than any cone’s sensitivity curve it behaves as a single wavelength and narrowing it further changes nothing.

That is the trade a narrow primary buys a disagreement found for a display’s own white, arriving at a proof. The same narrowness that lets a display reach more of the print’s gamut is what makes its match to the print more personal. A wider-gamut proofing display is a proofing display on which fewer readers agree with the proof.

The reader beside the chain #

The delivery chain’s stages were measured in one unit: the power-corrected CAM16-UCS distance in a viewing booth. The reader’s mismatch can be put in the same unit.

In that unit the median reader’s mismatch is 2.53 and the ninety-fifth percentile reader’s 4.58. The chain’s profile stage is 0.42, its separation 1.45, its rendering intent 1.50, its room 4.30, and the whole chain end to end 5.05. The median reader is larger than three of the four stages, and the ninety-fifth percentile reader is larger than every one of them.

The comparison is not quite like with like, and the difference is worth stating rather than hiding. The chain’s stages are errors between what was asked for and what was delivered, judged by the standard observer. The reader’s stage is an error between two things the standard observer calls identical, judged by somebody else. The first kind can be reduced by better engineering; the second cannot, by any stage that uses the standard observer.

A tolerance read as a share of readers #

A percentile becomes a pass rate as soon as a tolerance is attached to it.

On the OLED panel the median reader’s mismatch, median over the thirty patches, is 2.05. A soft proof accepted against a tolerance of two colour differences is therefore outside that tolerance for about half the population on a typical patch, and a tolerance of 5.45 — more than two and a half times as loose — still leaves one reader in twenty outside it on that patch. On the laser projector, where the median reader sits at 3.09, a tolerance of two is outside for most of the population on a typical patch. On paper white on the OLED panel it is outside for more than half the population, because the median reader alone is at 6.0.

The reference observer the match was solved for is not a typical reader either. It is built from average parameters, and no reader has exactly those. One match names the observer: a match is a statement about the observer it was made for, and the reader’s stage is what that statement costs everybody else.

The proof that is exact for everybody #

There is a kind of proof with no reader stage at all, and it identifies what the soft proof is missing.

A hard proof printed on the same inks and the same paper as the job is the same spectrum as the print. Two identical spectra give identical cone responses for every observer, so a hard proof of the same materials matches for every one of the two hundred readers exactly — the computed mismatch is zero. The whole of the reader’s stage belongs to the difference between a display’s spectrum and a print’s.

A hard proof on other materials sits between the two. An inkjet proof imitating a press print with different colorants has a different spectrum from the print, so it has a reader’s stage of its own. But its spectra are reflectances, broad and smooth like the print’s rather than three narrow bands, and the argument of the fragile patches runs in its favour: the more alike two spectra are in shape, the less room readers have to disagree about them. The reader’s stage is a property of how different the two spectra are, not of whether the proof is on a screen, and a soft proof on narrow emitters sits at the far end of that scale.

That is why the proof is a different object in two senses. It is judged in a different room, which an appearance model can account for. And it is a different spectrum, which no model can account for on behalf of a reader whose eyes are not the standard’s.

The instrument agrees with the proof #

A soft proof is usually checked by measuring the screen and the print and comparing the readings. The instrument reports through one fixed set of colour-matching functions, so the instrument is one observer exactly, and when that observer is the one the match was solved for, it measures the proof as perfect to the same fourteen decimal places.

The check has the same blind spot as the match, because it is the same three numbers computed by the same rule. The spectra would show the difference at once — three narrow bands on the screen against a broad plateau on the print — but a verification that reduces both to tristimulus values has discarded the reader’s stage before anybody reads the result. A proofing check that wanted to see it would compute the match for several observers rather than one, from spectra the instrument has already recorded.

What a proofing workflow can do #

Three things, in increasing order of cost.

Stop anchoring on paper white alone. A soft proof’s paper simulation is the patch most readers see differently from the print, so a proof approved by comparing whites is approved on the least stable colour. Approving on saturated mid-tones — which are the most stable — says more about whether the proof represents the job.

Prefer broader primaries for proofing. A proofing display with broad primaries covers less gamut and matches more readers. Where the job’s colours are inside the broad display’s gamut, the broad display is the better proof for the population that will look at it.

Or proof on the materials. A hard proof on the job’s own inks and paper has no reader’s stage at all, because it is the same spectrum as the print. It costs a print where a soft proof costs nothing, and for the patches at the top of the fragile list — paper, the near-neutrals, the grey balance — it is the only proof every reader agrees with.

And state the reader’s allowance. An approval on a soft proof is an approval by one reader. The population’s spread for a given display and print is computable before anybody approves anything, and a specification could carry it: matched for the standard observer; ninety-fifth percentile reader within 5.4. That turns an argument after delivery into a number agreed before it.

What was computed, and how #

The prints are spectral reflectances from a four-colour press model with trapping, dot gain and a Yule–Nielsen exponent, at thirty coverages: every combination of none, forty per cent and solid in cyan, magenta and yellow, a fifty per cent black tint, and two ordinary colours. Each is lit by D50.

Each display’s three emitters are Gaussian in wavelength. The drives are found by solving the three-by-three system that equates the display’s cone responses with the print’s for the reference member of the population. The population’s two hundred members are drawn with a fixed seed from the reported distributions of lens density, macular density, cone optical density and pigment peak wavelengths. Each member’s pair of readings is adapted to D65 by CAT16 from the member’s own view of D50 and compared in ΔE₀₀; the chain comparison takes the same pairs through CIECAM16 at a booth’s adapting luminance and uses the power-corrected CAM16-UCS distance.

Where the measurement stops #

The displays are idealised. Real display primaries are not Gaussian, a real OLED’s green is broader at its base than its width suggests, and a real laser projector adds speckle. The trend with width is structural; the numbers per display are illustrative.

The population varies the eye’s filters and pigments and nothing downstream of them. People also differ in how they adapt and in how they judge colour differences, and those differences add to the reader’s stage rather than replacing it.

And the comparison is between a screen and a print viewed under matched conditions. A real soft proof is also viewed in a different room from the print, which is a separate term and a larger one on most desks.

The habit #

The habit is about an exact match that is exact for one instrument.

A calibration, a colour match, a metameric pair: each is exact for the device that defines it and approximate for everything else, and the size of the approximation depends on how different the two stimuli are in the dimensions the device does not see. A match between two stimuli with very different spectra is the most fragile kind, because a device that sees three numbers sees none of those differences.

The move is to ask how spectrally different the two sides of a match are before trusting it for someone other than its reference observer. Paper against three narrow emitters is about as different as it gets.

The failure mode is to certify the match with the instrument that made it. A proof that measures perfectly has been checked by the one reader for whom it was built to be perfect.

Who noticed it first #

Observer metamerism between displays and prints is well known in cross-media colour reproduction, and it is one of the reasons the CIE’s 2006 physiological observer and later work on observer variability were developed. That narrow-primary displays worsen it is widely reported for laser projection.

That paper white is the most fragile patch in a soft proof, and how large the reader’s stage is against a delivery chain’s own budgeted stages in one unit, are computed here; the sources consulted here discuss the effect for display whites and saturated primaries rather than for a print’s patches.

Still open: what readers actually report #

The population is a model of eyes, not of judgements. A panel of observers comparing a soft proof with its print — on a narrow-primary and a broad-primary display, patch by patch — would say whether the ordering here, paper first and yellows last, is what people report, and whether the ninety-fifth percentile reader’s mismatch of five colour differences is visible as a failed proof or tolerated as a proof that is merely a little off.