Colour Science & Perception
what the eye settles, and what it cannot
Concept

Acceptability — where it appears

Whether a colour difference passes, which is a commercial judgement about a tolerance and a viewing arrangement rather than a measurement. Perceptibility is the other threshold and it is much tighter, so a difference can be plainly visible and commercially acceptable at the same time.

Named by 16 essays across 6 fields — each of them below, with the objects they name alongside it.

A box tolerance and a ΔE tolerance around the same colour. A slice through CIELAB at L* 50, with the ΔE2000 = 1 contour traced point by point and a ±1 component box drawn over it. The contour is 2.1 times longer in one direction than the other, and the box is square. Of every sample either rule accepts, the two disagree about 74% — accepted by one specification and rejected by the other, on the same measurement.

A tolerance is a shape

A total colour difference below one, or every component within one — the two sound like the same requirement stated twice. They are different shapes, they disagree about most of what either accepts, and which one a supplier is held to is worth money.

difference · Metric What separates the separations, and under which light. 11 separations of a single colour, differing only in how much of it is carried by black rather than by the three chromatic inks. Under D50 they agree to ΔE00 = 0.00 — the solver was asked for that and delivered it. Under illuminant A they spread to 6.75. They are metamers of one another, and the whole family is invisible to any instrument reading a single illuminant.

The lamp in the shop decides

Two packages printed to the same specification, verified under the same standard illuminant and passed, can differ by nearly seven colour differences on a shelf under a tungsten lamp. Nothing went wrong at either press. The specification named one light, the separations that satisfy it are metamers of one another, and the shop chose the second light.

applied · Delivery One tolerance decision, at four spectral distances. Every column is a pair of samples ΔE00 1.0 apart for the observer a colorimeter models — solved to that value by bisection, so the instrument would report the same number for all four. What differs is how far apart the two spectra are, which is achieved by adding a metameric black the reference observer cannot see. The bands are what two hundred people report: from 1.13 at the ninety-fifth percentile when the spectra are the same shape to 2.32 when they are not, and the worst case reaches 3.7. No specification records the quantity on the horizontal axis.

A tolerance is a probability

A colorimeter reports one number and a specification compares it with another, and both are computed for an observer who does not exist. Handed to two hundred people, the same pair at ΔE00 1.0 is read from 0.8 to 3.7 — and which of those two ranges applies depends on something no specification records.

difference · Metric The three constants a specification does not quote. ΔE2000 is defined with three parametric factors in it — kL, kC and kH — which the CIE leaves to the industry using the formula rather than fixing. Graphic arts uses ones throughout; the textile standard weighs lightness at half, which is kL = 2. Applied to 4000 pairs at a tolerance of 1, the two settings accept 46 and 75 per cent, and 29 per cent of pairs change verdict — a larger disagreement than any between the formulae themselves. The reference conditions the ones assume are diffuse illumination at 1000 lux, a mid-grey surround, samples abutting, subtending over four degrees, differing by under five units, with no visible texture.

Three constants nobody quotes

CIEDE2000 is defined with three parametric factors in it, the CIE leaves them to the industry using the formula, and the two settings in ordinary use differ by a factor of two in one of them. Twenty-nine per cent of acceptance decisions change between the two — a larger disagreement than any between the formulae themselves.

difference · Metric Which of two reproductions is better depends on which statistic is asked. A specification for a proof or a print run is written against a set and has to reduce the set to one number. Here are two candidates: the one with the lower mean has the higher ninety-fifth percentile, so the mean prefers A and the tail prefers B. Across 2000 pairs of candidates generated the same way, the two statistics disagree about the winner 30 per cent of the time. Both numbers are honest; only one of them is what somebody notices.

A mean is not a difference

A specification for a proof, a profile or a print run is written against a set of colours and has to reduce that set to one number. The mean and the ninety-fifth percentile disagree about which of two reproductions is better in thirty per cent of cases, and both numbers are honest.

difference · Metric A colour rendering index, computed for everybody instead of for one observer. Each bar spans what 120 eyes make of one lamp: the same reflectances, the same reference illuminant, the same arithmetic, different colour-matching functions. The mark is the standard observer's own answer, which is the number printed on the box. One lamp's spread is 3.8 points wide while the whole range the standard observer puts these lamps in is 1.8 — so a ranking quoted to a tenth of a point is a statement about one set of tables. Two of the marks fall outside the population's range entirely.

The index is one observer's opinion

A colour rendering index is printed to a tenth of a point and computed for a single set of colour-matching functions that no standard names as a choice. Scored by two hundred eyes instead, one lamp's spread is wider than the whole range the standard observer puts five lamps in — and two lamps the standard separates by four tenths of a point come out the other way round for every member of the population.

light · Light One tolerance decision, about pairs that agree less and less about the spectrum. Every point is a pair of samples that the reference observer reports as exactly ΔE00 1.0 apart — the same number, the same decision, the same line in the same specification. Along the axis is how far apart their two reflectances are. Up the side is the 95th percentile of what two hundred other eyes report. It runs from 1.13 to 2.32. The document records the horizontal line and not the axis it is plotted against.

A tolerance needs a second number

Two samples one colour difference apart can be read almost identically by everybody or two units apart by the worst-off twentieth, and which of those it is depends on how far apart their spectra are — a quantity every spectrophotometer has already measured and none of them prints. Adding it as a second field predicts the population three times better, and at the tolerances where it matters it is right about a third of the decisions the difference alone gets wrong.

difference · Metric A viewing booth is a lamp, and a lamp has an angle. The same sample at five positions across a booth's plane, with the lamp 55 centimetres above it. The curve is how far each position is from the middle, in the units the judgement is made in. It reaches ΔE00 2.40 against a tolerance of 1, while the illuminance uniformity — the quantity the standard actually bounds — never falls below 73 per cent and stays comfortably inside it. The flat trace is the same booth with a source whose converter is the same thickness in every direction: ΔE00 0e+0, exactly, by construction.

The booth is a luminaire

A standard viewing booth is specified by its light's chromaticity, its rendering and the uniformity of its illuminance across the sample plane. Illuminance is a photometric integral, so two positions can be inside the uniformity tolerance and lit by two different spectra — and a sample at the far corner of a compliant booth is ΔE00 2.4 from one in the middle, against a tolerance of one.

applied · Delivery A tolerance of one unit, re-measured under every light in the census. Every one of the 23 pairs behind this figure is at exactly ΔE00 1.000 under D65 by construction. Each bar is what those same pairs measure under another light, after the observer has adapted to it: the line is the median and the bar spans the pairs. A tolerance is written as a property of a pair and it is not one — the light multiplies both members, and the difference between two products is not the product of the difference. The widest row is a lens at twenty against a lens at seventy, spanning 0.81 to 1.57.

One unit in another room

Twenty-three pairs built at exactly ΔE00 1.000 under D65, re-measured under every change of light this site models with the observer adapted to each, come out anywhere between 0.64 and 1.57. A tolerance is written as a property of a pair and it is a property of a pair and a room.

difference · Metric Four departures from the model equation, each at an ordinary strength. What each of the four assumptions inside a colour integral costs, in ΔE₀₀, on a stated sample under a stated light. The wavelength index is a coated printing paper measured with and without the ultraviolet of D50; the range is the same paper integrated from 300 nanometres and from 380; the place index is a pigmented plastic through a four-millimetre radius; the direction index is an eggshell paint beside a window. The spread is a factor of 7.0. This is a ranking of four examples rather than of four departures — each of them can be made larger by choosing a more extreme sample, and the marble in the same collection of materials reaches 12.7 on the index that comes third here.

The departures are larger than the tolerance

A delivery tolerance is written around one ΔE₀₀ and every one of this round's four departures is above it on ordinary material. A specification that names an illuminant, an observer and a tolerance, and does not name a measurement condition, an aperture and a field, has written a number that two honest laboratories can miss each other on by more than the number itself.

difference · Metric The three cone absorptances at two settings of the age of the lens. Solid and dashed are the same construction at the two ends of twenty years old against seventy. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 25.5 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The observer has no age

Five of the six arguments in this round are spreads — a population differs about them and the mean is a reasonable summary. The lens is not. Everybody's lens yellows in the same direction at about the same rate, so a standard observer with no age is not an average over a population; it is a snapshot of one moment in every reader's life.

eye · Cones The arguments a standard observer does not have. Seven choices inside a set of colour-matching functions, each with the shape it takes and what it is worth in ΔE₀₀ on a red pigment under a 6500 K radiator. Six are measurements: a field size, an age, a macular density, a cone optical density, three peak wavelengths and a rod contribution. The seventh is not — a change of basis is a change of curves and not a change of observer, and its entry is exactly zero because the space an experiment measures is what an observer is. Printing that zero beside the others is the clearest statement of what the other six are measurements of.

An observer is a contract

Six departures, all above a delivery tolerance, none dominant, and no reader matching the standard on any of them. That would be a demolition if the standard observer were a description of an eye. It is not — it is an agreement about what a number means, and an agreement is not falsified by being unlike anybody.

limits · Limits Each departure over forty-two surfaces rather than one. The same six departures measured over a family of forty-two analytic reflectances — an absorption band of stated centre, width and depth — with the smallest, the median, the ninety-fifth percentile and the largest marked. Every one of them spans more than a factor of three, and the ranking between them is not stable across the family: what decides a departure's size is which sample it is asked about, because a departure is a pairing and the sample is one of the two factors. Quoting any single number for what an observer's age is worth is quoting a choice of example.

A tolerance with an observer in it

A delivery tolerance is written in ΔE₀₀ against the 1931 observer, and six departures of that observer combine to about three of the same units on an ordinary saturated sample. A one-unit tolerance is being asked to contain a three-unit uncertainty that nothing in its budget mentions.

difference · Metric Every departure under every light. Six departures across six lights, each cell the difference between two observers in ΔE₀₀, drawn as a bar whose length is the number. The rows are not multiples of one another: the lens is worst under tungsten and the pigment peaks are worst under a three-emitter LED, because a departure is a pairing and which light is being paired with decides it. The laser projector's row is empty, and that is not a fact about lasers — on this collection's five-nanometre grid a three-line spectrum is a one-line spectrum, and a single wavelength is a stimulus every observer agrees about exactly.

The booth and the eye disagree

A viewing booth is specified to simulate daylight, and daylight is the light under which observers disagree least. So a booth is the condition in which a specification is least likely to be tested against the thing that breaks it, and the shop it will be judged in roughly doubles the term.

applied · Delivery Each departure over forty-two surfaces rather than one. The same six departures measured over a family of forty-two analytic reflectances — an absorption band of stated centre, width and depth — with the smallest, the median, the ninety-fifth percentile and the largest marked. Every one of them spans more than a factor of three, and the ranking between them is not stable across the family: what decides a departure's size is which sample it is asked about, because a departure is a pairing and the sample is one of the two factors. Quoting any single number for what an observer's age is worth is quoting a choice of example.

A brand colour for a population

A brand colour is chosen once, specified in a number, and seen by everybody. The observer audit says two candidate colours with identical specifications can carry observer spreads differing by an order of magnitude, and that the spread is computable from an ink's spectrum at the moment the ink is chosen.

applied · Delivery How often the choice of correction changes a pair's grade. Eighteen metameric pairs walked to each of eleven reference mismatches, with the share whose index falls in a different band under the two corrections the standard allows. At an exact match the share is zero and must be: there is nothing for either correction to correct. It rises to 44 per cent at a reference mismatch of 2, which is the quality a dyehouse reaches rather than the quality a laboratory constructs. The banding is a five-step convention at 0.5, 1, 2 and 3, stated here rather than quoted, and how much the count depends on it is drawn separately.

The ambiguity is largest where the index is used

The metamerism index is defined for a pair that matches exactly under the reference light, no real pair does, and the two corrections the standard allows for the residual give different answers. Over eighteen pairs at eleven match qualities the gap is nearly a function of the mismatch alone — its middle half spans a factor of 1.4 at the mismatches a dyehouse reaches — so it could be tabulated. And it is largest exactly there: zero at a laboratory's match, and re-grading eight pairs in eighteen at a trade's.

matching · Gamut

Named alongside it

The objects these essays reach for when they reach for this one.

Quality controlSpecificationToleranceΔEIndividual variationObserver metamerismStandard observerCIEDE2000Measurement uncertaintyMetamerismColour managementMeasurement error

All concepts