Quality control — where it appears
Named by 57 essays across 8 fields — each of them below, with the objects they name alongside it.
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.
Where the formula is not smooth
A colour difference formula is a distance, and a distance ought to vary gently. CIEDE2000's does not everywhere — it carries a hue-rotation term with a hard edge in it, and the discontinuity sits where a great many industrial samples live.
A dot is larger than it was asked to be
Two quite different things make a printed midtone darker than its coverage says — ink spreading under pressure, and light scattering sideways inside the paper. Both bend the tone curve the same way and neither touches its ends, so the measurement every press is characterised by cannot say which happened. A patch that nobody measures can.
A profile is a table
An ICC profile does not contain a model of the device it describes. It contains a lattice of patches that were printed and measured, and everything between them is interpolation — which is exactly zero at every patch, so a profile checked against its own target reports perfection for ever.
The fourth ink is not for colour
Black is in every process set and it extends the gamut by more than a third — and at every lightness above about forty it extends the chroma boundary by exactly nothing. What it buys is depth at the bottom, a neutral that holds its hue when the press drifts, and a way to put a full-strength dark on a sheet that could not carry three inks' worth of it.
A black that is not black
The deepest colour a four-colour press can make is L* 2.4, and against its own paper that is a contrast of about 320 to 1 — less than a cheap display manages in a dark room. Everything a printed picture does in the shadows is done inside that range, and the two ways of fitting a picture into it destroy different things.
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.
The fifth ink buys a corner
Orange, green and violet are sold as the answer to a four-colour press's gamut, and each one adds seven to nine per cent of volume. All three together add 23 per cent — almost exactly the sum, with no interaction — and every bit of it lands in the region of the ink that was added, at lightnesses where that ink is dark.
The screen is not the room
A thousand-to-one display in an ordinary office is a hundred-and-thirty-seven-to-one display, and the signal value that means black comes out at the lightness of a dark grey card. Nothing is wrong with the panel. Light falls on the screen and comes back off it, and the two per cent it returns is added to every pixel — most of all to the ones with nothing else in them.
There is no D65 lamp
D65 is standardised by three numbers, and three numbers do not pin a spectrum. A source built to hit them exactly — matched to a part in a billion, with a third of the visible band nearly empty — separates pairs that D65 says are identical by up to eight and a half units of colour difference.
Five nanometres is a choice
Every integral here is taken in five-nanometre steps, and the interval has never had to be defended. Coarsening it to twenty costs daylight two hundredths of a colour difference and a fluorescent tube six and a half — and which way of coarsening is used decides a further factor of six.
A difference is not a distance
Two earlier essays here said that CIEDE2000 violates the triangle inequality and left it at that. Searching for the violation finds a detour half the length of the direct route, a smaller one inside a five-unit ball, and a second defect nobody mentions — ΔE94 is not even symmetric.
A difference has no size
A colour difference formula answers a question about two large patches seen side by side. Applied to a pattern, it reports fourteen units where the eye is left with less than one — and the ratio depends on nothing but how finely the difference is spread.
The model has no clock
An appearance model takes a stimulus and a situation and returns what it looks like. It does not take a time, and adaptation is not instantaneous — half a second after the light changes a judgement is three and a half CAM16-UCS units from the settled one, and a minute later it is still 1.3.
A lamp has a waveform
A lamp modulating a thousand times a second is a hundred times past the frequency at which flicker fuses, and it is plainly visible — as a dotted trail, during any glance across the room. The reason is not a new measurement; it is the spatial contrast sensitivity function, arriving from an unfamiliar direction.
White is a region
A lamp is not sold as a chromaticity. It is sold as 4000 K, and what that means is that its chromaticity fell inside a quadrangle — which two lamps can occupy at opposite corners, eleven ΔE00 apart. In a room with either of them, the same twelve surfaces differ by one unit.
Which of two is worse
Two colour-difference formulae disagree about which of two pairs is the larger difference in thirteen per cent of comparisons overall — and in forty-three per cent of comparisons among pairs sitting near a tolerance of one unit, which is where every acceptance decision is actually made.
A difference has no place
A colour difference formula answers a question about two patches somebody is looking straight at. Move the same pair ten degrees into the periphery and a third of it is left — and it has turned twenty-four degrees of hue, because the three channels give out at three different rates.
One match names the observer
A yellow at 589 nanometres set against a mixture of 545 and 670 is two equations in two unknowns. It has one solution for a normal observer, a solution somewhere else for an anomalous one, and no unique solution at all for a dichromat — whose two equations are one equation twice.
A catalogue is not a vocabulary
A colour order system is a regular lattice, because a person has to be able to find a page. Sorted by what its chips would be called, that lattice comes apart into piles differing by a factor of three — and a fifth of all one-step moves in it change the name.
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.
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.
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.
A lamp has a direction
A white LED is a blue die under a converter, and light leaving at an angle has travelled further through the converter than light leaving straight up. So the mixture is different in every direction, the beam is bluer in the middle than at its edge, and the number on the box is one direction's worth of a device that has no single colour.
Three ways to dim a lamp
"Dimmed to ten per cent" names three different colours. Switching the lamp on and off faster than anybody can see changes the chromaticity by nothing at all — exactly, to floating point. Reducing the current moves it a few units. Reducing the power to a filament moves it eighteen hundred kelvin down the Planckian locus, and stays on the locus exactly the whole way.
A lamp switched on is not the lamp measured
A luminaire takes about seven minutes to reach nine tenths of its working temperature, loses a quarter of its output on the way, and moves ΔE00 2.6 while it does. That is slower than every clock in the eye — so for the first minutes after a switch is thrown, both ends of the measurement are moving, and every appearance claim here has assumed one of them was still.
The room settles after the eye does
Four clocks run in a room and only three of them are in the observer. The slowest is the lamp, which takes four hundred seconds to reach nine tenths of its colour change — so a minute after the light goes on, when the eye is conventionally said to have settled, most of what is left is the lamp, and three quarters of that could not be adapted away by an observer of any speed.
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.
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.
Fitted to an eye nobody has
A camera profile's residual against the observer it was fitted to is under a unit, and that is the number everybody quotes. Against a person drawn from a population it is 3.35 at the ninety-fifth percentile — and a camera with no spectral error whatever, reporting the standard observer's tristimulus values exactly, would carry 3.47. The camera is not the problem.
The shutter samples the lamp
A lamp switched between two drive currents at a hundred hertz is one steady colour to a person and two spectra to a camera. A thousandth-of-a-second exposure catches whichever phase the shutter opened at — two and a third stops of exposure and five units of colour, decided by nothing but timing — and a rolling shutter writes the difference across the frame as bands.
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.
Measured with an aperture, seen with an eye
A spectrophotometer averages a halftone patch and reports one reflectance. An eye blurs it first and compresses afterwards, and the average of a concave function is below the function of the average — so a resolvable screen looks darker than it measures, by fourteen lightness units at a coarse ruling and by nothing at a fine one. The correction a press applies is the same size and has no viewing distance in it.
What a second model changed
Thirteen claims here, each computed with one model and recomputed with two. Ten of them move by half again or more. Three of them do not move at all in the ordinary sense — the first model's answer is exactly zero, not because it computed zero but because it has no variable for the quantity — and every one of those three is a join that supplied a state or a device rather than a spread.
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.
An instrument has a geometry
Every reflectance here arrives through a model with a bandpass, a sampling interval and no position at all. Real instruments say where they were standing, and the two standard answers disagree by ΔE00 8.35 on a dark gloss sample — a difference that adds rather than multiplies, and that no adaptation removes.
An instrument brings its own light
ISO 13655 names four measurement conditions and they are usually read as four degrees of care. They are not. They are four different quantities — on an unbrightened sheet all four agree to a rounding, and on a brightened one they are up to seven and a half units apart, with every instrument in calibration and every answer correct.
Whiteness is mostly the lamp
The CIE whiteness formula ranks white samples the way people do, which is what it was built for and is not in question. What is in question is what it is a measurement of — take the ultraviolet out of the instrument and 82 per cent of the scale collapses, because the part that separates a premium sheet from an ordinary one was contributed by the lamp.
A tolerance cannot cross a condition
If two measurement conditions disagree by seven units, the obvious repair is a correction matrix fitted between them. The best least-squares 3×3 over seventeen printed patches leaves 23 per cent of the disagreement and makes five patches worse than doing nothing — because the term it is trying to remove is proportional to how much paper is showing, and no linear map on three numbers can express that.
The brightener is being used up
The molecule that absorbs an ultraviolet photon occasionally does something other than re-emit it, and what it does is break. So a sheet's whiteness has a half-life, the fall is steepest at the start, and a specification quoting a whiteness figure without a date is quoting a property of a sheet that no longer exists.
A profile is a fit between its nodes
A printer profile is a table, exact at every patch that was printed and interpolated everywhere else — and everywhere else is where every job lives. Going from a hundred and thirty-five patches to three and a half thousand is twenty-seven times the work for eight times the accuracy, and the exponents say that is as good as it gets.
Which index to buy an instrument for
Four departures from the colour integral, ranked by what they cost and by what it would take to remove each one. The ranking by cost and the ranking by price are almost exactly reversed — the two largest are removed by specifying a lamp and by widening a table, and the two that need new hardware are the two smallest.
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.
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.
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.
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.
The instrument is one observer exactly
A spectrophotometer has no observer uncertainty. It computes through the 1931 tables to the last bit, reproducibly, forever — which is its whole value and is also why it cannot report the three colour differences of observer spread between itself and whoever is looking at the sample.
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.
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.
What one number accepts
A delivery tolerance is written as a single colour difference and it acts on three tristimulus values, so what it actually accepts is a closed surface. Measured over sixty-four colours in the sRGB cube, the volume inside that surface varies by a factor of a hundred thousand and its longest axis is between three and thirty times its shortest. The same contract, applied to a dark colour and a light one, is two different requirements.
A stated lightness is two requirements
A specification quotes an appearance to a stated precision — a lightness to a tenth of a unit, say — and the same precision everywhere. Inverted, a twentieth of a unit of lightness fixes the luminance to nine tenths of one per cent at the bottom of the scale and to a tenth of one per cent at the top, a factor of 9.3. Read in absolute luminance it is the other way round by a factor of 6.5, and both readings are true.
A tolerance has a grain
A colour tolerance pulled back into tristimulus values is a long thin shape, and across the whole sRGB cube its shortest axis points the same way, fifteen degrees off at the median — the direction in which X rises as Y falls, which is the direction of a*. So what one colour difference allows depends on which way a delivery drifts. An instrument's X filter may age 1.4 per cent before the tolerance is used up, its Z filter 5.1, and the light on the sample 9.3.
A press is charged for the direction it barely moves
A press run varies almost entirely along the direction a colour tolerance forgives. Split along the tolerance's own axes under four stated mixes of press variation, its tightest axis holds about one per cent of the sheet-to-sheet variation and pays a quarter to a third of the price — and on a blue overprint four fifths, for the balance between two inking units rather than the level of either.
The metamerism index has two corrections
The index for a metameric pair is defined for a pair that matches exactly under the reference light, and no real pair does. The standard's remedy is to correct the sample first, and it names two corrections — scale the tristimulus values, or add the difference. On six pairs matched to one colour difference, the two answers differ by a tenth to four tenths of an index unit; at two, by a whole one.
A profile interpolates light
A profile is exact at its patches and wrong between them, and how wrong has been measured twice. Which way it is wrong has not. At a nine-step lattice the mean signed lightness error between the nodes is +0.136 against a mean colour difference of 0.133 — the error is not a scatter but a bias, and it lightens. The repair costs nothing measured and is forbidden by how a profile is checked: let the table be wrong at its own patches.
The scale hangs from one measurement
Black point compensation is a straight line between two blacks, and the destination's is a measurement of one patch at the darkest place a spectrophotometer is ever asked to read. The lightness scale's slope is 903 units per unit of luminance factor there and 43 at the paper, so a thousandth of a reflectance is worth nine tenths of a lightness unit at the black and four hundredths at the white. That one number moves a mid grey by nearly a quarter of a delivery tolerance, and no specification names it.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
SpecificationToleranceΔEAcceptabilityCIEDE2000Measurement errorStandard observerIndividual variationObserver metamerismColour managementIlluminantMeasurement condition