Metric — the series
-
How far apart are two colours
ΔE is meant to be a distance with the property that the same number means the same perceived difference everywhere. Three successive formulae have tried, they disagree with each other by more than a just-noticeable difference, and the disagreement decides real matching questions.
-
MacAdam measured it
In a perceptually uniform space the just-noticeable-difference contours would be circles of equal size. MacAdam's ellipses are neither, by a factor of eighty — and transforming them into each candidate space settles which spaces improved matters and by how much.
-
The midpoint is not half
Code 128 sits halfway along the sRGB scale and carries about a fifth of white's luminance. Half the luminance is code 188. Almost every gradient, blur and resize on the web gets this wrong, and the errors are visible once known.
-
A threshold is not a unit
MacAdam measured the smallest difference anyone could detect. ΔE2000 was fitted to how far apart plainly different colours look. The two are quoted interchangeably, and the contours they produce are not even the same shape.
-
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.
-
How many colours are there
Sixteen point seven million counts code values in a file format. Ten million distinguishable colours is a volume divided by the size of a just-noticeable difference — and the two difference formulae this site implements disagree about that size by a factor of nearly five.
-
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.
-
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.
-
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 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.
-
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.
-
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.
-
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 tint at the edge of a page
The last phase left this join open and guessed at its answer — how visible a halftone tint is away from the centre of gaze should be the product of two effects it had measured separately. It is not the product. At five degrees the guess is fifty-three times too generous, and by twenty it is out by eight orders of magnitude.
-
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.
-
A halftone is a luminance object
The eye's three spatial channels resolve a screen at 55, 15 and 10 cycles per degree, so at any ruling a press actually runs only one of them can see it at all. The corollary corrects a guess already published here — rotating a screen matters more to the chromatic channels, not less — but only at rulings so coarse that nobody prints there.
-
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.
-
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.
-
No diagram makes them circles
Every chromaticity diagram is a projective picture of the same measurement, so how badly MacAdam's ellipses fail to be circles can be minimised over the whole family of them. The best plane there is still leaves the average ellipse twice as long as it is wide — which makes the residual a fact about the eye rather than about anybody's choice of primaries.
-
A difference needs a basis too
A linear change of coordinates leaves every colour match exactly where it was. A cube root does not commute with one — so a lightness–chroma space, and every colour difference computed in it, is a property of the basis that happened to be in place before the nonlinearity. CIELAB's basis was chosen in 1931 for reasons that had nothing to do with difference.
-
A compression goes below the floor
Elsewhere this collection minimised the anisotropy of MacAdam's ellipses over every chromaticity diagram there is, found 2.02, and called the residual a property of the eye. It is a property of the eye seen through a projective picture. A cube root after the right basis reaches 1.61 on the same twenty-five ellipses.
-
The exponent was never the argument
A century of colour science has argued about whether the eye's response is a cube root, a square root or a logarithm. Minimise the anisotropy of MacAdam's ellipses over every basis, at each of eight exponents, and the floor moves by under three per cent between a cube root and a tenth root — while the basis moves it by a factor of two.
-
How wrong would the data have to be
Twenty-five ellipses measured on one observer in 1942 are the ruler every colour space here is judged against, and they have never been given an error. Rather than invent one, the question is turned round, and asks how large an error would have to be before the ranking changed.
-
An ellipse is not a ring of points
For eleven rounds of argument the distortion a colour space does to MacAdam's ellipses by mapping forty-eight points round each one and dividing the longest radius by the shortest. The minimum sits in a notch whose width is the reciprocal of the answer, so the method was accurate wherever the answer was small and short by a factor of two where it was large.
-
Three numbers for one ellipse
How far a colour space is from making a discrimination contour circular has three different answers — what a coarse sample of the boundary reports, what a converged sample of a contour of stated size reports, and what the map's own derivative says. They differ by up to a factor of two, they mean different things, and only one of them is what the question is asking.
-
Twenty-five is a sample of the diagram
A colour space's uniformity score is the mean of twenty-five numbers, and a mean of twenty-five numbers has a standard error those twenty-five numbers determine. Nothing has to be quoted to compute it, and three of the seven adjacent pairs in this collection's ranking survive it.
-
A lattice is a quadrature rule
Walking a set of test surfaces more finely does not converge on a better answer, because refining a lattice under a constraint changes which corners of the region get sampled and not only how densely. The lattice used here turns out to be a two per cent biased estimate of the integral it stands for.
-
Saturation is nearly everything
The set of test surfaces has three numbers describing it, and only one of them matters. How saturated the surfaces are carries an elasticity of about 0.7 on every result computed over them; how bright they are carries 0.10. A test chart's chroma range decides its answer and its lightness range does not.
-
The error on a gap is not the errors at its ends
Comparing two rows of a table by looking at whether their error bars overlap is the wrong comparison, and here it is wrong by a factor of up to 3.4. The same 125 surfaces score both rows, so the difference between them is quieter than either — and how much quieter is a measurement of how alike the two rows are.
-
The weighting is the disagreement
Five colour-difference formulae, three decades and two committees, and the single property that predicts which of them agree is whether a chroma difference gets divided by the chroma it was measured at. It sorts the menu exactly, it cuts across the distinction between a matching difference and an appearance one, and it halves the census's largest sensitivity.
-
Two departures that partly cancel
A glossy translucent sample has two of this round's four departures at once, and the expectation was that they would compound. They do the opposite. An aperture takes light away that went into the material and came back too far out; an interface returns light that never went in at all — so measuring either alone overstates what both together do, on every material tested.
-
A dial through a discrete menu
ΔE*94 is ΔE*ab with two weighting constants in it, and at zero those constants make every weight exactly one — so the two ends of the oldest disagreement in colour difference are joined by a line rather than separated by a choice. Walking it gives a derivative where a menu gives only a spread, and the derivative says the published weighting is on the far side of the interesting part.
-
The disagreement is at the near end
Every colour-difference formula on the menu was fitted to threshold data, so the expectation is that they agree about pairs an observer can only just tell apart and diverge on large differences. They do the opposite. Proportionally the disagreement is largest at the near end, by a factor of six for the appearance unit, and the cause is an exponent of 0.63.
-
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.
-
A neutral has no grid
A perfectly flat reflectance computes to exactly the same colour on every wavelength grid, through every slit, at every origin, and for every observer — not nearly, but to the last bit of a floating-point number. The condition is an identity rather than a limit, and what makes it one is the white point.
-
The normaliser carries the error too
A five-nanometre sum gets a red pigment's tristimulus value wrong by two hundredths of a per cent and its colour wrong by six hundredths of a unit. Those two numbers are not the same size because the grid appears twice in a colour — once in the sample and once in the white — and the two errors are largely the same error.
-
A departure is straight in the excitations
Walk a sample a quarter of the way from the light towards its own reflectance and exactly a quarter of the observer disagreement remains — in cone excitations, to two parts in a hundred. In ΔE₀₀ the same quarter leaves 0.347 where proportionality wants 0.428, and the discrepancy belongs entirely to the unit.
-
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.
-
A distance raised to a power has no length
CAM16-UCS's colour difference is its Euclidean distance raised to the power 0.63 and multiplied by 1.41. That is still a metric — the triangle inequality holds on every one of four thousand random triples — and it has no length. A grey ramp from black to white measures 25 units in one step, 137 in a hundred and 755 in ten thousand, growing as the number of steps to the power 0.37, and halving the size of a step triples the number of steps that fit.
-
Two yellow filters cancel on a slope
An older lens and a denser macular pigment both take blue out of the light, and read before adaptation they move a colour in nearly the same direction, eight degrees apart. Once each eye has adapted to its own white they point a median 156 degrees apart on smooth reflectances and together cost less than the lens alone. On surfaces with a narrow absorption band they still sit 26 degrees apart and add. What decides it is the width of the surface's own features.
-
Two filters cancel only in a bright enough room
An older lens and a denser macular pigment cancel each other once an eye has adapted — and that result belongs to the end of a dial nobody stands at. Read at the degree of adaptation CIECAM16 gives an ordinary room, the two barely cancel; in a living room they add, and in a cinema they cost six times what they cost under the sky. The room has to be about as bright as an office before the cancelling begins at all.
-
A tolerance has no light level
Twenty-three pairs built at exactly one colour difference stay at exactly one in every room, because the formula has no argument for the room. Read in the unit that does have one, the same pairs are 0.72 in a cinema, 1.04 in an office and 1.30 in direct sun — and inside any one room they spread by half again, so no single conversion between the two units exists at all.
-
A difference has no rate
A colour difference formula answers for two patches that are both there and stay. Alternate the same two colours and the difference is not scaled but taken apart: the colour half is gone by fifteen hertz and the lightness half is four times louder at eight, so twenty-three pairs the formula calls identical run over a factor of six at the rate the eye is best at, and are worth nothing at all above sixty.
-
Adaptation turns more pairs off than on
One pair of observer departures was followed across the degree of adaptation and found to cancel only in a bright enough room. The same calculation takes any two, and run over all fifteen pairs it says something the single pair does not: adaptation is a rotation rather than a mechanism for making departures oppose each other. Five pairs lose their cancellation as the eye adapts, three gain it, three keep it and four never have it — and the pair everybody quotes is one of the three it turns on.
-
Quadrature is exact in one room
An observer allowance is built by adding the departures in quadrature, which assumes they are mutually perpendicular. Over fifteen pairs their angles run from 18 degrees to 179 and hardly any are perpendicular. Measured against the real combination, quadrature is too small in a cinema by eight per cent and too large under the sky by fourteen, crossing at an adapting luminance of 22 candelas a square metre — and on individual surfaces it is out by a third in both directions in every room.
-
The room a surface needs is written in its band
Whether two yellow filters cancel on a surface depends on the room, and each surface has its own crossing — the degree of adaptation at which the shared yellowing falls to the size of what is left underneath. Those crossings run from 0.68 to 0.99, and where a surface's absorption band sits accounts for almost all of the spread while how much light it returns accounts for almost none. The reds need a room brighter than a graphic-arts viewing booth, which is brighter than any room a sample is judged in.
-
Two units with a light level disagree about lightness
ΔE₀₀ has no argument for how bright a display is. Two colour differences do: CAM16-UCS takes the room's adapting luminance, and ΔEITP — the difference defined for high-dynamic-range television — takes the stimulus's own absolute luminance. Twenty-three pairs at exactly one ΔE₀₀ grow in both as the display brightens, 2.1 times in ΔEITP and 1.5 in CAM16-UCS from a 5 to a 5,000 cd/m² white. But in ΔEITP the lightness part grows fastest, 2.7 times, and in CAM16-UCS it does not grow at all.
-
The units part by hue, not by light level
Two colour differences with a light level in them were compared on a display running from 5 to 5,000 cd/m², and a prediction was drawn from how each divided a difference between lightness and chroma. Built into pairs that differ in lightness alone and in chroma alone, both units say the same thing about light level: as a display brightens, chroma differences gain on lightness differences — ΔEITP by a tenth, CAM16-UCS by a quarter. Where they part is hue. The appearance model moves every colour's balance by the same factor; ΔEITP moves the violets, reds and cyan-blues the other way, and at nine of twelve base colours the two units disagree about the direction.
-
The shadows a unit counts are the ones a room removes
ΔEITP's growth with display brightness is largest in the dark greys, and dark greys are where a lit room's light reflected off the screen sits. One candela a square metre of veiling luminance removes 22 per cent of the difference the unit gives a step at the bottom of the scale on a 1,000-candela display and nothing measurable at the top. The same veil raises the growth the unit reports across display levels from a factor of six to a factor of seventeen, because it destroys a dim display's shadows first.
-
A lit room brings the units' medians together
As a display brightens, CAM16-UCS says chroma differences gain a quarter on lightness differences and ΔEITP says a tenth. All of the appearance model's movement comes from what the viewer is adapted to, and every calculation had the viewer adapted to the display alone. Give the room its share of the adaptation and the model's movement shrinks at every step: with a 20 cd/m² room supplying two thirds of it, the two units' medians fall by the same amount. What does not shrink is their disagreement about direction. The model still moves every colour the same way, ΔEITP still moves violets, reds and cyan-blues the other way, and in a lit room that becomes the whole of what separates them.
-
A guessed veil halves the error
A colour difference that takes a display's absolute luminance leaves out the light a room reflects off the screen, and on an ordinary display in an ordinary room that makes it wrong about the darkest greys by a factor of three. Giving the unit the veil as a declared argument fixes that when the veil is known. The worry was that it never would be — that a guessed argument is no better than none. It is better: any declared veil up to about twice the true one beats declaring none, and one middling guess for every room halves the worst error. What a guess cannot do is reach ten per cent; that needs the veil known within a sixth, which is what a luminance meter aimed at a black screen gives.
-
The hue disagreement is the quantiser's
As a display brightens, the appearance model shifts every colour's balance between lightness and chroma by one factor, and ΔEITP shifts violets towards lightness and yellow-greens towards chroma. The proposed source was the perceptual quantiser acting on three cone-like signals at unequal levels. Replacing the quantiser with a pure power law and changing nothing else removes the disagreement exactly: every colour moves by a factor of one. With the quantiser, how far a colour moves follows the spread of its three signals, and which way follows where its S signal sits — above the other two, towards lightness; below, towards chroma.
-
A dimming panel has no single black
ΔEITP reads a display's shadows correctly only when it is told the floor under every pixel, and that floor has two parts: the room's light reflected off the screen and the display's own black. They fold into one declared number exactly, and on a bright LCD the display's part is the one that matters — leaving it out misreads the deepest shadows seventeenfold. A local-dimming panel breaks the folding, because its black changes with the picture: in a dark room its floors vary twenty-six times across one scene, and no single declaration comes within a factor of two and a half. A lit room squeezes them back into one number.
-
Two floors trade the screen for the halo
A local-dimming panel in a dark room has no single black: its floor varies twenty-six times across a scene, and one declared floor misreads ΔEITP's grey steps by a factor of 2.6. The proposal was two floors, one for dimmed zones and one for lit ones, on the reasoning that a picture's zones cluster at the two ends. They do cluster, and two floors still do not work. Placed for the worst zone they halve the error and misread almost the whole screen a little; placed on the two clusters they read most of the screen exactly and misread the halo between as badly as one floor. How many floors a panel needs is set by its diffuser, not by the picture — and the only declaration that works everywhere is the backlight map.
-
At the gamut's edge the reds move as far as the violets
As a display brightens, ΔEITP shifts a saturated colour's balance between lightness and chroma by an amount set by its three quantised signals, and CAM16-UCS shifts every colour alike. The largest shifts found so far were a yellow-green at ×0.63 and a dark blue at ×1.62, both at the census's edge — and the blue turns out to be a colour no BT.2020 display can show. Walked out to the display's real boundary, the yellow-greens go lower, to ×0.54, and the dark blues never pass ×1.35, because BT.2020's blue edge is at low chroma. The top of the range goes to the reds and red-purples at ×1.6: at the edge the L-minus-M term grows to two thirds of the S term. Pairing the two extremes still needs a third of the observers the violet experiment needs.
-
A display's red takes the reds' move and leaves the pair
At BT.2020's edge ΔEITP moved a dark red's balance between lightness and chroma furthest of any colour, ×1.64 from a dim display to a bright one, and the reason offered was BT.2020's red primary, a line far out at 630 nanometres. Moving that primary in along the spectral locus confirms it: the reds fall faster than any other hue, to ×1.40 at 615 nanometres and ×1.25 at 605, and Display P3, whose red is a 615 nm line to three ten-thousandths, gives the reds the same. The top of the range goes to a red-purple, which rises as the red moves in because BT.2020 had pushed it past its own peak. And the forced-choice pair the experiment needs is the same two colours on every display.
-
The eye's own glare hides most of the halo
A local-dimming panel's black can be declared as two floors, and the pair misreads only the diffuser's halo round the bright content — by up to a factor of 2.7. The halo sits next to the light, and light scattered inside the viewer's eye puts a floor of its own there. Added under every grey step, the eye's veil hides the whole misreading in six of nine cases: every window, and the highlight and subtitles behind the narrowest diffuser. It leaves a sixth of the misreading's share for a small highlight behind the widest diffuser, and a quarter for subtitles, all of it in the halo's inner half — not its outer edge, as predicted. The panel dims by a zone's brightest pixel and the eye veils by its average, so a line of text lights the backlight fully and the eye a quarter. The viewing distance cancels.
-
A coloured highlight tints the halo it cannot hide
A local-dimming panel lights a zone for its brightest channel, so a pure red or blue highlight drives the backlight as hard as a white one and sends a fifth or a fourteenth of the light into the viewer's eye. The prediction was that a saturated highlight's veil would hide the halo's misread greys as a white one does, and add a colour. It hides far less. Behind the middle diffuser a white highlight hides the whole misreading; drawn red, blue, green or even yellow — nine tenths of white's luminance — it hides none of it. The yellow fails because a veil hides a grey step only in the cone signals it reaches, and yellow light reaches a fifth of the short-wave one. And where the veil does fall on a misread floor, it colours the error: the darkest greys are tinted by up to fifteen ΔEITP, and behind a red window, where the veil hides the lightness almost entirely, a fifth of the screen is tinted by more than a unit.
-
A warm room tints the black, not the halo
A local-dimming panel's black can be declared as two floors, the room's light reflected off the screen folded in, and the earlier censuses gave that light a hundredth of a candela, grey. Under a warm lamp it is not grey. The prediction was that a warm room would hide the halo's misreading in the long and middle cone signals, leave its short-wave part exposed, and tint the halo's dark greys towards blue. The tint is real and it is none of those things. With the floors declared in grey, a 2,700 K room putting a tenth of a candela on the screen tints every zone of a dark picture by more than one ΔEITP — up to 17.7 at the darkest grey — and the tint points towards the lamp's own orange, opposite blue. It is not the halo's: it is the whole black's, because a grey declaration has the floor's colour wrong everywhere. The prediction's conclusion holds by a different road. A grey step laid on a warm floor is partly a change of colour, so the warm room leaves seven tenths of the moon picture's grey steps misread where a grey room leaves none; and declaring the floors in the room's colour removes all of it but the halo's own.
-
Adapting to a warm room deepens the shadows' tint
A warm room's light reflected off a local-dimming screen tints the shadows of every dark picture when the screen's black is declared in grey — by up to 17.7 ΔEITP — and ΔEITP has no viewer in it. A viewer who has sat in a 2,700 K room all evening is adapted partly to the room, and adaptation to a warm white discounts warm light. The prediction was that a viewer adapted a third of the way to the room would see under half the tint, and one adapted two thirds of the way would see the darkest greys turn blue. Read through CIECAM16, the opposite happens in a dark picture. The tint the viewer sees grows at every step of adaptation: in the moon picture's darkest grey from 2.7 CAM16-UCS units for a viewer adapted to the display to 3.3, 3.9 and 4.4. The darkest greys never turn blue; they stay orange and fade. What turns blue is the mid-greys, whose light is the display's own and now looks cool. In the bright window picture the tint shrinks, and declaring the floor in the room's colour still removes it for every viewer.
-
A room sensor must read the lamp to a hundred kelvin
A local-dimming panel in a 2,700 K room leaves a dark picture's shadows tinted towards the lamp unless its black floor is declared in the room's colour, and declared exactly, that tint falls below a ΔEITP unit almost everywhere. A display learns its room from a sensor, and sensors are not exact. With the room putting a tenth of a candela on the screen, a temperature reading 14 mireds out — about a hundred kelvin, warmer or cooler — puts the tint back over a unit in the moon picture; so does a level read 12 per cent low or 13 per cent high, or a white placed a Duv of 0.003 off the locus. The tolerance is even in mireds and lopsided in kelvin, and it narrows to a third or a quarter for every tenfold rise in the room's light: ±54 mireds in a room of a hundredth of a candela, ±5 in a room of one. A bright picture forgives six times as much as a dark one. Declaring the room's colour solves the tint only for a display that can measure the room about as well as a colour meter does.
-
Lamp and daylight together sit below the locus
A display that declares its room's light can remove the tint a warm room leaves in a dark picture's shadows, if it reads the light to about fourteen mireds and a Duv of 0.003. An evening room is often lit by a lamp and the last of the daylight at once, and a sensor that reports a colour temperature names a point on the Planckian locus that such a mixture need not occupy. The prediction was that a lamp-and-daylight mixture sits well above the locus, so a declaration from its temperature tints the moon picture beyond a unit at a tenth of a candela for every mixture. The mixtures sit below the locus, at a Duv of −0.002 to −0.005, because a straight line between two points on a curve that bends upward lies under it. Declared from their temperature, they tint the shadows beyond a unit only when a quarter to a half of the light is daylight, up to 1.24 units. Daylight alone sits above the locus, at +0.003, and its temperature-only declaration tints by 0.67 at a tenth of a candela and 1.39 at one, where a grey declaration — the display's own white — tints nothing. Declared in its own chromaticity, every mixture's tint stays at the halo's.
-
A sensor calibrated on lamps cannot read an LED
A display that declares its room's light in the light's own chromaticity keeps a dark picture's shadows untinted, and the chromaticity has to come from a sensor. The prediction was that a small three-channel sensor calibrated on a 2,700 K and a 6,500 K lamp reads mixtures of a lamp and daylight within 0.001, because they are mixtures of its calibration lights, and misreads phosphor LEDs by 0.003 to 0.006. The mixtures nearly hold: misread by up to 0.0023, past 0.001 from half daylight, because daylight is not a 6,500 K lamp — and at a tenth of a candela no mixture tints the moon picture by a unit. The LEDs are three times worse than predicted. Every one of thirty white LEDs built onto the Planckian locus is misread by 0.007 to 0.017, and every one tints the shadows by 1.7 to 3.6 units. The divide is not lamp against daylight but smooth against spiky: every Planckian lamp and mixture under 0.0035, every LED and fluorescent tube over 0.007.
-
No calibration reads the lamps and the LEDs together
A three-channel ambient sensor pinned on two Planckian lamps reads every lamp and every lamp-and-daylight mixture well enough to keep a dark picture's shadows under a ΔEITP unit, and misreads every white LED badly enough to tint them by two to four. Its errors on the LEDs all point one way, and the prediction was that a matrix fitted in least squares to every light in a census would bring every LED under 0.004 while the lamps rose only towards 0.003. It does not. Fitted to the census, each light held out, the sensor's worst LED error falls from 0.017 to 0.0066 and its worst lamp error rises from 0.0033 to 0.0126; thirteen of forty-seven lights still pass a unit, among them the 2,700 K lamp the original calibration read exactly. A matrix exact on the lamp, daylight and one 4,000 K LED reads every mixture and every 4,000 K LED nearly perfectly and fails the 2,700 K LEDs, none read better than 0.0063. A fourth channel leaves six lights beyond a unit. Three broad channels have one matrix, and it can be right about one kind of spectrum.
-
Seven channels end the trade and lose the tube
A three-channel ambient sensor fitted to a room's forty-seven lights trades its error on LEDs against its error on lamps, and a fourth channel moved that trade without closing it. The prediction for more channels was that six, spread from 445 to 650 nm, bring every lamp, mixture and LED under a ΔEITP unit with the lamps within 0.0025 in the CIE 1960 plane, and that nothing short of eight reads the halophosphate tube. Six channels leave the 2,200 K lamp beyond a unit and the lamps at 0.0040; seven bring every lamp, mixture and LED in, with the LEDs and lamps both under 0.001, and the trade is gone — both families improve together. The halophosphate tube is read from six. But the triphosphor tube, held out of its own fit, is read only by three and four broad channels and lost by every finer sensor, its tint growing to thirty-three units at twelve channels. A sensor learns the lights it was fitted on, and a finer one extrapolates further from a light with no relative in the census.
-
Relatives, not twins, teach a sensor a tube
An ambient sensor of seven evenly spread channels, fitted to a room's forty-seven lights, reads every lamp, mixture and LED within a ΔEITP unit with each held out of its own fit, and loses the triphosphor tube, which nothing else in the census resembles — thirty-three units out at twelve channels. The prediction was that four triphosphor siblings, the same phosphors mixed for 3,000 to 5,000 K, would bring the tube within a unit at seven and eight channels and stop its rise past eight. They do both: the tube reads at 0.04 with seven channels and 0.06 with twelve, and seven or eight channels then read all fifty-one lights. A twin is not what does it. Three siblings, every one warmer than the tube and the nearest sixty mireds from it, read it within a unit at every count from five. What the siblings cost is paid at the finest sensors: at twelve channels the Planckian lamps' worst error rises fivefold, while from five to eight it moves by under a quarter.
-
Seven channels carry their noise as lightly as three
An ambient-light sensor of seven narrow channels, fitted to a room's forty-seven lights and four triphosphor siblings, reads every one of the fifty-one within a ΔEITP unit of a dim moon picture's tint, each light held out of its own fit. A fine sensor was expected to read chromaticity from small differences between neighbouring channels, with large weights of both signs that multiply every channel's noise. The prediction was that seven channels stay within a unit at a quarter of a per cent of channel noise and are no better than five at one per cent. The first half holds. The second fails completely: at one per cent seven channels still read every light's every one of a hundred readings within a unit, while five lose twenty-two lights. The premise was wrong. Seven channels' matrix barely cancels — its contributions sum with one sign — and per unit of noise it moves the reported chromaticity no more than three broad channels do.
-
A tilt moves every light's reading alike
An ambient-light sensor of seven narrow channels reads all fifty-one of a room's lights within a ΔEITP unit of a dim moon picture's tint and keeps them there through one per cent of independent noise on every channel, because its matrix barely cancels. A drift shared by the channels does not average out: as a photodiode warms its response tilts, rising at long wavelengths and falling at short. The prediction was that a tilt reaching ±1 per cent at the ends of the range leaves the seven-channel sensor within a unit for every light and that the twelve-channel sensor, whose Z row cancels, loses more lights than seven at every tilt. Seven channels hold to ±2 per cent, the worst light at 0.56. Twelve loses two lights at every tilt — the two it misreads with no tilt at all — and none to the tilt. Every sensor's reported chromaticity moves by about seven ten-thousandths in u′v′ per per cent of tilt, every light nearly the same way.
-
A dark offset pulls every light toward one colour
An ambient sensor of seven narrow channels reads all fifty-one of a room's lights within a ΔEITP unit of a dim picture's tint through independent noise and a gain tilt, because its matrix barely cancels. A dark current is different again: it adds the same signal to every channel whatever the light, and at the dim end of a room's lighting it is a larger share of a weak channel than of a strong one. The prediction was that an offset of a quarter of a per cent of the strongest channel costs the seven-channel sensor lights, while three broad channels move least. Seven channels hold every light to two per cent. Three move furthest. And the offset does something simpler than either sensor's design suggests: it draws every light's reading straight toward the one colour the sensor reports for equal signals in every channel.
-
A light's distance from the equal-signal colour sets when it goes
An uncorrected dark offset draws every light an ambient sensor reads straight toward the one colour its matrix reports for equal signals in every channel, and a seven-channel sensor holds the room's fifty-one lights within a ΔEITP unit to an offset of two per cent of each light's strongest channel. The prediction was that the first light goes near three per cent and is the warmest, that each light's crossing offset falls with its distance from the equal-signal colour, and that two readings a light predict its crossing within a fifth. The warmest goes first — the 2,200 K radiator — but at 2.1 per cent. The twelve 2,700 K LEDs go together, between 3.9 and 4.4. Crossing follows distance at r = −0.93, and a straight line through each light's tints at one and two per cent predicts its crossing within 8 per cent, always early. Below half a per cent nothing moves at all.