A room sensor must read the lamp to a hundred kelvin

A display’s shadows sit on a floor made of two things: the panel’s own black, and the room’s light reflected off the screen. A dimming panel has no single black found ΔEITP — the colour difference built for high-dynamic-range television — reading a display’s shadows correctly only when it is told that floor. A warm room tints the black, not the halo then lit the room with a 2,700 K lamp and found a floor declared in grey leaving every zone of a dark picture tinted towards the lamp, by up to 17.7 ΔEITP units at a tenth of a candela on the screen. Declared in the room’s own colour at the room’s own level, the tint fell by more than a factor of ten, below a unit everywhere but on the widest diffuser.

Adapting to a warm room deepens the shadows’ tint asked what a viewer adapted to the room sees, and found the colour declaration still removing the tint for every viewer. So the repair is settled in principle: tell the colour engine the room’s colour as well as its level. Both essays declared the room exactly, as an input known from outside. A display that wants to make this declaration itself has to read the room from a sensor, and the question this essay asks is how good that sensor has to be.

Three things a sensor can get wrong are computed here, each on its own. It can read the lamp at the wrong colour temperature. It can read the right temperature at the wrong level. And it can report only a temperature for a lamp that does not sit on the Planckian locus, or place a Planckian lamp’s white where an LED’s would be; either way the declared white lands a little above or below the line of heated-body colours that a temperature names.

A hundred kelvin, a tenth of the level, a Duv of 0.003 #

In the warm-room census’s 2,700 K room putting a tenth of a candela on the screen, the moon picture on the middle diffuser, a floor declared from a temperature 14.1 mireds warmer than the lamp or 13.9 cooler — 99 K low or 105 K high — leaves the worst tint at one ΔEITP unit, where the exact declaration leaves 0.19. A level read 11.5 per cent low or 12.8 per cent high does the same, and a white 0.0031 to 0.0032 off the locus either side. The tolerance in temperature is symmetric in mireds to within a tenth at every room level and narrows with the room’s light: ±55 mireds at a hundredth of a candela, ±14 at a tenth, ±5 at one. The subtitle picture tolerates about ±26 mireds at a tenth of a candela and the bright window picture about ±85.

• The precision needed is that of a colour meter, not of a rough estimate. A hundred kelvin at 2,700 K is about four per cent of the temperature.
• Level and colour matter equally. A sensor that reads the colour well and the level to a quarter still tints the shadows by nearly two units.
• The brighter the room, the finer the sensor, because the room’s light is a larger share of the floor and every error in it is a larger share of the black.

Each curve is a V with its point at the true temperature, where the only tint left is the halo’s. The three rooms’ Vs are nested: the dimmest room’s arms reach one unit about 55 mireds out, the middle room’s about 14, the brightest room’s about 5 — and the brightest room’s V starts at 0.65, close to a unit already, because at one candela the halo’s own small misreading of the room’s level costs that much. The arms are nearly straight. Each mired of error costs the moon picture about 0.06 units at a tenth of a candela and about 0.12 at one.

Reading the axis in mireds is a choice, and the next figure is what justifies it. A mired is a million divided by the temperature. A step of a hundred kelvin is a large step of colour for a candle-warm lamp and a small one for a blue sky, and mireds correct for that, so that equal steps in mireds are close to equal steps in the lamp’s chromaticity across the range of room lighting.

Even in mireds, lopsided in kelvin #

In the dimmest room a reading 357 kelvin too warm and one 459 kelvin too cool tint the shadows equally, and those are +56 and −54 mireds. In kelvin the cooler side is wider by more than a quarter; in mireds the two agree to within a tenth, at every room level. At a tenth of a candela the asymmetry in kelvin shrinks to 99 against 105, small enough to state as a hundred kelvin either way; at one candela, 38 against 41.

That is the practical reason to specify a room sensor’s accuracy in mireds. A specification of “±200 K” means a different tolerance on a 2,200 K lamp than on a 4,000 K one, and for the warm lamps a living room actually uses it is looser on the cool side than it looks. A sensor good to ±14 mireds, at any lamp, is the sensor this census asks for at a tenth of a candela on the screen — and a tenth of a candela is a dim room with a lamp on, not a bright one.

The level counts as much as the colour #

A sensor that reads the colour perfectly and the level wrong declares a floor of the right colour and the wrong strength. The declared floor is then the panel’s black plus too much or too little of the room’s warm light, and the difference is warm light — a tint in the room’s colour, of a size set by the error. At a tenth of a candela the moon picture reaches one unit with the level read 11.5 per cent low or 12.8 per cent high, and reaches 1.9 units with the level read a quarter high. In the dimmest room the tolerance widens to about 27 per cent low and 31 high; in the brightest it tightens to 7 per cent low and 3 high, lopsided because the halo’s own error already sits on the high side there.

Laid beside the temperature, the level is the stricter requirement. A 12-per-cent error in level costs what a 14-mired error in colour costs, and a sensor’s level reading is the harder of the two to make right: it depends on how much of the room’s light reaches the screen and is reflected towards the viewer, which a sensor on the bezel facing the room does not see. The census’s room light is the light the screen reflects, and that is the number a declaration needs — the veil a guessed veil halves the error found a colour difference getting three times wrong in the darkest greys when it was left out.

A white off the locus #

A colour temperature names a point on the Planckian locus — the colours of heated bodies — and a lamp’s white need not sit there. Warm-white LEDs commonly sit a few thousandths above or below it in the CIE 1960 plane, the distance called Duv. A sensor that reports only a temperature, and a colour engine that declares the corresponding point on the locus, misplace any such lamp’s white by its Duv. At a tenth of a candela the moon picture reaches one unit with the declared white 0.0032 below the locus or 0.0031 above it; at one candela, at about 0.0012. In the dimmest room no Duv within the census’s ±0.006 reaches a unit.

That is a tighter tolerance than the temperature’s, measured the same way. Along the locus, the 14 mireds that reach a unit move the white 0.0048 in the 1960 plane; across it, 0.0031 does. The tint is half again as sensitive to an error towards green or magenta as to one towards warmer or cooler, so a sensor’s error budget is not a circle round the lamp’s white but an ellipse lying along the locus. The declaration needs the lamp’s chromaticity, two numbers, not its temperature, and a sensor’s report of a temperature alone discards half of what the floor needs whenever the lamp is not a heated body.

The darker the picture, the finer the sensor #

The moon picture is the census’s darkest — a bright disc on a nearly black sky — and the room’s light is nearly the whole floor across most of its screen. The subtitle picture has a bright strip at the bottom and dark above; the window picture is bright almost everywhere. At a tenth of a candela the moon tolerates ±14 mireds, the subtitles ±26 and the window ±85, and the window’s V stays under a unit for eighty mireds either way. Moved to one candela, every picture’s V steepens; moved to a hundredth, every one flattens, and the window’s never reaches a unit within the scan.

The ordering is the warm-room essay’s in another form. There, a grey declaration tinted every zone of the dark pictures and about half the window picture; here, a coloured declaration with an error in it tints the dark pictures’ shadows in proportion to how much of their black the room supplies. A display showing mostly bright content can live with a rough sensor — helped, in front of a real viewer, by the light a bright picture scatters inside the eye, which the eye’s own glare hides most of the halo found masking errors near the light. One showing a film’s night scenes in a dim room needs the fine one.

The diffuser barely matters, except in the one case where the halo has already spent the budget. On the moon picture’s widest diffuser — the property two floors trade the screen for the halo found deciding how many floors a panel needs — the exact declaration leaves a worst tint of 1.01 units — the halo’s luminance error weighted by the room’s colour, which the warm-room essay found as the residue a coloured declaration cannot remove — and no sensor, however good, brings it under a unit. Everywhere else the tolerance is a property of the picture: ±14 mireds for the moon on the two narrower diffusers, ±26 for the subtitles except on the widest (±18), ±85 for the window on all three.

What a display maker should take from this #

A declared room colour is only as good as the room sensor behind it, and the sensor this census asks for is a colour meter. To keep a dark film’s shadows within a ΔEITP unit in a warm room at a tenth of a candela, the display must know the light the screen reflects to within about 14 mireds in temperature, about 12 per cent in level, and about 0.003 in Duv — the lamp’s chromaticity, in other words, to a few thousandths, which is the precision of a calibrated colour meter rather than of a sensor that estimates a colour temperature. In a brighter room all three tighten by about a factor of three.

A coarse sensor is still worth having, because the grey declaration it replaces is far worse: 17.7 units in the moon picture at a tenth of a candela, against one unit for a sensor 14 mireds out and about four for one 60 mireds out. What a coarse sensor cannot do is make the tint vanish, and a display maker who quotes a declared room colour as the fix for warm-room shadows should quote the sensor’s accuracy beside it. The input nobody declared made the general case that every input a colour pipeline assumes should be stated; this is what stating it costs when the input has to be measured.

How the readings were computed #

The panel, pictures, diffusers and room are the warm-room census’s: a 1,000 cd/m² local-dimming panel of 32 × 18 zones, three pictures on three diffuser spreads, its two floors declared — the dimmed zones’ and the lit — and the eye’s veil from each picture’s bright content added to every zone. The room reflects the light of a 2,700 K Planckian radiator off the screen at 0.01, 0.1 or 1 cd/m².

A sensor reading is a declared room light: a Planckian radiator at another temperature, from 2,000 to 4,000 K; or the true temperature at a level from half to twice the truth; or the true temperature moved off the locus by a Duv between −0.006 and +0.006, perpendicular to the locus in the CIE 1960 plane. The declared floor in each zone is the panel’s declared black plus that light; the true floor is the panel’s actual black plus the true room light. The tint is the chroma part of ΔEITP between a grey on the declared floor and the same grey on the true one, the worst over every zone and over the census’s dark grey levels. Read exactly, every case’s worst tint is the warm-room census’s coloured declaration to a part in a billion. The tolerance is the reading, interpolated between the scan’s steps, at which the worst tint first reaches one unit on either side of the truth.

What this does not reach #

One error at a time. A real sensor gets the temperature, the level and the Duv wrong together, and its errors may cancel or add; the census prices each alone.

One lamp. Every room is lit by a 2,700 K radiator. A cooler lamp, or daylight through a window mixed with a lamp, puts the true floor elsewhere and may change how fast the tint grows with each kind of error.

The screen’s reflection. The level the census needs is the light the screen reflects, which depends on the screen’s coating and the geometry of lamp, screen and viewer; a sensor sees the light falling on the display, not what leaves it.

ΔEITP’s unit. The tolerance is set at one ΔEITP unit, the unit’s own nominal threshold. The essays on adaptation found a viewer’s own state changing what a unit looks like in the dark.

Still open: whether daylight in the room moves the tolerance #

A living room in the evening is often lit by a warm lamp and the last daylight from a window at once. The room’s light is then a mixture whose chromaticity sits between the two, usually off the Planckian locus, and a sensor’s temperature for it names a point the mixture does not occupy.

The calculation is this census with the room lit by the 2,700 K lamp and D65 daylight at shares of a quarter, a half and three quarters, the floor declared from the mixture’s correlated colour temperature on the locus, and from its true chromaticity. The prediction is that the declaration from the correlated temperature tints the moon picture beyond a unit at a tenth of a candela for every mixture, because a mixture of a warm lamp and daylight sits well above the locus — by more than the 0.003 the census allows — and that the declaration from the true chromaticity stays under a unit throughout. If the correlated temperature suffices, the locus error is smaller for real mixtures than for the off-locus lamps priced here, and a temperature-only sensor is enough for a room lit by daylight and a lamp. Lamp and daylight together sit below the locus makes that calculation.

A fix is specified by the accuracy of its input #

The habit here is about what is owed after a repair has been found.

The warm-room census found that declaring the room’s colour removes the tint, and stated it as a fix. It was a fix for a display that knows the room exactly, which no display does. The question that turns a finding into a specification is how wrong the input can be before the fix stops working, and the answer — fourteen mireds, twelve per cent, a Duv of 0.003 — is the part a display maker can build to.

The failure mode is to report that declaring an input repairs an error without reporting how precisely the input must be declared. The test is to perturb the declared input along each direction it can be wrong, find where the repair fails, and state that tolerance in units that mean the same thing across the input’s range — here mireds rather than kelvin, chromaticity rather than temperature.