A warm room tints the black, not the halo

A display’s shadows sit on a floor. Part of it is the display’s own black — light leaking through a liquid-crystal panel set to show nothing — and part is the room’s light reflected off the screen. A dimming panel has no single black found ΔEITP reading a display’s shadows correctly only when told that floor under every pixel, and found the two parts folding into one declared number exactly on a panel whose black does not change with the picture. A local-dimming panel’s black does change: each of its zones is backlit only as brightly as its content needs, and the diffuser spreads each zone’s light into a halo round any bright object. A declaration of two floors — the dimmed zones’ and the lit zones’ — misreads only that halo.

Two essays then asked what light outside the panel does to the halo. The eye’s own glare hides most of the halo added the light scattered inside the viewer’s eye from the picture’s bright content and found it hiding the halo’s misreading in six cases of nine. A coloured highlight tints the halo it cannot hide coloured that highlight and found its veil hiding the halo only in the cone signals it reached, and turning the declaration’s misread floor into a tint of up to fifteen ΔEITP.

Every one of those censuses put the room’s light on the screen at a hundredth of a candela and made it grey. A room lit by a 2,700 K lamp, the colour of an ordinary warm-white bulb, reflects that colour off the screen. The prediction was that a warm room hides the halo’s misreading in the long and middle cone signals as a grey room would, and leaves the short-wave part of every dark step exposed — so that a declaration made in grey misreads more of the screen in a warm room than in a grey one of the same brightness, and tints the halo’s dark greys towards blue by more than a unit. If it did, a declaration’s floor would need the room’s colour as well as its level.

The black is tinted, everywhere, towards the lamp #

With the panel’s two floors declared in grey, a 2,700 K room putting a tenth of a candela on the screen tints every one of the 576 zones of the moon and subtitle pictures by more than one ΔEITP, and at one candela every zone of every picture. The worst tint, always at the darkest grey the census reads, is 4.5, 17.7 and 38.4 ΔEITP in the moon picture as the room’s light rises tenfold twice. It points towards the lamp’s own colour, between the display’s red and its orange in ICtCp’s chroma plane, and opposite its blue. A grey step laid on the warm floor changes colour as well as lightness, which a grey declaration does not expect: in the moon picture the warm room leaves seventy-one to seventy-six per cent of the screen’s grey steps misread by more than ten per cent at a tenth of a candela, where a grey room of the same light leaves at most six. Declared in the room’s colour at the same levels, every case’s tint falls by more than a factor of ten, below one unit everywhere but on the widest diffuser, and the misreading returns to the grey room’s.

• The tint belongs to the black, not to the halo. A declaration made in grey has the floor’s colour wrong in every zone, whether or not its level is right.
• Its direction is the lamp’s. The prediction had it blue, reasoning from the short-wave signal the warm light lacks; the tint is the warm light itself.
• The misreading does grow, as predicted, by another mechanism. Grey added to a warm floor moves its colour towards grey, and that colour change is part of every dark step.
• The prediction’s conclusion stands. A declared floor needs the room’s colour, and with it the problem nearly vanishes.

Each group of three bars is one picture on one diffuser, its bars the three rooms. In the dimmest room, a hundredth of a candela — a dark living room — the moon picture’s screen is already ninety-two per cent tinted beyond a unit and the subtitles’ three per cent; the window picture, which is bright, nowhere. At a tenth of a candela, a dim room with a lamp on, every zone of the moon and subtitle pictures is tinted, and the window picture about half; at one candela, a lit room, all of every picture. The diffuser’s spread, which decided almost everything in the earlier censuses because it decides how wide the halo is, changes these bars by at most two zones in a hundred. That is the first sign the tint is not the halo’s.

Why the halo does not matter here #

The earlier tints came from the halo because the halo was the only place the declaration was wrong. A zone in the halo is backlit at some level between the dimmed and the lit, and a two-floor declaration gives it one of the two, so its declared floor’s luminance is wrong. Everywhere else the declared floor is exact. The tint was what that wrong luminance looked like through a coloured veil.

A declaration made in grey is wrong somewhere else as well. The true floor in a warm room is the panel’s own black, which is grey, plus the room’s light, which is not; the declared floor has the right luminance and no colour. In a dimmed zone of the moon picture, where the panel’s black has been dimmed to almost nothing, the room’s light is nearly the whole floor, and a declaration that calls it grey has the floor’s colour wrong by the whole difference between a 2,700 K white and daylight. That is true of every zone in which the room’s light is a large share of the floor — which, in a dark picture, is every zone. The halo’s luminance error is still there, but it is a small addition to an error the whole black now carries.

The darkest greys carry it #

The tint is a colour difference between two greys, each seen on a floor, and the floor matters most when the grey is darkest. In a warm room of a tenth of a candela, the darkest grey the census reads, 0.005 cd/m², is tinted by 17.6 ΔEITP in the moon picture’s darkest zone; the tint falls below one only once the grey itself reaches about 5 cd/m², fifty times the room’s light. In the dimmest room it falls below one at 0.28 cd/m²; in the brightest, at about 90. A display’s shadow detail — the greys below a few candelas that a picture uses for night, interiors and the bottom of every gradient — is exactly the range the tint covers.

That makes the tint a statement about what a colour engine thinks the shadows look like. An engine told that the floor is grey renders its darkest greys for a grey floor, and a viewer in a warm room sees them on a warm one: browner than intended, by a margin that is many times a just-noticeable difference wherever the room’s light is more than a small share of the floor.

Towards the lamp, not towards blue #

Every case’s worst tint points between 111 and 122 degrees in ICtCp’s chroma plane — between the display’s red at 90 and its orange at 124 — and more than 135 degrees from its blue. The prediction reasoned from what a warm light lacks: little short-wave signal, so the dark steps’ short-wave part left exposed, and a tint towards blue. What the census computes is the difference between the floor a viewer actually has and the one the engine assumed, and that difference is simply the warm light minus a grey of the same luminance — the lamp’s own colour.

The coloured-highlight essay’s tints pointed at the highlight’s colour for the same reason: a veil adds its own light. A room’s light is a veil whose colour is the lamp’s, and what it adds to the dark greys is that colour, in proportion to how much of the floor it is.

The room’s light, picture by picture #

How large the tint gets depends on how much of each zone’s floor is the room’s light, and that depends on the picture as well as the room. The moon picture, nearly all dark, reaches 4.5 ΔEITP in the dimmest room, 17.7 in the middle one and 38.4 in the brightest; the subtitles, a dark frame with a bright line, 1.3, 9.7 and 34.0; the window, a bright picture, 0.3, 2.9 and 19.7. The window starts lowest because its bright content scatters enough light inside the viewer’s eye to put a grey veil of at least 1.1 cd/m² over every zone — against the moon’s 0.006 in its darkest — and a grey veil dilutes the room’s colour in the floor. It rises fastest because the room’s light grows past that veil.

The pattern is the one the shadows the unit counts are the ones a room removes found for a grey room’s luminance: one candela of reflected light took a fifth of the difference ΔEITP gives a step at the bottom of a 1,000-candela display’s scale and nothing at the top. A warm room takes that fifth and adds a colour to what is left. And a display in a room is a smaller display found the room’s light shrinking what a display can show; in a warm room what is left is not only smaller but tinted.

The census sets the room’s light as known. A guessed veil halves the error found that a declared veil does useful work even when it is only guessed, by an amount the guess’s error sets; a guess at the room’s level that is right and at its colour that is grey would, on these numbers, leave the dark pictures’ shadows tinted by more than any error in the level a reasonable guess would make.

The misread steps #

The prediction’s middle claim was that a warm room leaves more of the screen’s grey steps misread than a grey room of the same brightness. In the dark pictures it does, by a wide margin, though not through the cone signals the prediction named.

In the moon picture, a warm room of a tenth of a candela leaves seventy-one to seventy-six per cent of the screen misread, where a grey room of the same light leaves none to six; at one candela the warm room leaves ninety-eight per cent and the grey room none. The subtitles behave the same way at one candela, eighty-three per cent against none. A grey room misreads less as it brightens — the earlier censuses’ finding that a room’s light hides the halo — and a warm room more.

The reason is that adding grey to a warm floor changes its colour as well as its lightness. A five-per-cent grey step at 0.005 cd/m², laid on a warm floor of a tenth of a candela, moves the colour a little from the lamp’s towards daylight’s as well as raising it, and ΔEITP counts both: the step is 0.060 units, against 0.046 for the same step on a grey floor — 31 per cent larger, with a chroma part of 0.039 beside an intensity part of 0.046. By 0.05 cd/m² the difference is twelve per cent, by 0.5 under one. A grey declaration expects every dark step to be a step in lightness alone, and in a warm room the dark steps are partly steps in colour, so the engine’s model of how far apart two shadow greys are is wrong by more than a tenth across most of a dark picture.

A lit room brings the units’ medians together found a room’s light doing much of what the eye’s veil does to a display’s differences; here the same light does something the eye’s grey veil cannot, because it is not grey.

Declaring the room’s colour #

The repair the prediction named is to declare the room’s colour along with its level: each floor as the panel’s grey black plus the room’s light at its own chromaticity. Declared that way, every case’s worst tint falls by more than a factor of ten — the moon’s from 38.4 to between 0.1 and 2.0 at one candela — and below one unit everywhere but on the widest diffuser, where what remains is the halo: zones whose declared floor has the wrong luminance, so that the room’s colour is weighted wrongly with it. The misread share returns to within six hundredths of the grey room’s in every case. The units disagree in the dim found the choice of colour difference itself mattering most in a dim display’s dark greys; the room’s colour is a larger effect in the same place. The warm room’s whole excess was the colour of a number the declaration already had.

For a display pipeline that declares a floor — an HDR mastering monitor’s ambient compensation, a television’s room-light sensor — that is the practical result. A sensor that reads the room’s illuminance and not its colour leaves the shadows tinted by many times a visible difference under a warm lamp, and the tint is largest in the darkest content, where viewers in dim rooms look most. A colour sensor fixes almost all of it.

How the rooms were set #

The panel, pictures and diffusers are the two-floor census’s: a 1,000 cd/m² local-dimming LCD of 32 by 18 zones at a native contrast of 3,000 to 1, showing a moon, a window and a line of subtitles, each zone’s backlight the largest of its neighbours’ drives spread by a Gaussian of half, one or two zones. The viewer’s eye veil is the eye-glare census’s, from a white highlight at living-room distance. The room’s light on the screen is 0.01, 0.1 or 1 cd/m², either at D65’s chromaticity or at a 2,700 K Planckian radiator’s. Each zone’s true floor is the panel’s native black at its backlight, grey, plus the room’s light; the declared floors are the darkest zone’s and the brightest zone’s luminances, each zone given the nearer in ratio, made either grey or as the panel’s black plus the room’s light. Through every floor the eye veil is added. The misreading is the census’s: the largest ratio, over grey levels from 0.005 cd/m² to the white, between a five-per-cent grey step’s ΔEITP on the declared floor and on the true one. The tint is the chroma part of ΔEITP between a grey on the declared floor and the same grey on the true one, worst over the same levels, and its direction the angle of that difference in the plane of half Ct and Cp. With a grey room at a hundredth of a candela the census reproduces the eye-glare census’s misread shares exactly.

What the census does not reach #

One warm lamp. A 2,700 K radiator is the commonest warm light; an LED lamp of the same correlated colour temperature has a different spectrum, and a screen does not reflect all wavelengths alike, so the floor’s colour would differ by a little from the lamp’s.

The viewer adapted to the display. A viewer in a warm room is partly adapted to the room, which would make the warm floor look less warm than ΔEITP computes. ΔEITP has no adaptation in it, and what the tint means to a viewer half-adapted to the lamp is a question for an appearance model.

A grey screen. A real screen’s reflection is not neutral; a matte surface scatters, a glossy one mirrors the lamp, and either can have a colour of its own.

Still open: what a viewer adapted to the warm room sees #

The tint is computed in ΔEITP, which takes absolute colour and no viewer state. A viewer sitting in a 2,700 K room for an evening is adapted partly to the room and partly to the screen, and adaptation to a warm white discounts warm light — the very light that makes up the floor.

The calculation is this census read through CIECAM16, with the viewer adapted to a mixture of the display’s D65 white and the room’s 2,700 K white at shares of nought, a third and two thirds, and the tint taken as the colourfulness and hue difference between a dark grey on the declared and the true floors. The prediction is that a viewer adapted a third of the way to the room sees under half the tint ΔEITP computes, and that at two thirds the darkest greys turn the other way, towards blue, because the declared grey floor then looks cool against an adaptation that expects warmth. If that holds, the colour a declaration should give the room’s light is not the lamp’s but the share of it the viewer has not adapted to — which a room sensor alone cannot know.

A wrong number in every cell is not a local error #

The habit here is about where to look for an error that a model makes.

The earlier censuses found the declaration wrong in the halo, because that was the only place its luminance was wrong, and asked every new question about the halo. A grey declaration in a warm room is wrong somewhere the earlier ones were not: in the colour of every floor, including the floors whose luminance is exact. The question of what a warm room does to the halo was the wrong question, because the warm room’s error is not confined to the halo at all.

The failure mode is to look for a new error where the old one lived. An assumption that is wrong everywhere — a grey floor in a coloured room — produces an error everywhere, and the place the earlier error was concentrated is only where the two add.