A dimming panel has no single black

A guessed veil halves the error gave ΔEITP an argument it lacks: the veil, the room’s light reflected off a screen, added to both members of every pair before the perceptual quantiser. Declared correctly it makes the unit exact about a display’s shadows; declared as nothing it misreads the darkest grey steps by a factor of three on an ordinary display in an ordinary room. A guess in the middle of the rooms halves the worst error, and a cheap meter reading removes it.

That essay ended with the floor’s other half. A display’s black is not zero: an LCD leaks a fixed share of its white through a closed pixel, and an OLED’s black is dark until the room’s light lands on it. Both the display’s black and the room’s veil lie under every pixel, and they scale differently — the first with the display’s white, the second with the room. The prediction was that they fold into one declared floor without loss, “because ΔEITP sees only the sum at each pixel.” The awkward case it named was a local-dimming panel, whose black under a dark part of the picture is far lower than beside a highlight: “the floor is not one number at all.” The question was how much that floor may vary across a scene before a single declaration does worse than none.

One number, when there is one #

For any panel whose black does not depend on the picture, declaring the display’s black and the room’s veil as one summed floor makes ΔEITP exact on every grey step. On a 1,000 cd/m² LCD at 1000:1 in a dark room, declaring the room’s veil and leaving out the display’s black misreads some step by a factor of seventeen; on an OLED in the same room it costs two per cent. A local-dimming LCD’s floor is many numbers: in a dark room it varies twenty-six times across one scene, and the best single declared floor still misreads by a factor of 2.6. A single floor keeps every step within ten per cent only while a scene’s floors vary by less than a factor of about 1.3 to 1.9 — which an office provides and a dark room does not.

• Folding is exact. ΔEITP cannot tell which part of a floor came from where, so the two parts should be declared as their sum.
• The display’s part dominates on a bright LCD. Its black at 1000:1 is a candela a square metre, a hundred times a dark room’s veil.
• Local dimming breaks one floor in the dark. A dimmed zone’s black and a zone beside a highlight differ by a factor of a hundred on the panel, and a dark room adds too little to both to close the gap.
• The room closes it. The veil adds the same candelas to every zone, and in an office that is enough to squeeze the panel’s floors within the third that one declaration tolerates.

Where the floor matters #

The veil census measured one-unit lightness steps from L* 2 upwards, relative to the display’s white. That is the right scale for a veil, which sits around a candela, and the wrong one for a display’s black. On a 1,000 cd/m² display L* 2 is 2.2 candelas; a high-dynamic-range picture puts detail far below that, and a display’s black lives down there too. So the steps here are placed by luminance rather than by lightness: grey pairs five per cent apart at every quarter decade from 0.005 cd/m² up to the display’s white, each read in ΔEITP with the floor added to both members.

Above ten candelas the three readings agree: a floor of a candela is nothing beside a grey of a hundred. Below one they part. With the true floor — the LCD’s black of a candela plus a hundredth from the room — a step at 0.1 cd/m² is barely visible to the unit, because it rides on a candela and five per cent of a tenth is a two-hundredth of what is there. Declared as nothing, the unit reads that step as if it were on a black display, where it is a clear difference. Declared as the veil alone, it reads it almost exactly as nothing does, because a hundredth of a candela is a hundredth of the true floor.

That is the first practical point, and it inverts the emphasis of the veil essay. On an LCD the display’s own black is usually the larger part of the floor. At 1000:1 a 100 cd/m² display leaks a tenth of a candela and a 1,000 cd/m² display a whole one: as much as an office’s veil, a hundred times a dark room’s. A black that is not black was the collection’s first look at a display’s floor; here it is priced in the unit that most needs it.

Three panels, three rooms #

For the LCD without dimming, the best floor is exact in every room, and declaring the veil alone is badly wrong in every room but the brightest: a worst log-error of 2.83 in a dark room, 1.69 in a dim one, 0.54 in an office. On a 100 cd/m² display the same pattern is smaller, 1.27, 0.45 and 0.07, because the display’s black is a tenth of a candela. For the OLED, the veil alone is as good as the whole floor, within two per cent in a dark room and nothing measurable in lighter ones: its black is two thousandths of a candela and contributes nothing a room’s veil does not swamp.

For the local-dimming LCD, no single floor is exact. In a dark room the best errs by 0.96, in a dim room by 0.49, in an office by 0.11. Those are the numbers the proposal’s awkward case produces, and they are large.

Why a dimming panel’s floor is many numbers #

A local-dimming LCD divides its backlight into zones and turns each down under dark parts of the picture. The model here is a panel of 3000:1 native contrast whose zones dim to one per cent. Its black in a dimmed zone is a hundredth of its black in a zone at full backlight — and a zone is at full backlight whenever it contains or borders a highlight. A single scene with a bright window and a dark corner has both. On a 1,000 cd/m² display that is a floor of 0.0033 cd/m² in the corner and 0.33 beside the window, before the room adds its share.

Each curve is a V, and its bottom is the best a single declaration can do. Declaring too low misreads the zones beside highlights; declaring too high misreads the dimmed ones. In a dark room the scene’s floors run from 0.013 to 0.34 cd/m², a factor of 26, and the best single floor, about 0.08, misreads the extremes by a factor of 2.6 either way. Declaring the lowest floor — what a meter reads on a black screen, where every zone is dimmed — or the highest gives exactly the same worst error, because a log-error is symmetric in the two directions; the best lies between, and halves it.

That also answers the proposal’s question in the form it was asked. How large can the floor’s variation be before a single declared floor does worse than none? It never does worse than none, if the declaration is sensible: declaring nothing is itself a floor, the lowest possible one, and the best declaration is always at least as good. The useful question is how large the variation can be before a single floor is good enough to trust.

How much variation one floor tolerates #

A single floor keeps every step within ten per cent only while the scene’s floors vary by less than a factor of 1.85 if the lowest floor is 0.005 cd/m², 1.40 if it is 0.05, and 1.31 if it is 0.5. The allowance tightens as the floor rises, because the steps that decide it are those at about the floor’s own level, and at a higher floor those steps are brighter and more of them are readable by the unit. It is the same on a 100 and a 1,000 cd/m² display, for the same reason: the steps near the floor decide the error and the display’s white never enters.

Those are small allowances. A scene whose floors differ by a half is at the edge of what one declared floor can cover to ten per cent; a local-dimming panel in the dark offers a factor of twenty-six.

The room squeezes the floors together #

The veil adds the same candelas to every zone, so it compresses the panel’s ratio towards one. With no veil the ratio is the panel’s own, a hundred. On a 1,000 cd/m² display a tenth of a candela of veil brings it to 4.2; a candela brings it to 1.33. It falls below one and a half — about what one floor tolerates — at a veil of 0.7 cd/m² on a 1,000 cd/m² display and 0.07 on a 100 cd/m² one. In an office the local-dimming panel’s floor is one number again, to within the tolerance, and the folding the proposal predicted works.

That makes the answer depend on the room in a way that is easy to state. The shadows the unit counts are the ones a room removes found that a lit room takes away the shadow differences ΔEITP counts most; here the same room takes away the local-dimming panel’s disagreement with itself. The dark room is where local dimming is worth having and where its black cannot be declared, and the lit room is where it can be declared and matters less.

Why the deep shadows are the ones to measure #

The veil census could stop at L* 2 because it was measuring a room, and a room’s veil of a candela swamps everything below that anyway. The display’s own black is different, and so is the content it is asked to show. How bright is white followed the move from encodings that describe a fraction of whatever a display can manage to one that names candelas, and the reason for the move was the shadows as much as the highlights: an encoding that names candelas can ask for a hundredth of one, and a high-dynamic-range picture routinely does. Those are the levels where a panel’s black decides whether the detail is there at all.

So the unit’s shadows are where this whole question lives. ΔEITP reads a five-per-cent step at a tenth of a candela as 0.93 on a black display — about the size the unit treats as just noticeable — and as 0.17 on a 1000:1 LCD at a thousand candelas, and at a hundredth of a candela as 0.38 against 0.018. Every result above is that one fact priced in different rooms and on different panels. The units part by hue, not by light level found the appearance model and ΔEITP disagreeing about how a display’s level acts on colour; here the unit and the display disagree about where the display’s own floor is, and only a declaration can settle it.

It also explains why a tolerance has no light level matters more for high-dynamic-range delivery than for ordinary displays. A relative unit has no floor to declare. ΔEITP has one and must be told it, and the telling is only as good as the floor’s constancy — which, on the panels most often used to show high-dynamic-range pictures, is exactly what local dimming removes.

What a tolerance should carry #

Declare the floor, not the veil. A display tolerance in ΔEITP needs the sum of the display’s black and the room’s veil, and for an LCD the display’s part is usually the larger. A delivery tolerance is three tolerances split a colour’s journey into a profile, a gamut mapping and a room; for a display judged in ΔEITP the room’s share is this floor, and on an LCD most of it is not the room’s at all. Both are measurable with one instrument: a luminance meter aimed at the screen showing black reads their sum directly, as a guessed veil halves the error proposed for the veil alone.

For a local-dimming panel, a black screen is the wrong thing to measure. A black screen dims every zone, so the meter reads the lowest floor the panel has — and a real scene’s floors run from there up to a hundred times higher. In a dark room no single number serves; a tolerance for such a panel should either be stated for the zones beside highlights and the dimmed zones separately, or stated with the room’s veil high enough to fold them, which in practice means an ordinary lit room.

And OLEDs can declare the veil alone. Their black is too small to matter beside any room’s light, and a veil measured with the display off is the whole floor.

How the floors were computed #

Grey steps are D65 greys at luminance Y and 1.05 Y, at every quarter decade from 0.005 cd/m² to the display’s white divided by 1.05, with a D65 floor added to both members and read in ΔEITP through BT.2020 RGB, ICtCp’s cone-like matrix and the SMPTE ST 2084 quantiser. The error of a declared floor against a true one is the largest absolute natural logarithm, over the steps, of the step read with the declared floor over the step read with the true one.

The panels: an LCD at 1000:1, black one thousandth of white; a local-dimming LCD at 3000:1 native contrast with zones dimming to one per cent, black between a hundredth of a three-thousandth of white and a three-thousandth of white; an OLED with a black of 0.0005 cd/m². A scene’s floors are nine values spaced geometrically between its lowest and highest, and the best single floor minimises the worst error over them by ternary search in the logarithm of the floor.

What this leaves out #

Blooming is not modelled as a shape. A real local-dimming panel’s floor rises smoothly from a dimmed zone towards a lit one, over a halo whose width depends on the panel’s diffuser. The census treats a scene as a set of floors and asks only for their range; a halo would add every intermediate floor, which the geometric spacing already includes.

The steps are greys. A coloured step riding on a floor loses chroma as well as lightness contrast, and the floor’s colour matters: a panel’s black and a room’s veil need not be the same colour as each other or as the display’s white. Both are D65 here.

And the error is ΔEITP’s. A declared floor makes the unit exact about what it would say through that floor; whether what it says through a floor matches what a viewer sees is the question the veil essay left open, and this one leaves it there too.

Still open: whether a dimming panel should declare two floors #

The census says a local-dimming panel in a dark room has a floor that varies twenty-six times, and that one declared floor cannot cover it. It does not say whether two would. A panel knows which of its zones are dimmed; a colour engine that knew the backlight map could apply the dimmed floor to one part of the picture and the lit floor to the other.

The calculation is this census with two declared floors, one for zones below a stated backlight level and one for zones above, and the question is where to split and how far each part’s floors still vary. The prediction is that two floors bring the dark-room error from a factor of 2.6 to within a quarter, because the floors in a scene cluster at the two ends of the backlight’s range — dimmed and full — with the halo between them a small share of the picture. If they do not cluster, the halo’s width, a property of the panel’s diffuser rather than of the picture, becomes the thing a tolerance has to state.

A folded number is only as good as its constancy #

The habit is about checking that a quantity is one number before folding it into one.

The display’s black and the room’s veil add, and ΔEITP sees only their sum, so they fold into one declared floor — exactly, and that part of the prediction held without qualification. What the folding assumed, silently, was that each part was itself one number across the picture. For every panel but one it is. For the local-dimming panel the display’s part varies a hundredfold with the content, and a sum of a constant and a variable is a variable. The room’s veil, which the folding was meant to combine with the black, turned out to be what rescues it, by being large enough to make the variable part small.

The failure mode is to fold two terms by their units and not by their behaviour. Two quantities in candelas a square metre add; whether their sum can be declared once depends on whether each is the same everywhere it is added.