The eye's own glare hides most of the halo

ΔEITP, the colour difference written for high-dynamic-range television, takes a display’s absolute luminance and so has something to say about its shadows: how large a five-per-cent step in a dark grey is depends on how dark it really is. A guessed veil halves the error and a dimming panel has no single black found that it says it correctly only when told the floor under every pixel — the room’s light reflected off the screen plus the display’s own black — and that a local-dimming panel, whose backlight is set zone by zone, has no single floor to tell it. Two floors trade the screen for the halo tried declaring two: the dimmed zones’ own floor and the lit zones’ own floor. The pair read most of the screen exactly and misread the halo — the ring of zones round the bright content that the diffuser lights partly — by up to a factor of 2.7 in some grey step.

The halo is always next to the light, and the light is always in the viewer’s eye. A bright highlight scatters in the cornea, the lens and the retina, and adds a veil of luminance to everything near it in the visual field — the reason a star is invisible beside the moon and a room’s dark corner beside a window. The closing section of the two-floors essay asked whether that veil covers the halo. The prediction was that next to a full-brightness highlight the eye’s own glare is larger than the panel’s halo, so that the misreading is hidden there, and that the declaration’s real failures are confined to the halo’s outer edge, where the panel’s floor has fallen less than the eye’s glare has. If so, the cluster pair is the right summary after all, for a reason the display alone could not supply.

The eye hides the halo except behind sparse light #

Added under every grey step, the eye’s veil hides the cluster declaration’s whole misreading in six cases of nine: the window behind all three diffusers, and the small highlight and the subtitles behind the narrowest. For the small highlight behind the widest diffuser the misread share of the screen halves, from 16.0 per cent to 8.3; for the subtitles it falls from 13.9 per cent to 0.7 behind the middle diffuser and from 24.3 to 6.6 behind the widest. Every case’s worst misreading shrinks, from 0.44 to 1.00 in log to 0.45 at most. In the zone beside a full-brightness highlight the veil is ten to seventy times the halo’s extra floor, as predicted. But what survives is not the halo’s outer edge: for the subtitles every zone still misread lies in the halo’s inner half, and for the highlight they are split evenly. The viewing distance cancels exactly.

• The prediction is right about the light and wrong about the edge. Next to a bright source the eye’s veil swamps the panel’s halo; what it fails to swamp is set by how much light the source sends into the eye, not by distance from it.
• Sparse bright content is the failure case. A line of text drives the backlight to full as a solid white zone would, and puts a quarter of the light into the eye.
• The window is fully hidden. A large bright region veils its whole surroundings.
• Distance does not matter. A zone’s solid angle and the square of its angle from the source both fall as the inverse square of the distance.

In each pair of bars the upper is the two-floors essay’s result and the lower is the same declaration read with the eye’s veil under every step. Six lower bars are empty. The three that are not belong to the highlight behind the widest diffuser and the subtitles behind the two wider ones.

A glare law and a panel #

The panel is the two-floors essay’s, and before it the dimming essay’s panel with its zones made explicit: 32 by 18 dimming zones, a 1,000 cd/m² white at 3,000 to one, in a dark room whose own veil is a hundredth of a candela a square metre, each zone driven at the level its brightest content needs and never below one per cent, and a diffuser that spreads each zone’s light over its neighbours with a standard deviation of half a zone, one zone or two. The three pictures are a small highlight on black, a bright window filling a fifth of a dark room, and a line of subtitles on a dark frame. Each zone’s floor is the room’s veil plus the panel’s native black times the zone’s backlight, and the cluster declaration gives every zone whichever of the two clusters’ floors is nearer its own in ratio.

The eye’s veil is the Stiles–Holladay law, the oldest and plainest description of disability glare: a glare source that puts an illuminance E at the eye, at an angle θ degrees from where the viewer looks, adds a veiling luminance of ten times E over θ squared. It is an average over young eyes and grows with age, and below about a degree it is not the law the eye follows, so the angle is held at a degree or more. Each zone’s content is a glare source at the luminance the picture asks of it: for the highlight and the window, filling the zone; for the subtitles, a quarter of it, because text is thin strokes on a dark ground. The panel is a 65-inch set seen from 2.5 metres, each zone a little over a degree across, and again from 1.2 metres.

The declaration’s error is the two-floors essay’s: the worst log-ratio, over every grey level from 0.005 cd/m² to white, of the five-per-cent step’s ΔEITP read with the declared floor to the step read with the true one. With the eye, both floors carry the veil: the viewer’s eye adds it whatever the declaration says, so what the declaration misreads is the panel’s part of a floor that now also holds the eye’s. With the veil set to nothing the census is the two-floors essay’s to the last digit, which is checked.

Walking away from a highlight #

A zone next to the highlight receives a veil of 3.0 cd/m² from it — three hundred times the room’s own veil, and nine times the panel’s native black at full backlight. The halo there is 0.04 cd/m² behind the narrowest diffuser and 0.29 behind the widest. Two zones out the veil is 0.76 and three zones out 0.34, falling as the inverse square of the distance; the halo falls as a Gaussian, and behind the two narrower diffusers it has gone within two or three zones.

The veil lies above the halo everywhere, behind every diffuser. That is the prediction’s first half, and it holds with room to spare next to the light. But lying above is not enough. A declared floor misreads a step by more than ten per cent until the floor the eye adds is about ten times the gap between the declared floor and the true one; behind the widest diffuser, two to four zones out, the veil is only three or four times the halo, and those zones stay misread. The margin needed is set by ΔEITP’s steepness in the dark: a step at 0.005 cd/m² with a floor of 0.1 under it reads very differently from one with 0.35 under it, even when 0.34 of that is the eye’s.

Where the misreading survives #

For the small highlight behind the widest diffuser the survivors are a ring, not an edge: 24 of the 36 zones in the halo’s inner half and 24 of its 75 in the outer. The inner zones next to the highlight are hidden; the survivors are the zones two to four out, where the halo is still near its peak and the veil has already fallen by a factor of nine. The prediction pictured the halo falling slower than the veil only at its far edge. Behind a wide diffuser the halo falls slower than the veil almost from the start.

For the subtitles the survivors are all in the halo’s inner half, the rows just above and below the text, where the veil is 0.46 to 0.88 cd/m² — as large as the veil two zones from the highlight — and still not enough. The reason is the difference between how a panel dims and how an eye scatters. A dimming zone is driven at the level its brightest pixel needs, so a single line of white text sets its zone’s backlight to full exactly as a solid white patch would, and the diffuser spreads that full backlight into the halo. The eye’s veil is set by how much light the zone sends, which for thin strokes on a dark ground is a quarter of what a solid patch sends. The panel responds to the text’s peak and the eye to its average, and the halo is the panel’s.

That is the case a subtitled film puts on the screen at every line of dialogue, and the one a local-dimming panel is most criticised for: a bloom round white text on a dark frame. The two-floors essay’s cluster declaration misreads the bloom’s dark steps, and the viewer’s eye is not bright enough there to hide the misreading.

Which steps are still misread #

In the zone the eye hides least — just below the text, behind the widest diffuser — the panel’s floor is 0.11 cd/m², the declaration gives it the lit cluster’s 0.34, and the eye adds 0.46. Without the eye, every step below about 1.6 cd/m² is misread by more than ten per cent, the darkest by a factor of 2.2, all in one direction: the declared floor is too high, and ΔEITP reads the step as smaller than it is. With the eye, the darkest steps are misread by 0.26 in log — a factor of 1.3 — and the error falls below ten per cent by about 1.5 cd/m². The veil shrinks the misreading by two thirds and leaves it where the shadows the unit counts are the ones a room removes found ΔEITP’s growth with brightness concentrated: in the darkest greys.

The distance cancels #

The same census seen from 1.2 metres instead of 2.5 gives every zone the same veil to a part in a thousand. This is not a coincidence of the numbers. Halving the distance makes each zone subtend four times the solid angle, so a glare source puts four times the illuminance into the eye; and it doubles every angle, so the inverse-square law divides by four. The two cancel for every pair of zones as long as the angle stays above the degree where the law is held, and at both distances every zone is more than a degree across. A viewer can sit where they like: the eye’s veil on a panel is a property of the picture, not of the room.

The same law says what would change it. A younger eye scatters less and an older one more — the Stiles–Holladay constant is an average — and a lit room brings the units’ medians together found the viewer’s adaptation deciding how ΔEITP and CAM16-UCS divide a difference. Neither the eye’s age nor its adaptation enters here, and both would move the survivors.

What a display specification should take from this #

Declare the two clusters and add the eye for bright content. For a window, a bright sky, any large bright region, the viewer’s own glare hides the halo the cluster declaration misreads; the two-floor declaration is then as good as the backlight map for everything a viewer can see.

Do not rely on the eye for text or small points. The eye hides a halo in proportion to the light its source sends, and the panel’s halo grows with the light its brightest pixel asks for. Sparse bright content — text, a star field, a thin line — asks for full backlight and sends little light, and there the misreading survives. For those pictures the backlight map, zone by zone, is still the only declaration that works.

A tolerance written without the viewer’s eye is stricter than any viewer. A delivery tolerance in ΔEITP for high-dynamic-range content is checked against the display’s own floor, and near bright content that floor is not what the viewer’s retina receives. A tolerance has no light level found one colour difference meaning different things in a cinema and in sunlight because ΔE₀₀ has no argument for the room; ΔEITP has one for the display and none for the eye, and in the inner halo of a highlight the eye’s floor is the larger. A tolerance that allowed for it would pass shadow errors near bright content that nobody can see, and would still fail them near text, which is where they show. The units disagree in the dim is the reminder of how much of what the dark-adapted viewer sees the units already read differently; the eye’s glare is one more term the viewer supplies and the unit does not.

The diffuser’s width is the other half. Behind the narrowest diffuser the eye hides everything, even for text; the survivors appear only once the halo is wide enough to outlast the veil’s fall. Two floors trade the screen for the halo found the diffuser setting how many floors a declaration needs; it sets how much of that the eye forgives as well.

What this leaves out #

The glare law is an average. Stiles–Holladay describes young eyes looking just off a bright source; an older viewer’s veil is several times larger, and a viewer looking directly at the text rather than at the halo sees a different pattern of glare. The survivors would shrink for an older eye.

The content is stated. A highlight filling its zone, a window at eighty per cent, text covering a quarter of a zone. Real subtitles cover less, which would make the survivors worse, and a real highlight may be smaller than a zone, which would move the small-highlight case towards the subtitles.

The steps are grey. The census reads five-per-cent grey steps, as two units with a light level disagree about lightness and the essays after it did. Chromatic steps in the halo — a coloured subtitle, a coloured highlight — are read by ΔEITP’s other two terms, and the eye’s veil is itself coloured by the source.

Still open: whether a coloured source tints its own halo #

A white highlight veils its surroundings with white light. A coloured one — a red tail-light, a blue neon sign — scatters its own colour into the eye, and adds a coloured veil to the halo’s dark greys, pushing them towards its hue. The declared floors know nothing about the eye and so nothing about the tint.

The calculation is this census with the highlight and the subtitles coloured, the eye’s veil given the source’s chromaticity, and the declaration’s error read on chromatic steps as well as grey ones — ΔEITP’s full difference. The prediction is that a saturated source’s veil hides the halo’s lightness misreading as a white one does, but introduces a chromatic shift in the halo’s dark greys that the cluster declaration cannot represent at all, because it declares a luminance. If the shift exceeds a unit of ΔEITP in the halo’s inner zones, the declaration needs a chromaticity per cluster as well as a floor, and a panel specification needs the picture’s colours as well as its light.

A floor under a floor is a ratio #

The habit is about what it takes for one quantity to hide another.

The prediction reasoned that the eye’s veil hides the halo wherever it is larger. It is larger everywhere near a highlight, and it hides only where it is several times larger, because what a step’s reading depends on is the ratio of the floors under it, and adding a common term shrinks a ratio’s departure from one only in proportion.

The failure mode is to compare two contributions by which is bigger when what matters is how their difference compares to their sum. The test is to compute the quantity the reader cares about with both contributions in, rather than ranking them.