A coloured highlight tints the halo it cannot hide

ΔEITP, the colour difference written for high-dynamic-range television, reads a display in absolute luminance — a tolerance has no light level is why that matters — and so has something to say about its shadows: how large a five-per-cent step in a dark grey looks depends on what lies under it. 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, and that a local-dimming panel — one that sets its backlight zone by zone — has no single floor to tell. Two floors trade the screen for the halo declared two, one for the dimmed zones and one for the lit ones, and found the pair exact over most of the screen and wrong in the diffuser’s halo, the ring of partly lit zones round the bright content, by up to a factor of 2.7 on some grey step.

The eye’s own glare hides most of the halo then put the viewer’s eye into the calculation. Light from a bright highlight scatters in the cornea and lens and lays a veil of luminance over everything near it in the visual field, and under that veil the halo’s misreading mostly disappears: in six cases of nine the eye hid it completely. What it failed to hide was the halo of sparse light — one small highlight behind a wide diffuser, or a line of subtitles — because a panel dims by a zone’s brightest pixel and the eye veils by its average light.

Every highlight in that census was white. A saturated one has the same mismatch between panel and eye, and has it in colour as well as in amount. A pure red highlight needs the red channel at full drive, so the panel lights its zone exactly as it would for white, while the eye receives only red’s share of the light, a fifth of white’s luminance. And the veil a red highlight lays over its surroundings is red. The essay on the eye’s glare closed on the prediction that a saturated source’s veil hides the halo’s lightness misreading as a white one does, but adds a chromatic shift to the halo’s dark greys that a declaration of luminance cannot represent; and that if the shift passes one ΔEITP in the halo’s inner zones, the declaration needs a chromaticity per cluster as well as a floor.

Colour costs the eye its cover, and the cover it keeps is tinted #

Drawn in a saturated colour, a highlight hides much less of the halo than in white, in every case. Behind the middle diffuser a small white highlight hides all of the misreading the panel makes; drawn yellow, red, green or blue it hides none of it. Behind the widest, where white halves the misread share of the screen, red and blue leave all of it and yellow and green leave most. The yellow is the surprise: its light carries 93 per cent of the white’s luminance and fails because it carries a fifth of the short-wave cone signal, and a veil hides a grey step only in the signals it reaches. Where a coloured veil falls on a misread floor it tints the grey: by more than one ΔEITP on up to 23 per cent of the screen, by as much as fifteen at the darkest grey, and behind a red window — where the veil hides the lightness error almost everywhere — on a fifth of the screen.

• The prediction is wrong about the lightness. A saturated highlight’s veil does not hide the halo as a white one does; for a small source it hides none of it.
• It is right about the colour, and by more than it asked for. The tint passes one ΔEITP in every case the panel misreads but one, and passes ten.
• The tint is the floor’s error, coloured. In a zone whose declared floor is right, no veil of any colour tints anything; so what the declaration needs is not a chromaticity but a floor it does not have.

The picture is the window scene the earlier census found wholly hidden, now drawn red. The dark zones round the window are its halo, and nearly all of them are pale — tinted but not misread in lightness. The eye’s veil still does most of the work it did in white: it lifts the floor under the halo’s dark greys far above the panel’s error, so a five-per-cent step reads nearly the same whichever floor is declared. What it cannot do is lift that floor in grey. It lifts it in red, and a grey laid over a red veil is a slightly different colour depending on how much grey the panel really put there.

Why a saturated highlight hides so little #

The census is the earlier one’s: a 65-inch, 1,000 cd/m² local-dimming panel of 32 by 18 zones at 3,000:1 in a dark room, seen from two and a half metres; three pictures — a small highlight on black, a bright window filling a fifth of a dark room, a line of subtitles on a dark frame — behind diffusers of three widths; the Stiles–Holladay glare law putting a veil under every zone from every other zone’s light. The one change is that the pictures’ lit content is drawn in one of five BT.709 colours at full drive, while their unlit content — the window’s room, the subtitles’ frame — stays grey. A local-dimming panel lights a zone for the largest of its three channels, so the backlight, the floors and the two-floor declaration are the white picture’s in every colour. Only the light reaching the eye changes.

The first cost is plain arithmetic. A red highlight sends 21 per cent of the white’s luminance into the eye and a blue one 7 per cent, while forcing the backlight just as high. The veil next to a small red highlight is therefore a fifth of what it was, and the halo’s extra floor, which the white veil beat by ten to seventy times, is no longer beaten everywhere. Behind the middle diffuser the small highlight’s halo is misread on 3.5 per cent of the screen by the panel alone; through a white highlight’s veil on none; through a red, blue, green or yellow highlight’s on 3.5 per cent — all of it. Behind the widest diffuser white leaves 8.3 per cent of the panel’s 16.0, and red and blue leave the whole 16.0.

The subtitles tell the same story more gently, because the unlit frame round them is grey and veils a little in any colour. Behind the middle diffuser white subtitles leave 0.7 per cent of the screen misread; yellow and green leave 6.6 and red and blue 9.4, against the panel’s own 13.9. Behind the widest, white leaves 6.6 per cent and every colour between 12.5 and 13.5. The window is the robust case: a large bright region veils its surroundings heavily even at a fraction of its white luminance, and in yellow and green it still hides every misread zone. Red and blue behind the widest diffuser leave 4.3 and 2.6 per cent.

A yellow veil misses the blue #

The yellow does not fit the arithmetic. It carries 93 per cent of the white’s luminance, and yet behind the middle diffuser it hides none of the small highlight’s halo — no more than the red, which carries a fifth as much — and behind the widest it leaves 13.9 per cent where white leaves 8.3.

ICtCp does not see luminance. It sees three cone-like signals — long, middle and short-wave — each compressed by the same perceptual quantiser, and a colour difference is a distance between the three compressed signals. The hue disagreement is the quantiser’s traced one of the metric’s oddities to that compression acting on each signal separately; here the same separateness decides what a veil can hide. A veil hides a grey step by raising the signals the step is made of, so that the step becomes a small change on a large signal and the quantiser shrinks it. A grey step changes all three signals, and a veil hides it only in the signals it raises. Yellow light is red and green light together and carries almost none of the short wavelengths: it raises the long and middle signals nine tenths as far as white would and the short-wave signal a fifth as far. On a yellow veil, the grey step’s long and middle parts are hidden and its short-wave part is not. The step is no longer grey as the quantiser sees it — it is a step towards blue — and the misread floor misreads that step’s size almost as badly as it did with no veil at all. In ICtCp’s intensity channel alone, which is built from the long and middle signals, the yellow veil hides the misreading almost exactly as the white one does.

The picture shows that no coloured highlight escapes this. Red raises the long signal three tenths as far as white and the short a thirtieth; green raises the middle signal three quarters as far and the short a sixth; blue raises the short signal eight tenths as far and the other two a tenth. Every saturated colour leaves at least one of the three signals almost unveiled, and the grey step leaks through that one. The earlier census’s rule — the eye hides the halo in proportion to the light it receives — was a rule about white light. For coloured light it becomes a rule about the least-veiled cone signal.

The tint is the floor’s error, seen through a colour #

A declared floor that is wrong in a halo zone misreads the size of a grey step there. It also misstates the grey itself: the panel puts a certain luminance under the pixel, the declaration assumes a different one, and a colour calculation made on the declaration predicts a darker or lighter grey than the viewer gets. Through a white veil that difference is a difference in lightness only, because every mixture of grey and white light is grey. Through a coloured veil it is not. A grey laid over a red veil looks slightly red, and how red depends on how much grey there is: more grey dilutes the veil’s colour, less grey leaves it stronger. A floor declared too low predicts a grey more strongly tinted by the veil than the one the viewer sees. The chroma part of ΔEITP between the two is the tint.

In every case the panel misreads, except the window behind the narrowest diffuser, every coloured highlight tints some zone’s grey by more than one ΔEITP. Behind the widest diffuser red subtitles tint 22.6 per cent of the screen, a red or blue window 18.9 and 18.1, a red or blue small highlight 16.7. The worst single tint is the small red highlight’s behind the middle diffuser, 15.2 ΔEITP in the zone diagonally beside it; the blue reaches 10.6 in the same zone, the green 7.0 and the yellow 6.1. In white nothing is tinted anywhere, because a grey on a white veil is grey whatever the floor.

The window is where the tint and the lightness error part company most clearly. Drawn yellow or green, the window behind the widest diffuser leaves no zone misread in lightness by more than ten per cent — the veil still hides the step sizes — and tints 10.2 and 13.2 per cent of the screen. Red and blue tint nearly a fifth while misreading only 4.3 and 2.6 per cent. The eye’s veil hides the lightness error by the same mechanism that makes the colour error visible: it lays a large signal over the dark greys, which shrinks every step, and it lays a coloured signal, which turns the grey’s amount into a hue.

It is worth checking that the tint really is the floor’s error and not merely the veil’s own colour — which would tint every dark grey on the screen, correctly declared or not, and which no declaration about the panel could be blamed for. It is not. In every zone whose cluster’s floor is its true floor, the tint is zero to the last digit in every colour, because the calculation and the viewer then add the same grey to the same veil. The tint appears only where the declaration is wrong, and in proportion to how wrong it is.

The darkest greys carry it #

In every tinted zone of every case and colour, the tint is worst at the darkest grey the display is read at, 0.005 cd/m². There the declared and true floors differ by a large fraction of the grey itself, and the grey is a small fraction of the veil, so the balance between the two — which is what sets the mixture’s hue — moves most. In the worst zone the tint is 15.2 for red at 0.005 cd/m², 13.3 at 0.05, 5.1 at half a candela and 0.28 at five. The other colours fall alongside it, and by five candelas every one is about a quarter of a unit.

That profile needs the caveat the earlier essays on this panel attached to their own dark steps, and it matters more for a tint than for a lightness step. At a hundredth of a candela per square metre the eye is well into mesopic vision, where rods contribute and cone colour signals weaken — colour goes first in the dark counted how much sooner a chromatic difference runs out than a lightness one — and ΔEITP’s chroma terms were fitted to cone thresholds at photopic levels. The units disagree in the dim found two light-level-aware colour differences parting company exactly there. The tints at the very darkest steps are what ΔEITP computes, not what a viewer would report, and a viewer in a dark room would likely see much less colour there than fifteen units suggests. The finding does not rest on them. At half a candela — dim but photopic — the worst zone’s tint is between 2.8 and 5.1 in every colour, well past one.

What a declaration would need #

The prediction drew a policy from the tint: a declaration that exceeds a unit of chromatic error needs a chromaticity per cluster as well as a floor. The census does not support it. The tint is not something the display does that a chromaticity could describe; it is the declared floor’s error made visible by the colour of the viewer’s own veil. A declaration with the right floor under every zone would carry no tint in any colour, so the repair is the same one the two-floor essay already needed: more floors, or a floor per zone, for the halo. What the tint changes is the price of not making it. A floor error that a white highlight’s veil would have hidden in lightness is, under a coloured highlight, both less hidden and turned into a hue shift several times the threshold the metric is scaled to.

And the census says something about which pictures the declaration can be trusted with. Sparse light was the failure case for white. For colour it is almost everything. A small saturated highlight is not rescued at all; a saturated window is rescued in lightness and not in colour; subtitles in any colour but white leave about twice as much of the screen misread as white subtitles behind the widest diffuser, and ten times as much behind the middle one. A colourist grading on a two-floor declaration of this panel would see dark greys round a red tail-light, a blue sign or yellow text that differ in both lightness and hue from what a viewer’s eye delivers.

How the census was taken #

The panel, pictures, diffusers and declaration are those of the two-floors census; the veil is the eye-glare census’s, the Stiles–Holladay law of ten times the illuminance at the eye over the square of the angle in degrees, with the angle held at one degree or more, seen from 2.5 metres. The lit content — the zones whose drive is above a tenth — is drawn at full drive in BT.709 white, yellow, red, green or blue, and its veil carries that colour’s XYZ; the unlit content’s veil stays D65 white. Each zone’s floors and declared floor are unchanged, because a local-dimming panel’s backlight follows the largest channel. The misreading is the largest absolute log-ratio, over grey levels every quarter decade from 0.005 cd/m² to the white, of ΔEITP’s reading of a five-per-cent D65 grey step on the declared floor to its reading on the true one, both with the veil added; the tint is the largest chroma part of ΔEITP between a grey on the declared floor and the same grey on the true one, both with the veil added. With every colour white, the veils, misread shares and worst misreadings are the earlier census’s exactly, which is checked.

What the census leaves out #

The colours are primaries at full drive. Real highlights are rarely a display’s pure primary; a tail-light or a neon tube in a film is a saturated but mixed colour, with more luminance than a primary and less than white. It would sit between the white and the primary on every figure here.

The veil’s colour is the light’s colour. Light scattered in the eye’s media is slightly bluer than the light that entered it, because small particles scatter short wavelengths more, and the lens absorbs some of the short wavelengths first. Neither is modelled, and both would move a blue veil’s cone signals.

ICtCp’s cone-like signals are not cones. They come from a fixed matrix on BT.2020 values, chosen for a transmission format, as the cones an appearance model uses found of another model’s rows; a veil’s effect on a real eye’s cones is closer to the physiology of three cones, two axes. The mechanism — a veil hides a step only in the signals it raises — does not depend on the matrix, but the sizes do.

Still open: whether a warm room veils the halo in its own colour #

The eye’s veil is not the only veil. A room’s light falls on the screen and comes back off it as a floor of its own, and under a warm lamp that floor is yellowish, carrying — as the yellow highlight here does — most of a white floor’s luminance and a fraction of its short-wave signal. The dark-room census gave the room’s veil a hundredth of a candela, grey, and a lit room brings the units’ medians together found a room’s light doing much of what the eye’s veil does here.

The calculation is this census in a dim room lit by a 2,700 K lamp, the room’s reflected floor given the lamp’s chromaticity at the levels the earlier essays used, with the panel’s declaration made as a colour engine would — in grey — and the halo’s misreading and tint read as here. The prediction is that a warm room hides the halo’s lightness misreading in the long and middle signals as a grey room would, and leaves the short-wave part of every dark step exposed, so that a two-floor declaration 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 does, a declaration’s floor needs the room’s colour as well as its level, because a room’s veil is a declaration input and not a viewer’s accident.

A cover is only as wide as what it covers #

The habit here is about what a masking signal actually masks.

The earlier census found the eye’s glare covering the panel’s error, and the natural way to carry that forward was by amount: more light into the eye, more cover. The yellow highlight breaks it — nine tenths of the light and none of the cover — because the error lives in three signals and the light raised two of them.

The failure mode is to measure a mask by its total when the thing it hides has parts. The test is to ask, of any quantity that hides another, whether it reaches every component of what it is hiding — and then to look at the component it does not reach, because that is where the error will be seen.