The shadows a unit counts are the ones a room removes

Two units with a light level disagree about lightness found that ΔEITP’s growth with display brightness is concentrated in the dark greys: a one-unit lightness step at the bottom of the scale grows by a factor of six from a dim display to a bright one, and one at the top by very little. It closed on a second question that came with the same session:

ΔEITP’s growth is largest in the shadows of a bright display, and that is also where display blacks and viewing flare intervene; measuring the dark-grey steps with and without room light would say how much of ΔEITP’s shadow growth survives an ordinary viewing condition.

The calculation is one line — add a veiling luminance to both members of every pair — and the answer has two halves that point opposite ways.

The correction shrinks every difference and enlarges the growth #

On a 1,000-candela display seen through one candela a square metre of reflected room light, a one-unit lightness step at L 2 loses 22 per cent of its ΔEITP and one at L 90 loses nothing measurable. Through three candelas the deep step loses 46 per cent.**

• The same veil raises the growth across display levels. The step at L* 20 grows by a factor of 6.2 from a 1-candela white to a 10,000-candela one in the dark, and by 17.1 through three candelas.
• Both are true of the same veil because a fixed number of candelas is most of a dim display’s shadow and almost none of a bright one’s.
• Display black and room flare are different quantities. A display’s own black floor is a fixed share of its white and scales with it, so it changes nothing; the room’s reflected light is absolute, and it changes everything.
• There is no clean viewing condition. At a tenth of a candela — a dark grading suite with a good screen — the deep step has already lost 3 per cent.
• So the unit’s headline number and its per-pair numbers need opposite corrections, and neither correction is in the specification.

Two veils, and only one of them matters #

A display’s shadows are lifted by two things and they behave differently.

A display’s own black is what the panel emits with a signal of zero, and it is quoted as a contrast ratio — a thousand to one, a million to one — which means it is a fixed share of the white. Doubling a display’s brightness doubles its black in the same proportion, so every stimulus and every veil scale together and nothing in a ratio of differences moves. It is invisible to this calculation by construction, and the calculation is right about that: a display with a fixed contrast ratio has the same shadow structure at every brightness.

The room’s light reflected off the screen is not a share of anything. It is the room’s illumination times the screen’s diffuse reflectance, in candelas a square metre, and it sits there whatever the display is doing. A dark grading suite puts perhaps a tenth of a candela on the screen; a living room with lamps on, one to three; a bright office, five or more. Those are absolute numbers, and against a 5-candela display one of them is most of the picture while against a 5,000-candela display it is a rounding error.

The curves are flat at the top and fall away at the bottom, which is the shape the arithmetic demands: a veil of a given size is a larger fraction of a smaller stimulus. Through one candela, the step at L* 90 keeps everything, L* 50 keeps 99 per cent, L* 20 keeps 97, L* 5 keeps 88 and L* 2 keeps 78. Through three candelas the deep end keeps 54.

The shape matters more than any one number. ΔEITP’s case for taking absolute luminance seriously is built on the shadows — that is where the perceptual quantiser’s steps are finest and where a fixed relative change spans the most of them — and the shadows are the part of the picture a room removes. The unit is most distinctive exactly where it is least often seen.

That census is the measurement this essay is putting a condition on, and the condition is not small. Its pairs are surface colours spread across the space rather than deep shadows, so the veil takes less from them than from the L* 2 step above — a few per cent rather than a fifth — and the growth it reports, 2.1 times in ΔEITP, is a growth of a median over those pairs. The correction to it is in the same direction as the correction to the dark-grey step’s growth: the dim end of that census is pulled down more than the bright end, so the real growth in a lit room is larger than 2.1, not smaller. The units part by hue, not by light level found the other thing that census could not be read for; this is a second.

The headline moves the other way #

The number the earlier essay quoted is a growth: how much larger a difference becomes as the display brightens. A veil changes that too, and it changes it upward.

A fixed veil flattens the left of each curve and leaves the right alone. At a 1-candela white, one candela of reflected light doubles the total luminance of every stimulus and all but erases a dark step; at 10,000, it is one part in ten thousand. So the curve’s left end is pulled down and its right end is not, and the ratio between them grows: ×6.2 in the dark, ×8.3 through a tenth of a candela, ×17.1 through three.

That is an awkward result to state, because it points both ways at once. Every individual difference the unit reports in the shadows is too large for a real room, and the growth it reports across display levels is too small. They do not cancel, because they are different quantities — one is a reading, the other is a ratio of readings — and a specification that corrected for one would make the other worse.

The growth number deserves one more sentence, because its size is startling. A factor of seventeen across four decades of display white is not a small correction to a factor of six; it is a different claim about what a bright display buys. Read as a statement about a reader in a room it says that most of what a bright display adds in the shadows is recovering ground a dim display never had, since the dim display’s shadows were under the veil to begin with. That is a more interesting thing for a unit to be saying than the clean number, and the unit does not say it — the calculation that produces it is one the specification has no argument for.

What a tolerance would have to say #

A tolerance is a number a product has to meet, and the two corrections land on it differently.

A tolerance in the shadows is too tight. If a tolerance says that a difference of one ΔEITP is acceptable, and a real viewing condition removes a fifth of the difference at the bottom of the scale, then a product failing at 1.1 in the dark passes in the room it will be watched in. That is a real cost: shadow detail is expensive to encode, and banding is not a bit depth is the essay about what it costs to get it wrong in the other direction.

The cost is not symmetric either, which is what makes it worth quoting rather than absorbing. A tolerance is a decision procedure, and what one number accepts is the essay about the two things a tolerance is never quoted with — the spread of the process it judges and the cost of each kind of mistake. Here the veil moves the decision boundary in one direction only, and only in one region of the scale, so the products it changes the verdict on are a specific set: those whose worst error is in the shadows. A grading house rejecting a master for shadow banding it cannot see in its own suite is the case, and it is a common one.

A tolerance derived from the growth is too loose. If a tolerance for a bright display is set by scaling one written for a dim display by the unit’s own growth factor, the factor used is the clean one and the real one is larger — so the bright tolerance ends up tighter than it should be, or looser, depending on which way the scaling runs. The honest version does not scale at all: it states the display level and the room.

And neither of those is in the specification. ΔEITP takes absolute luminance and no viewing condition. The display is an unknown is the standing point about a page not knowing its own apparatus, and a colour difference that names candelas has made a stronger claim than a page does: it takes for granted that the number it is given is the light that reaches the eye, and in any lit room it is not.

The comparison with the other unit is instructive here rather than damning. CAM16-UCS does take a viewing condition — an adapting luminance and a background — and so has somewhere to put a room. What it does not have is a place to put a veil: its adapting luminance changes how the eye is tuned and does not add light to the stimulus, which is a different operation with a different consequence. So one unit has an argument for the room and the wrong one, and the other has none. A tolerance has no light level observed that ΔE₀₀ has no argument at all; three essays on, having an argument turns out to be necessary and a long way from sufficient.

The steps the unit is built from #

The reason all of this lands in the shadows is the quantiser.

The curve is steepest at the bottom. The perceptual quantiser was fitted to contrast-threshold data over four decades, and a fixed relative change in luminance spans many more of its steps in the dark than in the light — which is what makes a dark grey step a large ΔEITP on a bright display. A veiling luminance moves a shadow stimulus up the curve into the flatter part, so it does not merely reduce the contrast of the step; it reduces the number of quantiser steps that contrast spans, which is a second, larger reduction.

The three curves are the growth before any room is considered, and their separation is the thing the veil acts on. At a 10,000-candela white the dark grey’s step is several times the pale grey’s; at a 1-candela white they are close together. A room’s light pulls the dark curve back down towards the pale ones, and pulls it further at the dim end than at the bright — which is the same two-sided statement, drawn.

How the veil was added #

The veil is a D65-chromaticity luminance of a stated number of candelas a square metre, added to the tristimulus values of both members of every pair before ΔEITP is computed. Nothing else changes: the pairs are the same one-unit CIELAB lightness steps, the display’s white is the same multiplier, and the unit’s own arithmetic is untouched.

Adding it to both members is what makes it a veil rather than a change of colour. A veiling luminance is light reflected from the screen’s surface, so it arrives from every pixel equally and does not carry the picture’s own colour; adding it to one member would be a different and much larger effect.

The chromaticity chosen is the display’s own white, which is a simplification. A tungsten-lit room puts warm light on the screen and a daylit one cool, and either would shift the veiled pair’s hue as well as lifting its luminance. The effect on a neutral grey step’s ΔEITP is second-order and the effect on a coloured pair would not be.

What this leaves out #

The screen’s reflectance is a single number here. A real screen has a specular component and a diffuse one, and a matt anti-glare coating trades a mirror image for a larger diffuse veil. The veil computed here is the diffuse part and a specular highlight of a lamp is a local effect no census covers.

The eye’s own scatter is absent. Light entering the eye scatters inside it, and in an ordinary room a substantial veiling luminance is added on the retina rather than on the screen. It behaves the same way — a fixed addition to every stimulus — and it is larger for older eyes, so the honest total veil is the room’s plus the observer’s. The observer has no age is the standing reminder that the observer a specification names has no such parameter; here the consequence is that two readers in one room are behind different veils, and the older one’s is the larger.

The pairs are neutral. Every step computed here is a grey against a grey, which is the case the earlier census’s shadow result was about and is the easiest case for a veil. A coloured shadow — a dark blue, a dark red — is veiled by light of a different chromaticity, so the veil moves its hue as well as its luminance, and the ΔEITP of the pair changes for two reasons rather than one. Nothing here says which is larger.

And nothing here is a threshold experiment. These are model predictions about model readings. Whether a person’s shadow discrimination on a bright display in a lit room falls the way ΔEITP-through-a-veil says it does is the measurement, and it is a different one from the measurement of who is right about lightness.

Still open: whether the unit should take the veil as an argument #

ΔEITP takes one argument that a relative colour difference does not: the stimulus’s absolute luminance. The whole of this essay is the observation that the absolute luminance reaching the eye is not the absolute luminance the display was asked for, and the gap is a number a room has.

The computation worth running is a veiled ΔEITP — the same unit with a stated veiling luminance added before the quantiser, as a declared argument beside the stimulus — and the question is whether it behaves better than the unmodified one across the range. It would have to be checked two ways: that it reduces to the current unit at zero veil, which it does by construction, and that its predicted ratios between shadow and highlight differences are more stable across viewing conditions than the current unit’s, which is the property a tolerance actually needs.

The prediction is that it is more stable and that the improvement is largest at low display levels, where the veil dominates. The awkward possibility is the other one: that adding a veil argument makes a unit whose readings depend on a number nobody measures, which is how CAM16-UCS’s adapting luminance behaves in practice — quoted as 100 and never measured. A unit with an argument that is always guessed is not obviously better than one that leaves the argument out, and which of those a veiled ΔEITP would be is decided by whether a room’s screen luminance is easy to measure. It is: a luminance meter aimed at a black screen reads it directly.

A correction that goes both ways is two corrections #

The habit is about a single physical effect landing on two different quantities.

Adding a veil is one change to the model. What it does to a reading and what it does to a ratio of readings are opposite, and neither is more correct than the other — the reading is what a tolerance compares against and the ratio is what a summary quotes. An essay that computed only one of them would have been true and would have left the other pointing the other way.

The move is to ask, for each quantity the earlier work reported, what the correction does to that one, rather than asking what the correction does. Here there were two — a per-pair size and a growth factor — and they had been quoted in the same paragraph as though they were two views of one thing. A difference has no rate is the neighbouring caution about reading a rate off a quantity that is not a length; this is the same distinction made about a correction rather than about a derivative.

The failure mode is correcting a model and reporting one consequence. The consequence reported is usually the one the correction was proposed for, and the other one is the one somebody downstream is relying on.