PQ, the perceptual quantiser — where it appears
Named by 16 essays across 3 fields — each of them below, with the objects they name alongside it.
How bright is white
An sRGB value says a pixel is some fraction of whatever the display can manage. A PQ value says it is two hundred candelas. The change is the largest in display encoding since gamma, and what it removed was the honest admission that nobody knew.
Two units with a light level disagree about lightness
ΔE₀₀ has no argument for how bright a display is. Two colour differences do: CAM16-UCS takes the room's adapting luminance, and ΔEITP — the difference defined for high-dynamic-range television — takes the stimulus's own absolute luminance. Twenty-three pairs at exactly one ΔE₀₀ grow in both as the display brightens, 2.1 times in ΔEITP and 1.5 in CAM16-UCS from a 5 to a 5,000 cd/m² white. But in ΔEITP the lightness part grows fastest, 2.7 times, and in CAM16-UCS it does not grow at all.
The units part by hue, not by light level
Two colour differences with a light level in them were compared on a display running from 5 to 5,000 cd/m², and a prediction was drawn from how each divided a difference between lightness and chroma. Built into pairs that differ in lightness alone and in chroma alone, both units say the same thing about light level: as a display brightens, chroma differences gain on lightness differences — ΔEITP by a tenth, CAM16-UCS by a quarter. Where they part is hue. The appearance model moves every colour's balance by the same factor; ΔEITP moves the violets, reds and cyan-blues the other way, and at nine of twelve base colours the two units disagree about the direction.
The shadows a unit counts are the ones a room removes
ΔEITP's growth with display brightness is largest in the dark greys, and dark greys are where a lit room's light reflected off the screen sits. One candela a square metre of veiling luminance removes 22 per cent of the difference the unit gives a step at the bottom of the scale on a 1,000-candela display and nothing measurable at the top. The same veil raises the growth the unit reports across display levels from a factor of six to a factor of seventeen, because it destroys a dim display's shadows first.
A guessed veil halves the error
A colour difference that takes a display's absolute luminance leaves out the light a room reflects off the screen, and on an ordinary display in an ordinary room that makes it wrong about the darkest greys by a factor of three. Giving the unit the veil as a declared argument fixes that when the veil is known. The worry was that it never would be — that a guessed argument is no better than none. It is better: any declared veil up to about twice the true one beats declaring none, and one middling guess for every room halves the worst error. What a guess cannot do is reach ten per cent; that needs the veil known within a sixth, which is what a luminance meter aimed at a black screen gives.
The hue disagreement is the quantiser's
As a display brightens, the appearance model shifts every colour's balance between lightness and chroma by one factor, and ΔEITP shifts violets towards lightness and yellow-greens towards chroma. The proposed source was the perceptual quantiser acting on three cone-like signals at unequal levels. Replacing the quantiser with a pure power law and changing nothing else removes the disagreement exactly: every colour moves by a factor of one. With the quantiser, how far a colour moves follows the spread of its three signals, and which way follows where its S signal sits — above the other two, towards lightness; below, towards chroma.
A dimming panel has no single black
ΔEITP reads a display's shadows correctly only when it is told the floor under every pixel, and that floor has two parts: the room's light reflected off the screen and the display's own black. They fold into one declared number exactly, and on a bright LCD the display's part is the one that matters — leaving it out misreads the deepest shadows seventeenfold. A local-dimming panel breaks the folding, because its black changes with the picture: in a dark room its floors vary twenty-six times across one scene, and no single declaration comes within a factor of two and a half. A lit room squeezes them back into one number.
At the gamut's edge the reds move as far as the violets
As a display brightens, ΔEITP shifts a saturated colour's balance between lightness and chroma by an amount set by its three quantised signals, and CAM16-UCS shifts every colour alike. The largest shifts found so far were a yellow-green at ×0.63 and a dark blue at ×1.62, both at the census's edge — and the blue turns out to be a colour no BT.2020 display can show. Walked out to the display's real boundary, the yellow-greens go lower, to ×0.54, and the dark blues never pass ×1.35, because BT.2020's blue edge is at low chroma. The top of the range goes to the reds and red-purples at ×1.6: at the edge the L-minus-M term grows to two thirds of the S term. Pairing the two extremes still needs a third of the observers the violet experiment needs.
A display's red takes the reds' move and leaves the pair
At BT.2020's edge ΔEITP moved a dark red's balance between lightness and chroma furthest of any colour, ×1.64 from a dim display to a bright one, and the reason offered was BT.2020's red primary, a line far out at 630 nanometres. Moving that primary in along the spectral locus confirms it: the reds fall faster than any other hue, to ×1.40 at 615 nanometres and ×1.25 at 605, and Display P3, whose red is a 615 nm line to three ten-thousandths, gives the reds the same. The top of the range goes to a red-purple, which rises as the red moves in because BT.2020 had pushed it past its own peak. And the forced-choice pair the experiment needs is the same two colours on every display.
A quantiser keeps the blue a spike
A gamut margin moves a display's corners inward by multiples set by the unit it is written in. ΔE₀₀ and CAM16-UCS both blunt an sRGB or BT.2020 display's blue, CAM16-UCS to nearly a face, and the prediction was that ΔEITP — the difference built on ICtCp for high-dynamic-range television — would blunt it too. It does the opposite. With the white at 320 cd/m² the blue is ΔEITP's sharpest corner on both displays, moving 3.12 and 3.24 times a margin, about as far as in CIELAB; at the green, cyan, magenta and yellow the three tolerance units agree within a quarter, and at the blue they span a factor of three. ΔEITP's lengths alone would blunt the blue as ΔE₀₀ does. What keeps it sharp is the perceptual quantiser: ICtCp's chroma rows sum to nought, so under a response that compresses like a logarithm, dimming the blue primary is a step in intensity and nothing else. Replace the quantiser by a linear response and the blue falls to 2.15; by a logarithm, it rises to 3.39. A brighter display sharpens it further.
A warm room tints the black, not the halo
A local-dimming panel's black can be declared as two floors, the room's light reflected off the screen folded in, and the earlier censuses gave that light a hundredth of a candela, grey. Under a warm lamp it is not grey. The prediction was that a warm room would hide the halo's misreading in the long and middle cone signals, leave its short-wave part exposed, and tint the halo's dark greys towards blue. The tint is real and it is none of those things. With the floors declared in grey, a 2,700 K room putting a tenth of a candela on the screen tints every zone of a dark picture by more than one ΔEITP — up to 17.7 at the darkest grey — and the tint points towards the lamp's own orange, opposite blue. It is not the halo's: it is the whole black's, because a grey declaration has the floor's colour wrong everywhere. The prediction's conclusion holds by a different road. A grey step laid on a warm floor is partly a change of colour, so the warm room leaves seven tenths of the moon picture's grey steps misread where a grey room leaves none; and declaring the floors in the room's colour removes all of it but the halo's own.
A violet primary is no spike to the quantiser
ΔEITP makes a display's blue its sharpest corner, about three times a margin, and the account of why predicted that a shorter-wavelength blue would be sharper still — past four times by 450 nm. Moving a monochromatic blue primary from 490 nm to 440 does the opposite. ΔEITP's blue corner is sharpest at 485 nm, ×4.37, and falls at every step to ×1.23 at 440, where CIELAB's runs the other way, from ×1.92 at 480 to ×11.8, and ΔE₀₀ follows CIELAB. The spike needs the two primaries that can be added to the blue to move it in nearly the same direction. Adding red always raises the blue's L signal by the larger fraction. Adding green does so only while the blue carries enough M signal of its own; a violet primary carries almost none, so adding green raises its M by the larger fraction and the two steps split, from 37 degrees apart to 111. No cone response rescues it — a logarithm blunts the violet further — and a brighter display dulls it while sharpening the longer blues.
The green primary decides how sharp the blue is
ΔEITP makes a display's blue its sharpest corner when the blue sits near 485 nm and nearly a face when it sits at 440, and the turn between them is where adding green stops raising the blue's L signal by the larger fraction. The prediction was that the turn follows the green — near 445 nm with a 545 nm green, near 470 with a 515 nm one. It follows the green, by less than half as much at the short end: 461 nm with a 515 nm green, 446 with a 545 nm one, and with a 555 nm green there is no turn left in the range at all. What the prediction did not ask is larger. The green sets how sharp the blue can be: with the blue at 485 nm the corner moves 2.4 times a margin against a 505 nm green and 8.2 times against a 555 nm one, while the sharpest blue stays at 485 nm for every green. The red primary, moved from 615 to 690 nm, leaves the turn where it was to a hundredth of a nanometre. The appearance model follows the green far more gently, under half of ΔEITP's move at every green.
A broad green sharpens the blue; a broad blue dulls it
ΔEITP makes a display's blue corner sharp or blunt according to its primaries, and the census of single-wavelength primaries found the green deciding how sharp — the 485 nm blue's corner moving 4.37 times a margin against a 530 nm green and 8.19 against a 555 nm one. Real primaries have widths, and the prediction was that a broad green acts as a longer green, raising the spike and moving the turn towards the violet, while a broad blue barely matters. The first half holds: a green forty nanometres wide at 530 nm sharpens the 485 nm corner to 5.05 and moves the turn from 453.7 nm to 451.2, as a single-wavelength green at 535.8 nm would, though its dominant wavelength has moved only to 533. The second half does not: a blue twenty nanometres wide moves the turn by a nanometre but dulls the corner by a tenth, to 3.94. The two widths pull the corner opposite ways, and a display whose green and blue are both broad lands near where its line primaries were. The red, at forty nanometres, still changes nothing that matters.
A green's long tail sharpens the blue; its short tail does not
A quantum-dot green falls steeply on one side and trails on the other, and the prediction was that a tail on its long side, holding a third of its power, would make ΔEITP's blue corner treat the green as a line past 538 nm, further than a symmetric forty-nanometre green's 535.8, because all its spread is on the L side. It does: 540.7 nm, the 485 nm corner rising from ×4.51 to ×5.70. The control is the larger finding. The same tail on the short side costs the green far more purity — 0.77 against the long tail's 0.95 — and moves its equivalent line by under a nanometre and a half. The corner reads the green's ratio of L to M signal, to within a third of a nanometre for every long tail, and not its purity, its centroid or its dominant wavelength; a short tail lowers that ratio less than its colour suggests and brings S signal that pushes the corner back.
Brightness and the green sharpen the blue almost independently
ΔEITP's blue corner is sharper the longer a display's green, and sharper the brighter the display. The prediction was that the two compound — that the 555 nm green's lead over the 505 nm one, 3.42 times at 320 cd/m², would pass four by 4,000, because a brighter display narrows every angle and the long green's was narrowest — and that the turn, where adding green starts raising the blue's L by the larger fraction, would not move with the peak at all. Both halves fail. The lead grows by a twentieth, to 3.60 at 4,000 and 3.63 at 10,000; across thirty-five displays the corner is a green factor times a brightness factor to within 4.5%. And the turn moves at every step, two to six nanometres towards the violet from 100 to 10,000 cd/m², crossing the blue at which green raises L and M equally near 1,000. The quantiser weighs a fractional rise in L against one in M by their encoded levels, and brightness evens the scales.
Named alongside it
The objects these essays reach for when they reach for this one.
ΔEHigh dynamic rangeAbsolute luminanceGamutDisplay primariesToleranceChromaCone fundamentalsLightnessCIECAM16Narrow band displaysViewing condition