Every essay — page 36
What light is What the eye does Matching and measuring Difference and uniformity What the brain does What a scene does What a camera does Where the model breaks What it takes to deliver it
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Matching and measuring
CIE XYZ, chromaticity, and gamut — a system for predicting when two lights match, frequently mistaken for a system that predicts how they look.
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.
A tone-mapped blue turns where it lands
In ΔEITP a display's blue corner, and the turn at which adding green to it changes which side of ICtCp's red–green axis it moves the colour to, both shift with the display's peak, because the quantiser reads absolute levels. A high-dynamic-range picture graded on a bright master and shown on a dimmer panel is tone-mapped, its blues delivered below the levels they were graded at. The prediction was that a blue at a tenth of full drive on a 1,000 cd/m² panel turns where a 100 cd/m² panel's full blue does, and that the corner's move differs, because the dimmed blue no longer sits at a vertex. The turn agrees within a hundredth of a nanometre. So does the corner, within half a per cent: the steps both are read from are directions at one absolute signal, whatever drive delivered it. The tone map's whole effect on the blue is where it puts the blue. Through ITU-R BT.2390's curve, a master's bright blues are gathered near a dim display's peak and share one turn there — two nanometres from where the master turned them — while blues under the curve's knee keep their turns exactly.
A tone curve per channel turns a sky towards cyan
A pure blue tone-mapped from a bright master to a dim display turns, in ΔEITP, wherever its delivered level puts it, and any tone curve that delivers it to the same level gives it the same turn. A picture's blue is not pure. The prediction for a blue mixed with a little green was that a tone curve applied to each channel separately raises the green's share by about half — the blue channel compressed above the curve's knee, the dimmer green left near it — turning the mixture's hue several degrees towards cyan and its turn a nanometre or more from where a curve that scales all three channels together puts it. The turn does move, by 1.6 to 3 nanometres on a 100 cd/m² display and up to 6.5 on a 300. But the share is not raised by half: through BT.2390 to a 100 cd/m² display, a blue graded with a tenth of green arrives with its green at 69 per cent of its blue, nearly seven times as much, and its ICtCp hue turns 23 degrees towards the green. The scaled curve keeps every mixture's hue within three degrees and its turn within half a nanometre of the pure blue's.
An appearance model sees the per-channel sky turn twice as far
BT.2390's tone curve, applied to each channel of a 1,000 cd/m² master shown on a 100 cd/m² display, raises a sky-blue's green share from a tenth to 69 per cent of its blue and turns its ICtCp hue 23°, where the same curve applied to the largest channel with all three scaled keeps the hue within 3°. ICtCp's hue is not an appearance, and the prediction was that CIECAM16, read under the display's own white, still shows the per-channel turn as more than twenty hue-quadrature units and more than ten ΔEITP, the scaled curve under three of each. The appearance model sees it as fifty-two units, more than half the way from unique blue to unique green, and its lightness more than doubles. The scaled curve keeps hue and lightness to a quarter of a unit. And ΔEITP between master and display ranks the two curves backwards: in absolute light the per-channel sky is the nearer one.
A curve on intensity cannot see a blue's brightness
ITU-R BT.2390's tone curve applied to each channel of a bright master turns a tone-mapped sky's appearance fifty-two hue-quadrature units towards green on a 100 cd/m² display; applied to the largest channel with all three scaled, it keeps hue and lightness to a quarter of a unit. BT.2390 also describes applying the curve to ICtCp's intensity and scaling its chroma, which keeps ICtCp's hue by construction, and the prediction was that it keeps the appearance's hue within three units and its lightness within two. It keeps the hue, within 2.3 units. It cannot keep anything on the display: a saturated blue's intensity is the PQ level of 79 cd/m², under the 300 cd/m² display's knee, so the curve barely touches it and every sky asks for two to seven times the blue the display has. Clipped channel by channel, the sky turns as far as the per-channel curve turned it; scaled back into the gamut, it lands where the scaled curve put it. The step back into the gamut decides the appearance, not the curve.
Lowering only the chroma turns the sky white and its hue with it
A tone curve applied to ICtCp's intensity keeps a high-dynamic-range sky's hue, but a saturated blue's intensity lies under the curve's knee, so the colour it asks for lies outside every display's gamut. The prediction was that bringing it back by lowering its chroma alone — intensity and ICtCp hue held — keeps the CIECAM16 hue within three units, lifts the lightness by ten and halves the chroma: a paler blue of the right hue. The ICtCp hue and intensity are kept to a hundredth. Everything else fails. The chroma must fall to a fifth or less on a 100 cd/m² display, the sky rises from a lightness of 22 to 76 and higher, and its hue quadrature moves eight to seventeen units toward green — a pure blue's by 17. Holding ICtCp's hue while lowering chroma does not hold the hue a viewer sees, and the intensity the curve chose was never a blue's.
The sky a dim display can show best is the master's own
A tone curve applied to ICtCp's intensity maps a saturated high-dynamic-range sky to a colour no display can show, and bringing it back by lowering only its ICtCp chroma turns it pale and toward green. The prediction was that a return along CIECAM16's own hue line, at the lightness the curve chose, holds the hue by construction, needs a deeper chroma cut, and still lies at least twice as far from the master as simply scaling the drives. It holds the hue to a hundredth, keeps more chroma than ICtCp's return rather than less, and lies two and a half to four times as far as scaling — because holding the true hue removes only one or two of seventeen units of difference. The rest is the lightness the curve held. And the nearest a dimmer display can come to the master's appearance turns out to be the master's drives, shown unmapped.
What a scene does
A reflectance measured on a patch is a patch. Put it in a room and the light bounces, and a bounce is a multiplication — so shadows carry their own illuminant, highlights carry the lamp, and two surfaces that matched go on matching only until the second bounce.
