The thread: Say which colour — page 9
What the brain does
Stochastic dots hold the glow at every tint
On brightened paper a halftone tint keeps a hue turn that a reader fully adapted to the sheet cannot remove, because the paper's glow survives under the ink where the solid puts it out, and a dot's thin edge lets more of it back. A dot's size at a given coverage is set by the screen. Across conventional rulings from 100 to 300 lines the residue rises at every coverage for every pigment, a finer screen making every dot more edge. A stochastic screen of twenty-micrometre dots holds it flat — the orange within a quarter of a degree from five per cent to sixty, starting where a 300-line screen starts — as predicted. What the prediction did not say is where the switch costs: not the pale tints, by under a degree, but the mid-tones, by three or four, because a conventional screen's mid-tone dots are large and mostly full film. On ten-micrometre dots, all edge, the ramp turns over and the mid-tone keeps more than the pale tint. At any one coverage the residue is set by the dot's diameter alone, whichever screen printed it.
Difference and uniformity
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.
What the eye does
A second session keeps a band and the macula apart
A lens band and a macula peaking a few nanometres short look alike to a colour-matching fit that has only one of them, and an older eye may have both. Fitted with all six numbers — rod weight, lens age, macular density, the band's amplitude and centre, and the macula's peak — nine simulated observers at sixty, each with a band at 415, 430 or 445 nm and a macula moved three nanometres either way or not at all, test whether the matches can carry both. The prediction was that the band at 445 and a short macula would trade almost completely, a correlation beyond 0.95 and the band's standard error tripled. That is what one session does: correlations of 0.91 to 0.95 at 430 and 445 nm, and a band found in at most twelve experiments of twenty. Two sessions do not. Their correlations stay between 0.42 and 0.83, the band is found in twelve to twenty experiments for every observer, and a moved macula in twelve to nineteen — while an unmoved one is found moved in at most three. The price of the extra number is paid by the band nearest the macula, whose standard error rises by three quarters; the rod signal pays almost nothing.
What the brain does
Merged spots give the mid-tones half the glow back
On brightened paper a halftone tint keeps a hue turn a reader adapted to the sheet cannot remove, and a stochastic screen's small dots, being mostly thin edge, keep it high along the whole ramp — three times the 150-line screen's cost in the mid-tones. That census kept every dot separate. A real stochastic screen's spots touch and merge, and a shared edge between two spots is no edge of the ink. The prediction was that a merged screen would follow the separate-dot curve to about thirty per cent and then fall towards the conventional screens, giving back half the mid-tone cost by sixty. It does, almost exactly. Square spots twenty micrometres on a side, switched on in a dispersed order, stay apart up to a fifth coverage and start touching near thirty per cent; by sixty, nine in ten touch, the rim has fallen from 84 per cent of the ink to 50, and the merged screen keeps the orange's residue at 6.9 degrees against the separate spots' 8.6 and the 150-line screen's 5.7 — giving back 58 per cent of the cost. Every pigment gets back the same share, 55 to 58 per cent, because the share is set by the geometry of the ink, not by its colour.
What a scene does
The slot's loss survives every finer division
Read on the painted faces alone, a satin finish on a room's grey faces makes the paint more colourful in twenty-eight of the painted census's thirty rooms and less colourful in two: the tall narrow slot with its floor painted and with its ceiling painted, where the paint loses about a twentieth of a per cent of its chroma. A loss that small could belong to how finely the slot's faces were divided, and the prediction was that it does not — that the sign holds at seven and eight strips a side. It holds. Solved from one strip a side to eight, the slot's paint gains at one, two and three strips and loses from four on, every one of seventy-two paints crossing at the same division; the loss deepens at every finer division, to −0.055 and −0.059 per cent at eight strips, and run out to no strip width it settles near −0.058 and −0.065. The coarse census had the sign wrong; the census at six strips had it right. The bright, broad paints lose most, as they gained most everywhere else.
What a scene does
The finish stops costing the paint six tenths deep
In the tall narrow slot a satin finish on the grey faces costs a painted floor or ceiling a little of its chroma; in the tall room, the same box a full unit deep, it adds some. Solved at eight depths between, the sign turns at 0.62 of the box's width with the floor painted and at 0.63 with the ceiling — later than the prediction of 0.45 to 0.55, and far enough along that the loss belongs to a range of shallow boxes rather than to the slot alone. A finer division moves the turn a little deeper, not back. Every one of seventy-two paints turns at the same depth, and each paint's share of the change is the same at every depth, loss or gain. Brightness does not decide it: the finish brightens the painted floor by between half and more than double while hardly touching the painted ceiling, yet the two turn together. What decides it is which reflectance the finish favours — whether it multiplies the light that has been back to the paint by more or by less than the light that has never touched it.
What the eye does
A line on the macula's flank buys less than a repeated session
Fitted with six numbers, two sessions of colour matches keep a lens band and a moved macula apart, but the band at 445 nm pays for it: correlated with the macula's shift at 0.82, its standard error 1.8 times its value when the macula is not fitted. A moved macula changes its long flank past 470 nm, where no lens band reaches, so a third session — the LED against a lamp with a narrow line at 487 nm — was predicted to bring the correlation under 0.6 and the band's error within a quarter of its band-only value. The correlation falls to 0.80 and the error to 1.5 times. A third session that simply repeats the second does better on both errors. The flank line pins how much macular pigment there is, not where it peaks, and it ties the band's height to its centre. Moved to 465 nm, onto the macula's peak, the same session brings the band within about a fifth of its band-only error — but no position of the line brings the correlation below 0.78. The band at 445 nm and the macula's peak are told apart by their short flanks, and a third session adds matches rather than a new kind of evidence.
What a scene does
A taller box must be deeper before the finish adds colour
In a box one unit wide and two and a half tall, a satin finish on the grey faces costs a painted floor a little of its chroma when the box is shallower than 0.62 of its width and adds some when it is deeper. Whether that turn is set by the width or by the height was the open question, and the prediction was that it scales with the height, because the satin walls pipe the lamp down to the floor and a taller box is a longer pipe. It does, and faster than in proportion. A box 1.5 tall gains at every depth from 0.35 and turns shallower than that; a box 4 tall loses at every depth to half again its width and turns near 1.67. As a share of the height the turn rises from about 0.17 to 0.25 to 0.42 — close to a depth growing as the square of the height. The taller box pipes far more of the lamp to the floor, tripling its light at 0.35 deep, and at every depth of every box the paint's colour still follows which reflectance the finish favours. Six strips a side keep both new boxes' signs.
What a scene does
The width moves the turn only when it is the narrower side
In a box one unit wide and two and a half tall, a satin finish on the grey faces costs a painted floor a little chroma when the box is shallower than about 0.64 and adds some when it is deeper. The prediction was that the width hardly matters — that the two end walls a depth apart form the pipe that carries the lamp down, and wider walls only add more of it — so the turn would move by under a tenth between widths. Solved at six strips a side, a box two units wide turns between 0.5 and 0.65, within the tenth or so predicted. A box half a unit wide still loses at 1.5 deep, and its quarter-turned twin says it still loses at 2: its turn is more than a unit and a quarter deeper. With only the floor painted a box w wide and d deep is the box d wide and w deep, so depth and width are one question, and the answer is that the floor's shorter side decides: under about half a unit the finish greys the paint, past about 0.65 it colours it. The scan's first pass, at four strips, said otherwise, and got four of seven signs wrong in the long, thin boxes.
Difference and uniformity
A room sensor must read the lamp to a hundred kelvin
A local-dimming panel in a 2,700 K room leaves a dark picture's shadows tinted towards the lamp unless its black floor is declared in the room's colour, and declared exactly, that tint falls below a ΔEITP unit almost everywhere. A display learns its room from a sensor, and sensors are not exact. With the room putting a tenth of a candela on the screen, a temperature reading 14 mireds out — about a hundred kelvin, warmer or cooler — puts the tint back over a unit in the moon picture; so does a level read 12 per cent low or 13 per cent high, or a white placed a Duv of 0.003 off the locus. The tolerance is even in mireds and lopsided in kelvin, and it narrows to a third or a quarter for every tenfold rise in the room's light: ±54 mireds in a room of a hundredth of a candela, ±5 in a room of one. A bright picture forgives six times as much as a dark one. Declaring the room's colour solves the tint only for a display that can measure the room about as well as a colour meter does.
What the brain does
Squares of four print a pale tint like a 150-line screen
On brightened office paper a stochastic screen's twenty-micrometre spots are mostly rim while they stay apart, and the rim lets the paper's glow through, so the palest tints carry the screen's whole cost in hue a fully adapted reader still sees. Merging gives back half of it in the mid-tones, where the spots touch, and nothing in the pale tints, where they do not. A second-order screen switches its spots on in clusters from the first tint, and the prediction was that clusters of four would take the orange's pale-tint residue down by about a degree, to within half a degree of a 300-line screen, while the sixty-per-cent tints stayed where the merged first-order screen leaves them. Squares of four do better in the pale tints than predicted and differ where predicted to agree. At five per cent they take the orange from 8.94 degrees to 8.14 — 0.02 above a 150-line screen and 0.81 below a 300-line one — and every pigment lands within a tenth of a degree of the 150-line screen. At sixty per cent they keep the orange 0.9 degrees below the first-order screen, where pairs and Ls come back to within a quarter. From ten per cent on, the 150-line screen pulls ahead.
What light is
The notch fit declares the true width, and the true width runs out
A lamp's table declares the narrowest line width its peaks admit, and builds on it a ceiling for how high any line can rise between the entries. A reversed tube breaks both: its lines are notched by cooler gas, a plain fit reads each notched line as a wider one, and on a one-nanometre table the ceiling falls below the true peak from a column depth of a half, until at two the table refuses every line and declares nothing. A fit with the notch in it reads the yellow's notch on that table, and the proposal was to declare the line it finds underneath — notch taken back out — with the prediction that the ceiling then holds to a depth of three. It holds to two. The notch fit returns the tube's own 1.2 nm core within two hundredths of a nanometre at every depth, clean and in noisy readings, and the ceiling built on it is safe to two and fails from two and a half, in the window beside the reversed blue line. So does the ceiling built on the true width itself, at the same depths to within a hundredth. The repair is perfect, and what fails past two is the ceiling's rule, which assumes the lines it bounds are not notched.
What it takes to deliver it
Off the grey axis a knee trades hue for chroma
Along the grey axis a total-ink cap approached through a knee quiets the cast a four-ink table prints between its nodes, because the knee slows the chromatic inks' retirement where black takes over. In a saturated shadow the chromatic inks carry the colour, and the prediction was that a knee would quiet the hue error there in the same way, a fifteen-unit knee halving the worst segment's. On two rays of dark colours, a deep blue and a brown, it does quiet the hue — every wider knee lowers it on both — and halves the worst segment's on the blue, to 0.28 of the hard cap's, but not on the brown, at 0.68, whose inks the knee slows far less. And the hue was never the main error. Between nodes the table prints these colours duller than asked, its chroma error five to eight times its hue error, and every wider knee makes that loss slightly worse, so the table's total error rises as its hue error falls. The cap itself, met hard, halves the blue's error, as it removed the grey's cast; on the brown it changes almost nothing.
Difference and uniformity
Lamp and daylight together sit below the locus
A display that declares its room's light can remove the tint a warm room leaves in a dark picture's shadows, if it reads the light to about fourteen mireds and a Duv of 0.003. An evening room is often lit by a lamp and the last of the daylight at once, and a sensor that reports a colour temperature names a point on the Planckian locus that such a mixture need not occupy. The prediction was that a lamp-and-daylight mixture sits well above the locus, so a declaration from its temperature tints the moon picture beyond a unit at a tenth of a candela for every mixture. The mixtures sit below the locus, at a Duv of −0.002 to −0.005, because a straight line between two points on a curve that bends upward lies under it. Declared from their temperature, they tint the shadows beyond a unit only when a quarter to a half of the light is daylight, up to 1.24 units. Daylight alone sits above the locus, at +0.003, and its temperature-only declaration tints by 0.67 at a tenth of a candela and 1.39 at one, where a grey declaration — the display's own white — tints nothing. Declared in its own chromaticity, every mixture's tint stays at the halo's.
What the brain does
A growing clump prints like the screen with as many dots
On brightened office paper a halftone's ink lets the paper's glow through at its thin rim, and the share of the ink that is rim decides how much hue a fully adapted reader still sees turned. A stochastic screen of squares of four prints the palest tint like a 150-line screen and falls behind it from ten per cent, because its clusters multiply where a conventional dot grows. A hybrid grows each cluster as the tint darkens, the number of clumps held, and the prediction was that it keeps the squares' pale tint, reaches within a tenth of a degree of the 150-line screen by thirty per cent, and stays slightly above it through the mid-tones. With thirteen clumps on the census's tile it follows the 150-line screen within two tenths of a degree at every coverage, within a twentieth at twenty per cent, and dips just below it at sixty. The reason is a count. Thirteen clumps on a tile 640 micrometres across are as many dots per area as a 143-line screen; twenty-six follow the 200-line screen and fifty-two the 300-line. A clump's irregular place on the tile does not matter to the glow; how many clumps share the ink does.
What a scene does
A square floor needs more room than a long one
A satin finish on a room's grey faces costs its painted floor a little chroma when the room is narrow and adds some when it is wide, and in a box two and a half tall the turn was found on the floor's shorter side — 0.64 when the longer side is one unit, about 0.51 when it is two. The prediction for a square floor, with no longer side to speak of, was a later turn, near 0.7, because both pairs of walls are then equally close and both carry the lamp down. Solved at six strips a side, the square floor loses for every one of seventy-two paints at 0.5, 0.6 and 0.7 on a side and gains for every one from 0.8, turning near 0.78. A floor 0.7 by 0.7 loses where a floor 0.7 by one gains. The finish brightens the square's darkest floor by more than an oblong's at every shorter side — by a hundred per cent against forty-six at half a unit — and the turn falls steadily as the longer side grows: 0.78, 0.64, 0.51. The longer side matters, and the light-pipe account says why.
What it takes to deliver it
More nodes quarter the dulling and leave the knee a larger share
A four-ink table printing a dark saturated colour between its nodes prints it a little duller than asked, and a knee in the ink limit, which quiets the hue error, deepens that dulling by about a hundredth of a unit. The prediction was that doubling the table's nodes quarters the dulling — the square of the spacing — and the knee's added cost with it, so that on a dense table the knee's hue gain is all that remains. On tables of 9, 17, 33 and 65 nodes along a deep-blue and a brown ray, the dulling does fall about fourfold with each doubling, capped or not, to under a hundredth at 65 nodes. The knee's added dulling does not keep pace: on the blue it is 13 per cent of the hard cap's at seventeen nodes, 23 at 33 and 35 at 65, and the knee's whole error, an eighth more than the hard cap's at seventeen nodes, is a quarter more at 65. The knee keeps its hue gain at every density. A denser table shrinks every error and makes the knee's trade worse.
Difference and uniformity
A sensor calibrated on lamps cannot read an LED
A display that declares its room's light in the light's own chromaticity keeps a dark picture's shadows untinted, and the chromaticity has to come from a sensor. The prediction was that a small three-channel sensor calibrated on a 2,700 K and a 6,500 K lamp reads mixtures of a lamp and daylight within 0.001, because they are mixtures of its calibration lights, and misreads phosphor LEDs by 0.003 to 0.006. The mixtures nearly hold: misread by up to 0.0023, past 0.001 from half daylight, because daylight is not a 6,500 K lamp — and at a tenth of a candela no mixture tints the moon picture by a unit. The LEDs are three times worse than predicted. Every one of thirty white LEDs built onto the Planckian locus is misread by 0.007 to 0.017, and every one tints the shadows by 1.7 to 3.6 units. The divide is not lamp against daylight but smooth against spiky: every Planckian lamp and mixture under 0.0035, every LED and fluorescent tube over 0.007.
Difference and uniformity
No calibration reads the lamps and the LEDs together
A three-channel ambient sensor pinned on two Planckian lamps reads every lamp and every lamp-and-daylight mixture well enough to keep a dark picture's shadows under a ΔEITP unit, and misreads every white LED badly enough to tint them by two to four. Its errors on the LEDs all point one way, and the prediction was that a matrix fitted in least squares to every light in a census would bring every LED under 0.004 while the lamps rose only towards 0.003. It does not. Fitted to the census, each light held out, the sensor's worst LED error falls from 0.017 to 0.0066 and its worst lamp error rises from 0.0033 to 0.0126; thirteen of forty-seven lights still pass a unit, among them the 2,700 K lamp the original calibration read exactly. A matrix exact on the lamp, daylight and one 4,000 K LED reads every mixture and every 4,000 K LED nearly perfectly and fails the 2,700 K LEDs, none read better than 0.0063. A fourth channel leaves six lights beyond a unit. Three broad channels have one matrix, and it can be right about one kind of spectrum.
What light is
A ceiling that knows the notch holds to the deepest column
A lamp's table promises a ceiling for how high any line can rise between its entries, and for a reversed tube — every line notched by a cooler column — that ceiling fails on a one-nanometre table from a column depth of two and a half, because its rule assumes the line it bounds has no notch. The notch fit already reads the yellow line's notch, and the proposal was to build the ceiling for a notched line instead: in each window, the factor for a slit-blurred line carrying that window's notch. The prediction was that it holds to a depth of four. It holds to five, the deepest column the census runs, at every depth and in every one of 440 noisy readings. The fit's depth must be read as an optical depth, −ln(1 − d); taken as the first-order depth it fits as, the ceiling fails from four and a half. Part of the safety is the fit's own error: read that way, a deep notch comes out too deep — 4.25 for a true 2.29 at depth five — and an overstated notch only raises the ceiling.
What light is
A coarse table can borrow a notch, but not a phantom
A one-nanometre table can bound a reversed lamp by building its ceiling for the notch its own fit reads. A two-nanometre table cannot read the notch, and its ceiling, built for an unnotched line, fails from a column depth of three and a half. The proposal was to borrow the notch from the finer table, and the prediction that the coarse ceiling then holds to five with a wider margin. It does: 8 to 42 per cent above the reversed lamp's true peak at every depth, against the fine table's 1 to 29. But borrowed from the fine table's noisy readings, one notch in 440 sinks the coarse ceiling below the true peak — a notch of 0.13 the fit read in noise where there was no column at all. Under a wide slit a shallow notch flattens a line's top, two flanking entries see more of it, and a ceiling that assumes the notch is set lower; the phantom set it too low. Borrowing only notches the depth rule calls — deeper than 0.2 — keeps all 440 safe; borrowing those more than twice their error does not.
What the brain does
The rim was never most of the glow
On brightened paper a halftone tint keeps a hue turn a reader fully adapted to the sheet cannot remove, and five essays have chased the part of it that lives at the ink's thin rim — merging spots, clustering them, growing them — down to a rule: the clump count sets the residue, and only coarser patterns lower it. The proposal was a screen coarse in the pale tints and finer as the tint darkens, and the prediction that six clumps on the tile beat the 150-line screen by more than half a degree below twenty per cent. They beat it by 0.11 to 0.17. Scheduled six, thirteen and twenty-six clumps save a third of a degree at ten per cent and give back a fifth at sixty. The reason is the floor. One clump on the tile — the coarsest pattern it can hold, nearly all its rim gone — still leaves 7.48 degrees of an orange's 8.14 at five per cent and 5.30 of 5.65 at sixty. What screening can move is the rim's tenth; the other nine tenths is bare paper glowing beside ink that does not.
What it takes to deliver it
Three nodes at the cap's corner cut the dulling by a third
A four-ink table printing a dark saturated colour between its nodes prints it duller than asked, and at 65 nodes a fifteen-unit knee in the ink limit carries 35 per cent of that dulling on a deep-blue ray. The prediction was that the knee's added dulling sits in the two or three segments just below where the cap binds, and that three nodes placed there take its share back under a tenth. The first half holds: the knee's addition peaks one unit of lightness below the binding point and four fifths of it lies within seven. The second does not. Three nodes placed one, two and three units below the bind cut the hard cap's dulling by a third, 0.0097 to 0.0064, and the knee's by nearly two fifths, where three more evenly spaced nodes cut each by under a tenth — but the knee keeps a quarter of the dulling. The hard cap has a corner, which one node can catch; the knee has a bend spread over a dozen units, which three nodes split but do not straighten. A node at the binding point alone helps only the hard cap, and leaves the knee 41 per cent.
What a scene does
A long floor never loses its colour to the finish
A satin finish on a room's grey faces costs its painted floor a little chroma when the room is narrow, and the shorter side at which the cost turns into a gain fell as the floor grew longer — 0.78 for a square, 0.64 for a floor one unit long, 0.51 for two. The prediction was that it settles near 0.45 by four units, the limit of a slot whose far walls pipe nothing. Solved at six strips a side, floors three and four units long gain chroma for every one of seventy-two paints at every shorter side from 0.35 to 0.65: there is no turn to find. The floor two units long already loses only in a window, shorter sides from about 0.3 to just past 0.5, and gains on either side of it; by three units the window has closed, and a four-unit floor gains more than a three-unit one everywhere. The loss was never the slot's. It belonged to the far pair of walls, and moving them away removes it.
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