The thread: The instrument is the reader — page 14
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 light is
A stricter fit declares a wider line
A two-nanometre table of a mercury lamp whose every line is self-reversed admits every reversed line as a Gaussian within half a per cent, and declares a width its own ceiling cannot stand on from a depth of two and a half. The obvious repair is to fit harder. The prediction was that at a tenth of a per cent the table refuses the reversed blue and green lines, admits the least-reversed yellow, declares unsafely from it between — and that a threshold that strict would refuse even unreversed lines on a real instrument's noisy table. The refusals come where predicted: the blue from a depth of three, the green from four. But the stricter threshold makes the declaration less safe, not more. It narrows the range of widths each line admits from below, so the yellow, never refused, declares a wider width at every depth, and the ceiling built on it falls below the true peak from a depth of two instead of two and a half. And a tenth of a per cent survives a quiet instrument: no unreversed line is refused until the table's noise reaches half a per cent — and then the first line refused is the yellow, the one that declares.
Difference and uniformity
Adapting to a warm room deepens the shadows' tint
A warm room's light reflected off a local-dimming screen tints the shadows of every dark picture when the screen's black is declared in grey — by up to 17.7 ΔEITP — and ΔEITP has no viewer in it. A viewer who has sat in a 2,700 K room all evening is adapted partly to the room, and adaptation to a warm white discounts warm light. The prediction was that a viewer adapted a third of the way to the room would see under half the tint, and one adapted two thirds of the way would see the darkest greys turn blue. Read through CIECAM16, the opposite happens in a dark picture. The tint the viewer sees grows at every step of adaptation: in the moon picture's darkest grey from 2.7 CAM16-UCS units for a viewer adapted to the display to 3.3, 3.9 and 4.4. The darkest greys never turn blue; they stay orange and fade. What turns blue is the mid-greys, whose light is the display's own and now looks cool. In the bright window picture the tint shrinks, and declaring the floor in the room's colour still removes it for every viewer.
What a camera does
LEDs varied in their phosphors fall off every line
The merged smooth family estimates a camera's colour error from an ambient-light sensor's departures to ±0.127, and five new white LEDs, varied in their phosphors where the census's forty-four vary their pump, missed by ±0.196 because the family's line had learned almost nothing about the sensor's 640 nm channel. Rebuilt on forty-eight LEDs varied in pump, converter and red phosphor, the line learns it: its 640 nm weight goes from −0.13 to −0.74, most of the way to the −0.85 the new LEDs implied. The prediction was that the new LEDs would then land within ±0.13. They miss by ±0.229, worse than before, crossing to the other side of the line, and the census's own held-out error more than doubles, to ±0.294. No pool of LEDs restores it, and no line in the sensor's departures reads the grid's own LEDs better than ±0.29. Across the grid the camera's error is a V about the Planckian locus, rising away from it on the green side and on the pink — and every one of the census's LEDs sat on the green side.
What light is
Two nanometres hide the yellow's notch from any fit
A plain Gaussian fit admits the reversed tube's 578 nm yellow line at every threshold on a two-nanometre table, and the ceiling built on its width fails from a column depth of two and a half. A fit with the notch in it — an emitted Gaussian with an absorbed one taken out of its centre — might see what the plain fit cannot. The prediction was that two nanometres leave too few entries to determine the notch, and one nanometre finds it from a depth of two. Two nanometres hide it completely: the best notch fit carries a negative notch, a spike, at every depth, and the readings a two-standard-error rule calls reversed are the same noise draws at every depth, each fitting a notch that erases the whole line. One nanometre finds it sooner than predicted — in every reading from a depth of one and half of them at a half — and its fitted depth climbs with the column. But its standard error cannot be trusted with seven entries and four numbers: the rule calls a third or more of unreversed readings reversed. The notch's fitted depth itself separates them cleanly.
Where the model breaks
A harder search pulls the band pigments away from the slope limit
Every count in the pigment-limit censuses — how many directions of the object-colour solid a slow pigment cannot reach within one per cent of the ideal — compares a slope limit solved exactly with two band models searched from a few structured starts. Under the mercury lamp a search from 680 starts had already found the band model reaching further in seventeen of twenty-five directions. Searched from 594 starts under all nine lamps, both band models reach further in between three fifths and nineteen twentieths of the directions they lost, and their counts fall by a sixth: 395 to 335 for bands in nanometres, 370 to 311 for bands in energy, while the slope limit stays at 463. The rankings the censuses reported hold where they were stated. What moves is everything measured against the slope limit: its lead over the band models grows from a sixth to more than a third, the coating's odd ranking — bands losing more than the slope limit — disappears, the triphosphor tube passes the three emitters for bands in nanometres, and under the mercury lamp the band models' deep losses halve.
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 the eye does
Knowing the macula's density frees two sessions, not the line on its peak
Fitted with six numbers, an older observer's colour matches cannot fully split a lens band at 445 nm from a macula whose peak has moved: their correlation stays above 0.78 under every third session tried. The proposal was to measure the macular pigment's density from outside the matches, leaving five numbers, and the prediction was that a line on the macula's peak would then split the pair below 0.6 while two plain sessions stayed near 0.8. It runs the other way. With the density known exactly, two sessions fall from 0.83 to 0.62 and the line at 465 nm only from 0.86 to 0.74. The density was the road the band and the peak traded along — correlated with each at about −0.75 in two sessions' fit — and the designs that had already narrowed that road gain least from closing it. A realistic outside measurement closes almost none of it: the matches already know the density to 0.027, so a flicker measurement good to 0.05 moves the correlation by three hundredths. And far from the macula, at 415 nm, a known density binds the band to the peak more tightly than before.
Matching and measuring
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.
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.
Where the model breaks
The slope limit was exact all along
Every count of what a slow pigment cannot reach compares a slope limit, solved exactly on 161 levels of reflectance, with two band models found by searching. Searched harder, the band models lost a sixth of their losses, and the open question was whether the slope limit was being flattered by its own grid — whether 321 or 641 levels would lower its counts too. The prediction was a fall of under a twentieth. There is no fall at all: on every finer grid, under all nine lamps, every direction reaches exactly what it reached, and 463 directions are lost as before. The reason is the shape of the answer. The best reflectance that may change by at most an eighth per five-nanometre band is a staircase whose every step is a whole eighth, because a weighted sum is maximised at a corner of the allowed set and every corner is built from full steps off nought or one. A grid of only the nine eighths gives every answer to the last digit. The census's count is therefore not an estimate on a grid but an exact statement about every pigment that slow, and the slope limit's 1.38-fold lead over the searched band model is a floor that further search can only raise.
Where the model breaks
A slow pigment splits mercury's lines only if its swing fits between them
Under a clear mercury lamp a pigment whose reflectance may swing from nought to one over no less than forty nanometres loses 21 of the census's 148 directions, and every one of them asks it to reflect one of the lamp's green and yellow lines and absorb the other. The census samples the spectrum every five nanometres, which smears each six-nanometre line across a band, and the prediction was that a one-nanometre grid would let the pigment's cliff fall between the lines and cut the count by a third. It cuts it by nothing: 21 on either grid. Narrowing the lines to one and a half nanometres cuts it only to 17. What decides the losses is the lines' spacing, 31.5 nanometres, against the pigment's swing. With narrow lines a pigment whose swing is 30 nanometres loses no direction at all, and one whose swing is 34 loses fourteen; the step sits at the gap. The mercury lamp's cost to a slow pigment belongs to the lamp, not to how the census samples it.
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 a camera does
LEDs built on the locus still fall off the line
A camera's colour error under a lamp can be estimated from three narrow channels of a small sensor, read as departures from a smooth lamp of the same colour, and the estimate held for the census's white LEDs, which varied only their blue pump. Rebuilt on LEDs varied freely in pump, converter and red phosphor, it failed: the error was a V about the Planckian locus, and no line in the departures read it. A maker does not let the white fall where it falls, so the proposal was to build the LEDs as a maker does — the converter tuned for each pump and red phosphor until the white sits on the locus — and the prediction was that the V would go and the line return, the census's held-out error to within ±0.15. Thirty of thirty-six such LEDs can be built. On the locus the V is gone and the line is not: the LEDs alone are missed by ±0.25 to ±0.28, the census's lamps by ±0.27. Taken one pump at a time, the departures read the LEDs pumped at 452 nm to ±0.05 and those at 440 and 465 nm no better than ±0.17. Within one pump the LEDs are readable, and across pumps they are not.
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.
Matching and measuring
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.
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 the eye does
A density a tenth wrong costs the band more than fitting it
An older observer's colour matches carry a lens band and a macula that can trade against each other, and fixing the macular pigment's density from an outside measurement breaks much of that trade when the density is right. A flicker measurement and a colour match average the pigment over different fields, so the fixed density can be wrong by a tenth or more, and the prediction was that a tenth too high takes about a third of a standard error off a band at 445 nm and moves the macula's peak by under half a nanometre. It takes 1.4 standard errors off the band and moves the peak 1.25 nm short. At 415 nm the same error pushes the band the other way, up by 2.4 standard errors, and runs its fitted centre 5.6 nm shorter and the lens's age three years younger. Bias and error together, a density fixed a tenth wrong gives the band at 445 nm a larger error than leaving the density free; the break-even is about eight per cent. Given as a measurement with its own standard error of 0.03 instead of fixed, the same wrong density biases the band by under half its error.
Where the model breaks
A band pigment must be narrower than the gap it splits
Under a clear mercury lamp a pigment built from absorption bands no narrower than forty nanometres falls short in fifteen of the twenty-five directions that ask it to reflect the green line and absorb the yellow, or the reverse — the count an earlier search left short however deep it cut its cliff. The slope-limited pigment's losses turned out to be the lines' 31.5 nm spacing against its swing, and the prediction was that the band pigment's are the same arithmetic, falling to nought near a band thirty nanometres wide. Searched on a one-nanometre grid with the lines narrowed, the count falls at every narrower band — fifteen at forty, eleven at thirty-five, nine at thirty — and reaches nought at twenty-five, not thirty. Every loss already splits the pair and falls short on both lines at once: a Gaussian band deep enough to absorb one line keeps absorbing a little of the other. One band of depth twelve, placed as well as it can be, errs by 3.2 per cent at forty nanometres, 0.8 at thirty and 0.2 at twenty-five; doubling its depth buys less than narrowing it by five nanometres.
Matching and measuring
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.
Matching and measuring
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.
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.
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