The thread: The instrument is the reader — page 13
What a camera does
A classifier that abstains gives up the tube
Found by the nearest other lamp, a lamp's family cost a two-stage estimate of a camera's colour error more than it bought, because five lamps were placed confidently in the wrong family. The proposed repair was a classifier that abstains — falls back on the census-wide line — unless a lamp's three nearest neighbours agree. It abstains on the wrong lamps. The misplaced ones have three agreeing neighbours, all white LEDs; the lamp it gives up is the halophosphate tube the two stages were built to catch, whose third neighbour is a cyan LED, and its miss returns from 0.011 to 0.445. Two agreeing neighbours look better than knowing every family. Chosen without looking at the lamp being estimated, the rule is worth exactly what the ratio alone is worth.
What the eye does
A lost lens band goes to age or the macula
Two colour-matching sessions determine the centre of a band of extra absorption in an older lens to about five nanometres, if a fit can find it. Fitted in full from eight starts across 400 to 470 nm on twenty simulated experiments, two sessions find a band at 415, 430 or 445 nm from every start in fifteen to eighteen experiments of twenty, against eighteen for a fit started at the truth. The prediction was that a low band would be lost from high starts to the macula's flank. The start barely matters with two sessions, and a lost band does go somewhere — but a band at 415 or 430 goes to lens age, three to five years of it, and only a band at 445 goes to the macula. Every loss is a worse fit than the session's best, so eight starts find the band as often as the truth does. With one session the start decides.
What light is
A reversed line is read as one line
A strong mercury line in a dense discharge absorbs its own centre on the way out: at an optical depth of one its top is flat, and beyond that it dips, until at four the line is two humps with a trough eighty per cent deep between them. The prediction was that a one-nanometre table refuses such a line from a depth of about one and a two-nanometre table reads it as a Gaussian about the width of its flat top, safely. Both hold, and the second only up to a point. A two-nanometre table admits the line at every depth to four, and from three and a half the width it admits is too wide for the humps: the ceiling built on it falls eleven per cent below the line's true peak. The only line that could make a declared width unsafe was one narrower at its peak than its entries suggest — and a reversed line is exactly that.
Difference and uniformity
The eye's own glare hides most of the halo
A local-dimming panel's black can be declared as two floors, and the pair misreads only the diffuser's halo round the bright content — by up to a factor of 2.7. The halo sits next to the light, and light scattered inside the viewer's eye puts a floor of its own there. Added under every grey step, the eye's veil hides the whole misreading in six of nine cases: every window, and the highlight and subtitles behind the narrowest diffuser. It leaves a sixth of the misreading's share for a small highlight behind the widest diffuser, and a quarter for subtitles, all of it in the halo's inner half — not its outer edge, as predicted. The panel dims by a zone's brightest pixel and the eye veils by its average, so a line of text lights the backlight fully and the eye a quarter. The viewing distance cancels.
Where the model breaks
A mercury lamp's few losses are deep
Every census of what a slow pigment can reach has counted the directions of the object-colour solid it misses by more than one per cent, and by that count a clear mercury lamp — four visible lines and nothing else — spares a pigment as well as three narrow emitters do. Read for depth, it is the one lamp of nine whose losses do not fall away: half of what a slope-limited pigment loses under it, it loses by more than five per cent, and its mean shortfall is half as large again as under the emitters or a triphosphor tube. Every one of those losses is the same kind of colour: one that reflects the mercury's green line at 546 nm and absorbs its yellow line at 578, or the reverse, 32 nm apart. The dark-share rule that ordered the counts orders the depths less well.
What it takes to deliver it
A closed counter adds a little to a junction
Sharpened on its stored values, black type's junctions — the inside angles where a bar meets a stem — gather error by the stem's width in pixels, and at equal widths a heavier letter gathers slightly more. A heavier letter differs in two ways: it is smaller around its stem, and its counters are narrower. Holding the stem and moving the spacing separates them. At equal stem widths, closing the counters adds about four hundredths of their share to the junctions and one hundredth to the stroke ends, and twice as much to E and H, whose bars face each other across a counter, as to L and T. The prediction was the counter, and the counter it is — by an amount no larger than a sub-pixel position moves it. Drawing the letters apart found the stem census's light H with its crossbar floating.
What light is
A notch in a line is never refused
A dense discharge's green mercury line loses its centre to the atoms between the glow and the tube wall, and those atoms are cooler than the glow, so their absorption is narrower than the line it cuts. With the absorbing layer half or a third as wide as the line, a one-nanometre table still refuses the line from an optical depth of one, exactly where it refused the broad dip. A two-nanometre table never refuses it at all: to a depth of five, with ninety-eight per cent of the centre gone, one Gaussian fits its entries within a seventh of a per cent. And the ceiling built on the width it reads fails from a depth of about two and a third — a whole unit sooner than behind a column as wide as the line — and never recovers, falling to three quarters of the true peak.
Difference and uniformity
A coloured highlight tints the halo it cannot hide
A local-dimming panel lights a zone for its brightest channel, so a pure red or blue highlight drives the backlight as hard as a white one and sends a fifth or a fourteenth of the light into the viewer's eye. The prediction was that a saturated highlight's veil would hide the halo's misread greys as a white one does, and add a colour. It hides far less. Behind the middle diffuser a white highlight hides the whole misreading; drawn red, blue, green or even yellow — nine tenths of white's luminance — it hides none of it. The yellow fails because a veil hides a grey step only in the cone signals it reaches, and yellow light reaches a fifth of the short-wave one. And where the veil does fall on a misread floor, it colours the error: the darkest greys are tinted by up to fifteen ΔEITP, and behind a red window, where the veil hides the lightness almost entirely, a fifth of the screen is tinted by more than a unit.
What a camera does
A family's line runs through its neighbours
The halophosphate tubes differ from one another by one number — where their main phosphor band sits — and so lie along a line in the three departures an ambient-light sensor reads. The proposal was to classify a lamp by the family whose line passes nearest, which would keep the tube a vote of neighbours gives up. It keeps the tube, under every version that does not rescale the distances. It also places eighteen white LEDs on the radiators' line, because that line — fitted to six radiators close together — runs along the LEDs' own and, extended, straight through the violet-pumped ones; and the radiators' estimate, extrapolated to them, misses the triphosphor tube by 7.6. Clamped to the stretch each family spans, the lines still cost ±0.285; given to the halophosphate family alone, its line claims a cyan LED and costs ±0.179. The one line classifier that comes in under the ratio line's ±0.141 does so by two thousandths, having placed the tube with the LEDs.
Matching and measuring
A display's blue is sharp where the rotation is not
ΔE₀₀'s rotation term shears chroma into hue near a CIELAB hue of 275 degrees, and at a press's blue corner it had nothing to act on because the corner was blunt. The prediction was that a display's blue — an additive primary — would be a sharp corner, and that there the rotation would change how far a safety margin moves it by more than a tenth. The first half holds: sRGB's blue moves 3.35 times a CIELAB margin and BT.2020's 3.17, against the press's 1.25, and insetting the curved gamut directly confirms it to the second decimal. The second half fails, twice. A display's blue sits at 306 degrees, thirty past the rotation's centre, where the term grips a quarter as hard; and ΔE₀₀ blunts the corner to 1.42 by compressing its chroma sevenfold. Along the edge from blue to cyan the hue does pass through 275 and the grip reaches −0.87 — where the edge is nearly a face. Nowhere near either display's blue does the rotation move a prediction by four hundredths.
What it takes to deliver it
Width and height each carry half the counter's gain
Closing a sharpened letter's spacing at a fixed stem width raised its junctions' share of the error the eye sees by about four hundredths, and the spacing moved the letter's width and height together. A type family's condensed and extended faces separate them: the counters across the letter narrow while its height and stem stay put. The prediction was that the condensed letters' junctions would carry the whole four hundredths. They carry half — 0.023 — with the stroke ends moving by four thousandths. Shortening the letter at one width carries the other half, also 0.023, and the two add to within four thousandths of what closing both did. Each half is found where its own counter lies — condensing gains most in the H, shortening in the E — and the T, which has no counter across it, gains nothing when condensed. Neither half, on its own, is larger than one and a half times the scatter a sub-pixel position produces.
Where the model breaks
A pair of lines asks for a cliff, not a gap
Under a clear mercury lamp, every direction of colour a slow pigment loses by more than five per cent asks it to reflect one of the lamp's green and yellow lines, 32 nanometres apart, and absorb the other. The prediction was that a pigment of two absorption bands with a narrow gap between them — a peak no single transition can make — would recover those deep losses. No direction asks for a peak. The lamp's four lines leave only one transition within a hundred nanometres of another, so what a splitting direction needs is a cliff: one flank falling from reflecting to absorbing in the twenty-five nanometres between the green line's last strong sample and the yellow's first. One band at the census's depth takes 27.8 to fall that far; two stacked at one centre take 24.9. Searched from 680 starts, the census's own band model does exactly that — stacks its bands on one side of the pair — and reaches further than the census found in seventeen directions of twenty-five. What stays deep spends a band on the blue.
What light is
A reversed tube declares from its least reversed line
A spectral table declares its lamp's line width as the narrowest width any of its peaks admits, and that declaration survived every reversed line so far because the tube's other lines were left unreversed to set it. A real discharge reverses its strong lines together. With every mercury line behind its own column, in proportion to its strength, the prediction was that a one-nanometre table would refuse every strong line and declare from the weak violet line, and a two-nanometre table would declare an unsafe width from a green-line depth of two and a half. The violet line is never read as a peak at all. The yellow line, the least reversed of the three that are, sets the declaration at every depth and widens it as it reverses. Through one nanometre the table refuses the blue and green lines and goes on declaring from the yellow — unsafely, in the violet's window, the one line the table never checked. Through two nanometres behind a cooler layer it refuses nothing, and from two and a half its declaration fails in the blue line's window, down to seven tenths of the true peak.
What a camera does
Radiators and LEDs are one family to the sensor
An ambient-light sensor's three narrow departures see the collection's six smooth radiators and forty-four white LEDs along one line: the radiators' own short line lies on the LEDs' long one. Estimating a camera's colour error family by family, the census had treated them as two, and every classifier that tried to tell them apart paid for it. Merged into one family of smooth broadband sources, found by the nearest other lamp as before, the two-stage estimate comes to ±0.127 over fifty-four lamps held out — below the ratio line's ±0.141, and below the ±0.133 the separate families managed when every lamp's family was simply given. The halophosphate tube is still caught. The radiators, which the prediction said the merge would cost a little, are estimated better inside it than inside their own family, because a three-coefficient line fitted over five radiators was worse for them than the census-wide ratio line.
Matching and measuring
The yellow is sharp where the tolerance unit does not compress
A safety margin moves each corner of a display's gamut inward by a multiple of itself that depends on the corner's shape. In CIELAB, sRGB's blue is its sharpest corner and its yellow among its bluntest; carried into ΔE₀₀, the order turns over, and the yellow becomes the sharpest corner of both sRGB and BT.2020. The prediction was that the yellow keeps its sharpness because its faces run along lightness, where ΔE₀₀'s weighting is largest at the yellow's L* of 97. Taking ΔE₀₀ apart length by length says otherwise. Its lightness weighting changes the yellow's move by nothing. Its chroma compression — the term that opens every other corner — does, on its own, bring every other corner of both displays under 1.35 times a margin, and leaves the yellow at 1.78. Of the yellow's three directions only one runs along chroma; at the other corners two or three do, and a metric that compresses chroma pulls those together and flattens the corner between them.
Matching and measuring
An appearance model flattens the blue by its hue
A safety margin moves a corner of a display's gamut inward by a multiple of itself set by the corner's shape, and the unit the margin is written in decides the shape. In ΔE₀₀ the yellow is the sharpest corner of an sRGB and a BT.2020 display, because its sharpness lies across hue where ΔE₀₀'s chroma compression cannot reach it. CAM16-UCS compresses colourfulness less steeply, and the prediction was that it would leave the blue sharper than the yellow. It leaves the yellow sharpest, at 1.66 times a margin on both displays, and flattens the blue to 1.17 and 1.10 — the bluntest corner of all twelve. Its colourfulness does what the prediction said: on its own it would sharpen the blue past the yellow. Its hue scale undoes that. At a display's blue one degree of CIELAB hue is three and a half degrees of the appearance model's, and a unit that counts hue that finely there spreads the blue's directions apart until the corner is nearly a face.
Matching and measuring
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.
What the eye does
A macula three nanometres short is a lens band
Two colour-matching sessions can fit a band of extra absorption in an older lens, its size and its centre, and the test proposed for real older observers was to count those with a band more than twice its standard error. That test assumes a significant band can only be a band. The observer model's macula peaks at 460 nm; a real one is two carotenoids whose mix moves its peak by a few nanometres. Simulated with its macula peaking three nanometres short and no band at all, an observer at sixty is fitted with a lens band of 0.06 at 438 nm, three standard errors, and noisy sessions find it in nineteen of twenty experiments. Six nanometres short, the phantom is larger than the band the earlier essays searched for. The confusion runs both ways: a real band fitted with the macula's peak free reads as a macula two to three nanometres short. Neither fit alone can tell them apart. Comparing the two can, with two sessions — never preferring the macula for a real band, and preferring it in sixteen to nineteen experiments of twenty for a short macula.
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 a camera does
New LEDs miss the line their cousins drew
An ambient-light sensor's three departures can estimate a camera's colour error under a lamp, and merging radiators and white LEDs into one smooth family brought that estimate to ±0.127 over fifty-four lamps, each left out in turn. Every one of those lamps had relatives in the pool. Fourteen lamps the census never saw test what the relatives were worth. The prediction was that new smooth lamps would land on the line and tinted incandescents fall off it by four tenths or more. The radiators and daylights land on it, within ±0.13 each. The tinted lamps do too — the pink-glass incandescent, placed among the LEDs by its nearest neighbour, misses by 0.12. The lamps that fall off are the new white LEDs: ±0.20, half again the census's error, two of them by a quarter. Their misses follow the sensor's 640 nm channel at a slope of −0.72, explaining four fifths of their scatter, because the line learned what that channel means from LEDs varied only in their blue pump. Adding the fourteen to the pool does not help.
Matching and measuring
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.
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 it takes to deliver it
A knee in the ink limit quiets the shadow
A cap on total ink coverage quiets a four-ink table's shadow, and the one segment where the cap is first reached is quiet or loud depending on where the binding point falls among the table's nodes: inside a segment it is quiet, within a quarter of a segment of a node it is not. A real cap is approached through a knee. The prediction was that a knee as wide as a segment would make the binding segment quiet wherever it fell, and that a knee much wider would turn the cap into a steep straight black that casts like the heavy-black strategy. The first half holds only in part: a five-unit knee halves the binding segment's cast and quiets three of the nine loud ones, but those whose binding point sits within a quarter of a segment of a node stay louder than a neighbour. The second half is wrong in sign. A wider knee leaves the whole capped shadow quieter at every step — its mean cast falls from 11.5 thousandths to 3.0 at fifteen units — because a knee spreads the chromatic inks' forced descent, and a slower descent is one the table's straight lines between nodes can follow.
381 essays on this thread, page 13 of 16 · all threads · all essays