Every essay — page 6
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What the brain does
Constancy, adaptation and simultaneous contrast — the reasons a patch of known radiance still has no determined appearance.
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.
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.
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.
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.
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.
A light ink can cancel the glow at one strength
A pale tint on brightened paper keeps a hue turn a reader fully adapted to the sheet cannot remove, and nine tenths of it survives every screen, because it is the tint's bare paper glowing beside ink that puts the glow out. A light ink — the same pigment diluted, printed over more of the paper — was the proposed lever, and the prediction that a quarter-strength ink lowers a five-per-cent orange's residue by a third. It does not lower it; it reverses it, from −7.2 degrees to +10.2. Somewhere between, the residue passes through nought, and for every one of eight pigments there is a strength that cancels it: 0.41 for the red, 0.54 for the orange, 0.80 for the blue and the cyan at a five-per-cent tint. The cancelling strength moves by under a tenth from five per cent to forty, so one ink per pigment keeps every pale tint within a degree and a quarter to twenty per cent, where full-strength ink leaves up to nine. The lever is real; it has a setting, and the light inks printers carry are diluted past it.
One light ink serves three papers within two degrees
On brightened office paper a pale tint keeps a hue turn even for a reader fully adapted to the sheet, and each pigment has one light-ink strength — the pigment diluted and printed over more of the paper — at which that residue vanishes. The prediction for a printer with several stocks was that the cancelling strength falls as the brightener loading rises, and that the office sheet's ink leaves a premium sheet's pale tints within two degrees and a lightly brightened sheet's within one. The strength does fall, at every step and for every pigment — by a fifth for the orange and the yellow, by under one per cent for the green. The office ink keeps the premium sheet within 1.8 degrees, as predicted, but the light sheet only within 1.8 too: it overshoots there, turning seven of eight pigments' residues past nought the other way, and falls short on the premium sheet for all eight. Either way it removes more than four fifths of what the full-strength ink leaves.
An ink for a fading sheet is set for its middle age
A light ink cancels a pale tint's residual hue turn on brightened paper at a strength that falls along a straight line in the sheet's glow, and a brightener bleaches with use, so a sheet's glow falls over its life. The prediction was that as the premium sheet's brightener bleaches, every pigment's cancelling strength rises back along that line, and that the fresh sheet's ink stays within two degrees until half the brightener is gone. Both hold. Bleached by a quarter, a half and three quarters, the premium sheet asks for strengths within 0.015 of the census line at its glow, always on or just below it; the fresh premium ink errs by 1.75, 1.80 and 2.35 degrees at worst. But the office sheet's ink, set for a glow the premium sheet passes through on its way down, keeps the bleaching sheet within 1.4 degrees at every stage after the first. An ink set for the sheet's middle age outlasts one set for its first day.
A yellowing base leaves the ink where the glow put it
A light ink cancels a pale tint's residual hue turn on brightened paper at one strength for each pigment, and as a premium sheet's brightener bleaches that strength rises back along the straight line in glow through three census sheets — a shade under it, by up to 0.013. Real photo-ageing yellows the base paper as well, and the prediction was that a base yellowed in step lifts the strengths onto the line within 0.01 and that the office sheet's ink still holds every residue within one and a half degrees. The ink holds, at 1.38°, 1.13° and 1.38°. The strengths do not lift: no pigment's moves by more than 0.0023, and its gap under the line by more than 0.0006. The yellowing raises the sheet's b* by 0.31 at most while the bleaching raises it by five. And the gap was never the base's: the office sheet itself sits 0.016 under the line, deeper than any bleached sheet. The line is a chord across a sagging curve.
The glow alone sets the light ink
A light ink cancels a pale tint's residual hue turn on brightened paper at one strength for each pigment, and that strength falls with the share of the sheet's luminance that is glow — along a curve, not the straight line through three census stocks, which runs as much as 0.016 above it. The prediction was that the strength is one curve in the glow whatever the stock: that a premium sheet bleached until its glow equals the office sheet's, or the light sheet's, needs that sheet's ink within 0.003 for every pigment. It needs it within 0.0007, though the two papers differ in base, in whiteness and in how much of the brightener their ink shields. Traced across eleven loadings of the premium stock, the curve runs through every census sheet within 0.003, sags under every chord, and falls five to nine times as steeply on a dim sheet as on a bright one for the orange, red and violet.
The glow's colour sets the blue ink and spares the orange
A light ink printed on brightened paper turns in hue, because the paper's glow passes through the ink's open area differently from the ink's own film, and a cancelling strength undoes the turn. Every sheet so far glowed with one brightener, and its ink was set by the glow's amount alone. The prediction was that a brightener emitting fifteen nanometres longer, nearer the blue and violet inks' hues, moves their strengths by more than a hundredth and the orange's and red's by under a fifth of that. It does: the blue's strength rises from 0.81 to 0.98, because a glow at the blue's own hue barely turns a blue tint, the violet's falls by 0.06, and the orange moves by a thousandth though the glow's share of the sheet's luminance nearly doubles. A brightener emitting fifteen nanometres shorter moves every ink, the orange by 0.04, and no curve in the glow's luminance reads any of them.
The glow's pull on the white sets every ink
A light ink on brightened paper is diluted to cancel the hue turn the paper's glow gives its tints, and on sheets that all glow with one brightener its strength is a single curve in the glow's share of luminance. Move the brightener's emission and that curve fails by up to 0.21. The prediction was that two numbers — the share and the glow's chromaticity — read every ink within a hundredth. Across thirty sheets, eight of them a grid of emission peaks from 420 to 455 nm, they miss by up to 0.07, and the share alone misses the blue by a quarter. The two numbers that work are the glow's pull: how far, in Oklab, it moves the paper's own reflection to the white an adapted reader sees. Read with their squares, they set every ink within 0.014 — and the warm inks need least strength just short of where that pull is strongest.