Delivery — the series
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A halftone is not a mixture
Forty per cent cyan and thirty per cent magenta are not stirred together anywhere. They are laid down as dots, and the sheet is a mosaic of four fully-inked regions in proportions the two coverages fix — which is why the colour is an area average of four spectra rather than a blend of two, and why it lands nowhere near where mixing would put it.
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A profile is a table
An ICC profile does not contain a model of the device it describes. It contains a lattice of patches that were printed and measured, and everything between them is interpolation — which is exactly zero at every patch, so a profile checked against its own target reports perfection for ever.
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A dot is larger than it was asked to be
Two quite different things make a printed midtone darker than its coverage says — ink spreading under pressure, and light scattering sideways inside the paper. Both bend the tone curve the same way and neither touches its ends, so the measurement every press is characterised by cannot say which happened. A patch that nobody measures can.
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Neither gamut contains the other
Converting a picture to CMYK is described everywhere as a reduction, as though the press were a smaller version of the screen. Measured as solids, the press reaches eleven per cent of its volume outside sRGB while sRGB reaches fifty-four per cent of its volume outside the press — and in the cyans the press wins by seventy per cent of chroma.
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The paper is the white point
A printed colour is reported against the sheet it sits on rather than against the light in the room, and the choice is a switch in every colour engine. Flipped one way, the same separation on coated stock and on newsprint is a 3.04 colour difference; flipped the other, it is 0.13 — and the two answers are about different questions.
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The fourth ink is not for colour
Black is in every process set and it extends the gamut by more than a third — and at every lightness above about forty it extends the chroma boundary by exactly nothing. What it buys is depth at the bottom, a neutral that holds its hue when the press drifts, and a way to put a full-strength dark on a sheet that could not carry three inks' worth of it.
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A black that is not black
The deepest colour a four-colour press can make is L* 2.4, and against its own paper that is a contrast of about 320 to 1 — less than a cheap display manages in a dark room. Everything a printed picture does in the shadows is done inside that range, and the two ways of fitting a picture into it destroy different things.
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The separation is not unique
A four-ink press has one more control than a colour has numbers, so most colours can be printed several ways. The alternatives agree to a hundredth of a colour difference under the light the match was made in — and they are metamers of one another, so under a tungsten lamp the same eleven separations of one colour spread by nearly seven.
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No mapping preserves everything
More than half the sRGB solid is outside a press's gamut, so something has to be done with it, and there are two things that can be done. One leaves every reproducible colour exactly where it was and delivers a gradient as a flat area. The other keeps the gradient and moves every colour that needed no help by about three.
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The lamp in the shop decides
Two packages printed to the same specification, verified under the same standard illuminant and passed, can differ by nearly seven colour differences on a shelf under a tungsten lamp. Nothing went wrong at either press. The specification named one light, the separations that satisfy it are metamers of one another, and the shop chose the second light.
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A brand colour is an ink
A named colour is a jar of pigment with a spectrum, and a four-colour build of it is three inks arranged to integrate to the same three numbers. Of 156 constructed single-pigment inks, 15 can be matched at all — and those fifteen drift by a median of 3.8 colour differences under a tungsten lamp, because the match was never a match.
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The fifth ink buys a corner
Orange, green and violet are sold as the answer to a four-colour press's gamut, and each one adds seven to nine per cent of volume. All three together add 23 per cent — almost exactly the sum, with no interaction — and every bit of it lands in the region of the ink that was added, at lightnesses where that ink is dark.
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The proof is a different object
A soft proof can be made colorimetrically exact and still not match the print, because the print is in a booth at two thousand lux with an average surround and the screen is in a dim room at a fifth of the luminance. The appearance model puts four CAM16-UCS units between them, with no change of stimulus anywhere — larger than the error any rendering intent is arguing about.
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The screen is not the room
A thousand-to-one display in an ordinary office is a hundred-and-thirty-seven-to-one display, and the signal value that means black comes out at the lightness of a dark grey card. Nothing is wrong with the panel. Light falls on the screen and comes back off it, and the two per cent it returns is added to every pixel — most of all to the ones with nothing else in them.
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Colour thrown away on purpose
Every video format in use discards three quarters of its colour information and keeps all of its luminance, because the eye resolves fine colour detail badly. On an edge that carries luminance the loss is exactly zero. On an edge of nearly equal luminance it is a colour difference of forty-three, and the two edges are the same edge to the codec.
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The booth is a luminaire
A standard viewing booth is specified by its light's chromaticity, its rendering and the uniformity of its illuminance across the sample plane. Illuminance is a photometric integral, so two positions can be inside the uniformity tolerance and lit by two different spectra — and a sample at the far corner of a compliant booth is ΔE00 2.4 from one in the middle, against a tolerance of one.
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Measured with an aperture, seen with an eye
A spectrophotometer averages a halftone patch and reports one reflectance. An eye blurs it first and compresses afterwards, and the average of a concave function is below the function of the average — so a resolvable screen looks darker than it measures, by fourteen lightness units at a coarse ruling and by nothing at a fine one. The correction a press applies is the same size and has no viewing distance in it.
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Dividing by the paper
Media-relative colorimetry divides tristimulus values by the substrate's, which is a von Kries adaptation applied in XYZ — the one basis the table here describes as the oldest mistake still shipping. On a paper-mill white it costs a few hundredths of a unit. On a tinted sheet it costs ten times what the same rule costs in a cone basis.
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A proof cannot glow
A proof is a different sheet of paper pretending to be the production one, and the pretence works by adding ink until the two agree. It cannot work for a brightened stock, because the direction the proof has to travel is towards more blue at the same lightness and every ink a proofer owns moves it towards less light instead.
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An instrument brings its own light
ISO 13655 names four measurement conditions and they are usually read as four degrees of care. They are not. They are four different quantities — on an unbrightened sheet all four agree to a rounding, and on a brightened one they are up to seven and a half units apart, with every instrument in calibration and every answer correct.
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A profile is a fit between its nodes
A printer profile is a table, exact at every patch that was printed and interpolated everywhere else — and everywhere else is where every job lives. Going from a hundred and thirty-five patches to three and a half thousand is twenty-seven times the work for eight times the accuracy, and the exponents say that is as good as it gets.
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Primaries chosen for their inverse
Moving a display's white point is a gain on its R, G and B, so a display adapts in the inverse of its own primary matrix — a basis chosen by committees for gamut coverage and phosphor availability. Pose the design problem properly and the answer costs one per cent of the gamut argument and reaches within two per cent of the best basis there is.
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The slope arrives before the bowl
The adaptation transforms colour management actually uses are not optima of anything. At every one of them the objective has a slope, and the slope is the larger term over almost the whole distance to the best matrix — so a table of curvatures taken there describes a bowl nobody meets on the way anywhere.
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A delivery tolerance is three tolerances
A colour reaches a reader through a profile, a gamut mapping and a room, and each has a number somebody chose. Each has an essay of its own here, and none of those essays had put the three costs in one column. Put there, the stage nobody controls carries ninety-seven per cent of the total.
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Best on the average, undefined at the edge
Bradford has the lowest mean residual of any adaptation transform over the census of illumination changes, which is why colour management uses it. Inside the family that census was drawn from, its middle row's reading of the white passes through zero — so the gain is a division by nothing, and the model stops being defined rather than merely doing badly. CAT16, which exists because its predecessor did this, does not.
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A tolerance is a region
How far a display's red primary can move before its adaptation behaviour costs anything is not a distance. It is a closed region on the chromaticity diagram, fifteen times longer one way than another, and about half of it lies outside the area a real primary can occupy — where the objective does not rise and the primary cannot go.
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Downhill from a published matrix
Walking steepest descent from each adaptation transform in use closes between a quarter and nine tenths of its distance to the best one, and most of that in the first step. The direction it sets off in is eighty to eighty-seven degrees away from the answer, and that turns out not to be an artefact of the three directions nothing can see.
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A budget drawn through one hue
The three-stage error budget this collection publishes for a colour-management chain is computed over twenty-four colours of a single hue at a single lightness. The quantity that actually varies with hue — how many distinguishable colours a rendering intent destroys — runs from nothing at all to more than a third, and the hue the budget uses is near the bottom of that range.
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A tolerance is a boundary through pairs
Twenty-four pairs of surfaces built to sit exactly on a ΔE2000 tolerance of one read from 0.69 to 1.93 in the other five units. A contract quoting "one unit" without naming the formula does not become slightly wrong in another; it accepts and rejects a different set of deliveries, and in one case rejects every single one.
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An aperture is a filter
A measuring aperture throws away the light that came back outside it, and the light that comes back furthest is the light at the wavelengths the sample absorbs least. So an aperture does not attenuate a translucent sample evenly — it attenuates its peaks more than its troughs, which is a filter whose transmission curve the sample itself decides.
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Either disc can be the wide one
Every standard on translucent samples says to illuminate a larger area than is measured, and explains it by saying that light leaks out of the lit spot. That is true and it is not the reason, because the instruction works equally well the other way round — measuring a larger area than is lit gives a reading just as exact. The error is a product of two apertures and either one being wide kills it.
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A dial has a price
Two rounds declined to give the appearance model's surround a continuous control, both times because the frames would be too heavy, and neither time was the weight taken. It is 2.25 kilobytes at the median — the light end of these figures rather than the heavy end — and one figure is already breaking the rule the deferral was made under.
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Which index to buy an instrument for
Four departures from the colour integral, ranked by what they cost and by what it would take to remove each one. The ranking by cost and the ranking by price are almost exactly reversed — the two largest are removed by specifying a lamp and by widening a table, and the two that need new hardware are the two smallest.
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The instrument is one observer exactly
A spectrophotometer has no observer uncertainty. It computes through the 1931 tables to the last bit, reproducibly, forever — which is its whole value and is also why it cannot report the three colour differences of observer spread between itself and whoever is looking at the sample.
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The booth and the eye disagree
A viewing booth is specified to simulate daylight, and daylight is the light under which observers disagree least. So a booth is the condition in which a specification is least likely to be tested against the thing that breaks it, and the shop it will be judged in roughly doubles the term.
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A brand colour for a population
A brand colour is chosen once, specified in a number, and seen by everybody. The observer audit says two candidate colours with identical specifications can carry observer spreads differing by an order of magnitude, and that the spread is computable from an ink's spectrum at the moment the ink is chosen.
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The budget adds two units
This collection publishes a three-stage error budget for a colour-management chain and prints its sum. Two of the three stages are colour differences between stimuli and the third is a distance between appearances, and the conversion between those is not a constant. Re-measured in one unit over the same colours the chain has four stages rather than three, its end-to-end error is 5.05 against a sum of 7.66, and the profile's contribution where a job actually lands is 3.2 times its published average.
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An average on the stored values
A resize, an antialiased edge, a transparency composite and a chroma subsample are all averages, and in almost every pipeline they are taken on the numbers as stored. The numbers as stored are encoded, the encoding is a compression, and a half-and-half blend of black and white taken that way lands 18.7 colour differences from the half-and-half blend of the light — 22.7 units of lightness darker, on every pair, always in the same direction.
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An intent is not a function of the colour
A rendering intent is chosen per job and applied per pixel, which suggests it is a function of the colour. The colorimetric ones are, exactly — the same colour from two documents comes out identical to the floating-point floor. The perceptual one is not — it compresses the whole source solid into the destination, so the same colour delivered from a wide document and from a muted one lands 2.6 colour differences apart, on colours the destination could hold either way.
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A chain measured in a unit that cannot add
A delivery chain's four stages, measured in the power-corrected appearance difference, sum to 7.66 while the chain end to end measures 5.05, and the shortfall was read as the stages partly cancelling. A chain whose four stages lay in a straight line and added exactly would still read 0.74 of its sum in that unit, because a distance raised to the power 0.63 cannot add. Measured in the model's own Euclidean space the same chain reaches 0.84 of its sum. Three quarters of the published shortfall was the exponent.
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A second conversion is not a repeat
A colour converted to a device and back is described as lossy where the device cannot hold it and exact where it can, which suggests that a colour surviving one round trip survives any number. One of the four intents is idempotent to the floating-point floor. The other two are not — a perceptual conversion moves a ramp 3.70 colour differences on its first pass and another 2.73 on its second, and after three passes it is still moving by 2.42.
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A resize with a negative weight in it
A blend taken on stored values is always darker than the blend of the light, because the encoding is concave and a convex combination of a concave function's values lies below the function of the combination. A bicubic or Lanczos resize is not a convex combination. Beside an edge its negative weights make the stored-value result lighter than the light's own — by up to 6.1 colour differences with bicubic and 12.2 with Lanczos on skin against its shadow — and on edges between full-scale values the clip hides the overshoot and the old guarantee appears to hold.
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A soft proof is exact for one reader
A display can be driven to match a printed patch exactly for the standard observer — three equations, three unknowns, agreement to fourteen decimal places. Two hundred observers drawn from a realistic population see the same screen and print a median of 2.1 colour differences apart on an OLED panel and 5.4 apart at the ninety-fifth percentile. On a laser projector the ninety-fifth percentile is 7.5. The patch that fails worst is unprinted paper, and in the chain's own unit the ninety-fifth percentile reader's stage is larger than every one of the four stages a delivery chain is budgeted for.
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The corner of a resized patch is lighter than its edges
A resize taken on stored values is darker than the resize of the light wherever its weights are positive, and lighter beside an edge where a kernel's negative lobes fall. In two dimensions the kernel is a product, and just outside a patch's corner a Lanczos magnification of skin against its shadow comes out 14.5 colour differences lighter — more than along either edge. A reduction to a quarter is mostly an average and errs lighter by at most two. And an unsharp mask, whose negative weights are its whole purpose, is lighter on the stored values at every amount on every pair, and never darker.
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A proof cannot be tuned for readers who disagree
A soft proof matched exactly for the standard observer is five colour differences wrong for one reader in twenty. Giving up that exactness to tune the display's three drives for a population instead moves the ninety-fifth percentile reader by 4 to 14 per cent even when the tuning is done on the very readers it is scored against — because what readers see is mostly each other's disagreement, and three drives act on every reader at once.
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The eye keeps the lightness errors
Four essays have priced what a resize taken on stored values costs, in colour differences between pixels. A reader does not see a pixel. Put the two versions of each image through the visual system's own three channels and the ranking reverses: the unsharp mask, the largest error per pixel at 16.6, is seen at 6.3 on a printed page, while the corner's 7.1 is seen at 9.9. What decides it is not the size of an error but how much of it is colour.
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A profile interpolates light
A profile is exact at its patches and wrong between them, and how wrong has been measured twice. Which way it is wrong has not. At a nine-step lattice the mean signed lightness error between the nodes is +0.136 against a mean colour difference of 0.133 — the error is not a scatter but a bias, and it lightens. The repair costs nothing measured and is forbidden by how a profile is checked: let the table be wrong at its own patches.
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The scale hangs from one measurement
Black point compensation is a straight line between two blacks, and the destination's is a measurement of one patch at the darkest place a spectrophotometer is ever asked to read. The lightness scale's slope is 903 units per unit of luminance factor there and 43 at the paper, so a thousandth of a reflectance is worth nine tenths of a lightness unit at the black and four hundredths at the white. That one number moves a mid grey by nearly a quarter of a delivery tolerance, and no specification names it.
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The inverse table errs dark
A profile's forward table predicts a print lighter than the press makes, and refitting its nodes removes the bias. The table a colour engine actually uses to separate an image is the other one — the inverse, from colour to ink — and it errs the opposite way: filled exactly from the press it asks for too much ink and prints dark, and built by inverting the ordinary forward table it prints darker still. Inverting the refitted forward table removes the inherited part and leaves the inverse's own. The round trip through both tables improves only when each is refitted against its own error, and then the two are no longer each other's inverse.
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The eye counts a corner's error, not its peak
A Lanczos-magnified patch errs a fifth more at its corner than along its edges, pixel by pixel, and an unsharp mask errs almost exactly as much at its corner as along its edges. Filtered by the eye over the plane rather than along a line, the two swap: the magnified corner is seen exactly as its edge is, and on a printed page the sharpened corner is seen at 2.4 times its edge. What decides it is whether the error changes sign. Ringing averages away and a one-sided halo does not, and a corner is where two edges' halos land on the same patch of retina.
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Sharpened type errs on its dark side
A sharpened square hides its halo along its edges and shows it at its corners, so a sharpened page of type was predicted to show its error at the corners of its letters, several times out of proportion to their length. Black type does the opposite: its outer corners and stroke ends hold between two thirds and nine tenths of their share. As the eye leaves it, the error lies on the dark side of every edge, and a corner holds as much of it as it has dark ground around it — a quarter of a disc where a black corner points out into paper, three quarters where black wraps round a pale one.
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A strategy keeps the refit only where black prints
Refitting an inverse table's nodes against their own error halves it, and in a four-ink table the refit has to leave the separation strategy's choice of black alone. Held to the strategy, it keeps the whole of its gain wherever the strategy prints black and almost none of it where the strategy does not — and the share it keeps equals the share of the grey ramp printed with black, to within three hundredths. The start of black generation, predicted to be where the refit would fail, is where the table needs it least.
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A serif moves the error and adds little
When a scanned page is sharpened on its stored values, the error the eye sees lies on the dark side of every edge, so black sans-serif type does not gather it at its corners. The worry was that a serif changes that: every stroke end gains a bar and every bar an inside angle, the configuration where large letters did gather error. It does not. Black serif type's brackets hold three quarters of their share of the error and its serif tips half. Reversed, the serif tips hold two and a half times theirs. Across both, serifs lengthen the outline by a tenth and the error by a few per cent — they move it, and in black type away from the corners.
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A little black ends the cast
A four-ink inverse table errs by a warm cast along the grey axis wherever the separation strategy prints only three inks, and almost only in lightness wherever it prints black. Real strategies start black gently, and the gentle start was expected to keep the cast until black carried much of the grey. It does not. The cast falls to a tenth of its three-ink size once black supplies a tenth to a sixth of the grey's darkening, at every toe from nothing to thirty units wide — because inside the toe the table's chord runs along the trade of black against the other three inks, which errs in lightness. What the toe does cost is the segment where black begins, which goes from the table's best to its worst.
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A hairline spills its error onto the paper
Sharpening a scanned page on its stored values errs on the dark side of every edge, which is why black type's serifs hold less than their share of the error at text sizes. A hairline serif, a tenth of a stem, was expected to change that at display sizes: its dark side is so thin that the halo would wrap its corners. It does not. From 12 to 48 point, black type's hairline tips hold a third to three fifths of their share, less than slab serifs' tips, and the share falls as the letter grows. What gathers at display sizes is the junction of bar and stem, with or without serifs — and where the scan lands the letter against the pixels moves a tip's share more than its size does.
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The cast returns where black is steep
Below a black-generation toe a four-ink table's grey picks up a small cast again, up to a third of the three-ink cast at the widest toe, and the explanation offered was the jump in black's curvature where the toe ends. It is not. A toe whose curvature is nothing at its end returns exactly the same cast, segment for segment, and a kink put into straight black casts in its own segment once in twelve tries. What the returned cast follows is how steep black has to be once the toe is done — how far the chromatic inks climbed while black was held back, and how fast they then have to come down.
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An ink limit takes the shadows' cast away
A cap on total ink forces black up and the chromatic inks down where it is reached, which is the descent that brought a small cast back below a black-generation toe, and the prediction was that a cap would bring one back too. Measured against what the same strategy prints with no cap, it does the opposite. Below where it binds the cap decides the separation outright — nine strategies print one table there — and in 32 of 33 cases its shadows cast less than the strategy's own would have.
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A junction gathers by the width of its stem
Black type sharpened on its stored values gathers its error at the junctions of bar and stem, and gathers more as the letter grows. The mechanism offered for that was the stem growing past the eye's pool, which predicts that size is only standing in for the stem's width in pixels. Drawn at three weights and five sizes, the junctions' share ranks with the stem's width at 0.97 and with the point size at 0.85, and where two weights have stems within six tenths of a pixel of each other their junctions agree to within a tenth. The width is nearly the whole story. The part it leaves over is small and one-sided: at the same stem width, the heavier letter gathers a little more in five pairs of six.
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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.
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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.
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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.
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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.
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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.
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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.
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Shared nodes belong in the deep shadow
Three nodes placed just below where each dark colour's ink reaches the press's cap cut a four-ink table's dulling of that colour by a third — but a profile's nodes along lightness are shared by every colour, and the colours' caps bind anywhere from L* 15 to 31. The prediction was that one shared placement keeps two thirds of the own-placement gain on a deep-blue ray and all of it on a brown. Placed once, one to three units below the median binding point, the nodes keep 63 per cent of the blue's hard-cap gain and 92 of the brown's — and the averages hide a split. Every colour whose cap binds more than two and a half units below the shared nodes keeps under a twentieth of its own gain; every colour whose cap binds more than two units above them keeps more than all of it, up to four times. For those colours most of the dulling was never at the cap's corner: it lies in the deep shadow, where black keeps climbing under the cap, and the shared nodes sit there. Spreading the three nodes across the binding points buys nothing three even nodes would not.
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Easing the cap reaches the deep shadow and no higher
A four-ink table prints dark saturated colours duller than asked between its nodes, and for colours whose ink reaches the press's total-ink cap high up the dulling lies mostly in the deep shadow below L* 20, where black climbs under a held total. The proposal was to let the total fall below the cap there, and the prediction was that easing the cap by a tenth or a fifth between L* 20 and the floor halves those colours' dulling on even nodes — more than three shared nodes do — at a cost of a unit or two of L* in the darkest colour the press can reach. There is no cost: every eased table still prints the floor at L* 14. Eased by a fifth, the deep-blue ray's dulling halves and the brown's falls to an eighth. But the eight colours that bind above L* 26 keep three fifths of theirs: the ease removes two thirds of their deep-shadow dulling and none of what lies between their binding point and L* 20. And the eased cap does not let black rise less steeply — it makes black rise faster.
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A higher ramp trades one shadow for another
Easing a four-ink table's total-ink cap by a fifth on a ramp from L* 20 to the floor halves the dulling of dark colours whose cap binds low, and leaves the colours that bind high with three fifths of theirs, because most of what is left lies between their binding point and L* 20, above the ramp. The prediction was that a ramp starting at L* 32 halves the high binders' dulling, at a small cost to the low binders. It does neither. Started at L* 26, the same fifth's ease does cut the high binders' upper dulling by more than half — the cap was its cause after all — but their deep-shadow dulling comes back to more than twice what the L* 20 ramp left, and their total is unchanged at 0.0052. The low binders give back nearly everything: on the brown ray from almost nothing to 0.0084 with the ramp at L* 32. Every ray, knee and group does best, or within a fiftieth of best, with the ramp at L* 20.
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A bent ramp takes more ink and dulls more
Easing a four-ink table's total-ink cap by a fifth on a straight ramp from L* 20 to the floor straightens the deep shadow's bend and halves the dulling of dark colours, and a ramp started higher trades the deep shadow's cure for the upper stretch's. The prediction for a ramp bent at L* 20 — a quarter of the ease spent between L* 32 and 20, the rest below — was that it keeps nearly all of the deep shadow's cure while taking a third off the high-binding colours' upper stretch, their total falling by a fifth. The bent ramp takes at least as much ink as the straight one at every lightness. It dulls every group more. The high binders' upper stretch improves by a sixth; their deep shadow loses half its cure, and their total rises from 0.0052 to 0.0060; the brown's low binders, left with almost nothing by the straight ramp, keep 0.0039. The deep shadow's cure follows how steeply the cap falls below L* 20 — a fifth of the cap over six units, not three twentieths — and not how much ink is taken there.
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A steeper ramp cures the shadow by overshooting it
A four-ink press's total-ink cap dulls the deepest colours it binds, and easing the cap by a fifth on a straight ramp from L* 20 to the floor halves the deep blue's dulling. A ramp bent to take more ink above L* 20 dulled every group more, so the cure seemed to follow how steeply the cap falls below L* 20. The prediction was that a ramp steeper still — the whole fifth spent from L* 17 — cures more. Read as the census has read every ramp, by the mean chroma lost, it does: every group dulls less at each step from L* 20 to 18.5 to 17. But the brown's low binders cross nought: their prints come out more chromatic than the colour asked, by as much as 0.07, and read by the error's size the brown ray's mean error more than doubles. The measure that ranked every earlier ramp was signed, and a signed measure cannot see an overshoot. Eased by a tenth, the steep ramp is no worse anywhere and better on three cases of four.
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Each dark ray wants its own ease
Easing a four-ink press's total-ink cap below L* 20 cures the dulling of the deepest colours it binds, and a steeper ramp — the whole ease spent from L* 17 — cures more on the signed mean, but eased by a fifth it prints the brown ray's low binders up to 0.07 more chromatic than asked and more than doubles the brown's error read by size. The prediction was that three twentieths from L* 17 is the ease the steep ramp wants: below every earlier setting on both rays. The brown still overshoots, by 0.039, and errs nearly twice as much as on the gentle ramp. The overshoot follows one number — how fast the eased cap gives ink back per unit of lightness — and the two rays want that number set differently. Hard, the blue errs least on three twentieths from L* 17 and the brown on three twentieths from L* 20; the brown's best costs the blue a fifteenth more error, the blue's best costs the brown four fifths more.