A black that is not black

A printed black looks black because there is nothing blacker on the page. Measured, it is a dark grey, and how dark depends on decisions that are made for reasons having nothing to do with how it looks.

The claim #

A reflective print has a lightness range of about 320 to 1 in luminance factor, the bottom of that range is set by how much ink the sheet will take rather than by the ink’s density, and fitting a picture into it is a choice between destroying the shadow levels and moving everything else.

What a black measures #

Four different things get called black on a press, and they are two lightness units apart in the wrong direction.

A hundred per cent of black ink on its own is L* 15.9, which is a dark charcoal. It looks black on a page because it is the darkest thing there, and set beside a rich black it is unmistakably grey — which is why any designer who has printed a large solid area has learned to add the other three inks underneath it, usually without a clear account of why it works.

The account is Beer–Lambert. Optical density adds, so a second film underneath the first multiplies the transmittance again; a single ink at density 1.7 through a double pass gives a reflectance factor near 0.02, and three more films take it below 0.003. The last factor of six in a printed black comes from ink that has nothing to do with being black.

The limit that is not about colour #

Which brings the argument to the constraint that decides the bottom of the range, and it is a constraint about liquid rather than about light. A sheet carrying too much ink will not dry: it offsets onto the next sheet, it curls, it blocks in the stack. Every printing condition therefore specifies a total area coverage limit, and it is usually between 240 and 320 per cent.

What it costs, measured:

Two things in that table are worth reading before the conclusion is drawn from it, and the first is an impossibility.

The 340 per cent row reports a larger gamut than the 400 per cent row. A tighter ink limit is a strictly smaller feasible set, so its image can only be a subset — the volume cannot go up. The difference is a hundred units out of four hundred thousand, 0.025 per cent, and it is the voxel estimator’s own noise arriving where it is visible.

That is worth having rather than tidying, because it calibrates everything else in the column. The measurement is good to about a hundred units, so the headline loss of 3,500 between 400 and 240 per cent is thirty-five times the noise and entirely safe, and the 1,000-unit step from 300 to 260 is ten times it and safe as well. A monotonicity violation is the cheapest error bar a table can give itself, and this one says the conclusions survive it by more than an order of magnitude.

The second is that the cost accelerates sharply. Dividing each step’s volume loss by the lightness it gave up:

The fourth lightness unit costs seven times what the first one does. The explanation the essay gives for the limit being cheap — that everything down there is nearly the same colour, so the region is thin — is right at the very bottom and stops being right almost immediately. The slices widen fast: at L* 2.4 the press’s solid is a point, and by L* 5 it has real chroma in every direction, so each further unit of black point removes a substantially larger slab.

That changes the practical reading. An ink limit is nearly free down to about 260 per cent and is not a smooth trade below it. A shop moving from 300 to 260 gives up a quarter of a per cent of the gamut; moving from 240 to 200 gives up five and a half, and it is the same two-unit shift in black point either time. The printer’s instinct that the limit is not something to relax casually is correct, and correct for a reason that only appears once the marginal cost is separated from the total.

It also puts the newsprint case in its place. Newsprint’s 240 per cent sits just past the knee — it has spent 0.86 per cent of the gamut and the next forty points of limit would cost another five. So the standard limits in use are not arbitrary round numbers scattered across a smooth trade; they cluster on the flat part of a curve that turns steeply just below them.

Dropping from 400 per cent to 240 — the difference between a coated sheet and newsprint — costs 0.9 per cent of the gamut and one lightness unit at the bottom. Dropping to 200 per cent costs 5.6 per cent of the gamut.

That is a much smaller effect than the number suggests, and the reason is CIELAB’s compression at the bottom. Between L* 2.4 and L* 3.4 there is a luminance factor ratio of 1.4, and the region of colour space between them is thin, because everything down there is nearly the same colour. A limit that removes 40 per cent of the ink removes one per cent of the colours, and the printer who resists relaxing it is right for a reason that has nothing to do with gamut.

The whole range, and what it compares to #

Paper at L* 94.8 is a luminance factor of 0.872. The deepest four-ink black at L* 2.47 is 0.0027. The ratio is 319:1.

That is the entire dynamic range available to a printed picture, and it is worth putting beside the numbers this site has quoted for emissive media. A display encoding absolute luminance is specified up to 10,000 candelas against a black of a hundredth, which is six decades; an ordinary display in a dark room manages a thousand to one; and the same display in a lit room manages 137 to 1, which is less than the print.

The last of those is the useful comparison, because it is the honest one. A print and a screen are both looked at in a room, and the room is what sets the black of the screen while the ink sets the black of the print.

The two ways to fit a picture in #

A source picture has tones below the destination’s black. There are exactly two things that can be done with them, and both are lossy in different currencies.

Clip. Everything darker than the destination black becomes the destination black. Tones above it are untouched — a mid grey is exactly where it should be, and every relation between tones in the upper nine tenths of the picture is preserved perfectly. What is lost is everything below the black point, and it is lost irreversibly: several distinct source values arrive as one number, and no later stage can tell them apart.

Compensate. Scale the whole lightness range so the source’s black lands on the destination’s. Nothing is clipped and every source level arrives as a different number. What is lost is exactness everywhere else: a mid grey moves.

Measured on eleven levels spanning the bottom twenty lightness units, into a destination whose black is L* 8:

• clipping keeps 6 of 10 steps as distinct values
• compensation keeps 10 of 10
• each surviving step shrinks from ΔE00 1.30 to 1.24
• and a mid grey at L* 50 moves to 54.0 — a shift of ΔE00 3.95

Between those two destinations there is a continuum, and both ends of it are worth drawing.

At the other end of the same continuum is a destination whose black is lighter than either, which is uncoated stock under a low ink limit.

Neither is right, and the choice is the same one the rendering intents make one rung above, in a different quantity: relative colorimetric clips and perceptual compresses, exactly as clipping and compensation do here. Black point compensation is a gamut mapping restricted to the lightness axis, and it is a separate switch in every colour engine for historical reasons rather than principled ones.

Where the argument gets interesting #

The received advice is that black point compensation should be on, and for photographs it is good advice. The case against it is worth stating because it is the case for clipping in general.

A picture with nothing important in the deep shadows loses nothing to a clip and gains nothing from compensation — and pays the 3.95 ΔE00 shift at the midtone anyway. The shift is not small: it is four times a paint contract’s tolerance, applied to every tone in the picture, in exchange for detail in a region that may be empty.

Compensation is insurance, and it is charged as a premium on the whole picture. Whether it is worth paying depends on the picture’s histogram, which no colour management system looks at.

Where this model stops #

Surface reflection is not modelled and it dominates in practice. Every number here is a diffuse reflectance measured at a geometry that excludes the specular component. A real printed sheet has a gloss, and the light bouncing off its surface adds to everything — which is a whole essay in an earlier field and is the reason a matte print looks flatter than a glossy one carrying identical ink. The 320:1 quoted here is the instrument’s number; the number a reader gets in a room is lower and depends on where the lamp is.

The ink limit is a single number here and is really a curve. Real limits depend on the ink sequence and on where the sheet is in the drying process; a shop will accept 340 per cent in a small area and refuse 300 across a whole page.

Nothing here covers black-and-white reproduction. A duotone or a quadtone splits the tonal range across several inks for exactly the reasons in this essay, and the analysis is the same with the chromatic constraint removed.

And the ΔE00 counts of “distinct levels” carry the usual caution. A ΔE of one is not a fixed perceptual step, and it is least reliable in the deep shadows, which is precisely where every count in this essay was taken. The direction of the comparison is safe; the counts are a formula’s opinion.

How many levels there are to lose #

A digital image carries 256 levels per channel and a press does not carry 256 of anything. It is worth knowing where a printed tone level comes from, because it bounds everything above.

A halftone cell is a small grid of imageable spots, and the number of tints it can produce is the number of spots in it plus one. At a screen ruling of 175 lines per inch on a plate written at 2,400 dots per inch, a cell is 2400/175 ≈ 13.7 spots across, so it holds about 188 levels — fewer than the file it came from, and the shortfall is spent at the coarse end of the tone scale rather than evenly.

Two consequences follow, and both are about the shadows.

The levels are equally spaced in coverage, and coverage is not lightness. The ramp is compressive at the light end and steep at the dark end, so the 188 levels are not 188 equal steps of lightness; they crowd where the curve is flat and spread where it is steep. The deep shadows, where the curve is steepest, get the fewest.

And the last few levels are structurally awkward. A 97 per cent tint is a cell with a handful of unimaged spots in it — a solid with holes — and whether those holes survive the plate, the press and the paper is a question about mechanics rather than about colour. Most printing conditions specify that tints above about 95 per cent be treated as solid for exactly that reason, which removes the top of the ink’s range and, in the shadows of a picture, removes the last distinctions the black point had left.

So the count of shadow levels lost to a clip, above, is an upper bound on what was available to lose. The press had fewer to begin with.

The number a printer would give #

One correction to the arithmetic above, offered in the spirit of the rest of this site. A pressman asked for the contrast of a printed sheet would not say 320 to 1; they would say the solid reads a density of 1.7 or 1.9, and would be quoting a logarithm.

Optical density is $-\log_{10}$ of the reflectance factor, so a density of 1.9 is a factor of 79 and a density of 2.6 — which is roughly the four-ink black here — is a factor of 400 against a perfect white, or about 320 against this paper. The two vocabularies describe the same measurement, and the logarithmic one is better suited to a press because ink density is what an operator adjusts and because density adds when films are stacked, which is the arithmetic of the rich black above.

It is worth being able to move between them. A density difference of 0.3 is a factor of two in reflectance; a density of 0.0 is a perfect white; and the black point of any reflective medium is its maximum density, which for print sits between 1.6 and 2.6 depending on how many films are down.

The generalisation #

The black point of a medium is not a property of its darkest material; it is a property of what the medium will physically tolerate, and it is usually set by a constraint from another discipline entirely.

Print’s black is set by drying. A display’s black is set by the light in the room reflecting off the screen, not by the panel. A photographic print’s was set by the silver’s maximum density and by the paper’s surface. In none of these cases is the limiting factor the one the specification talks about, and in all of them the number quoted on the datasheet is measured in conditions the medium is never used in.

The corollary is the practical one. Ask what the black is in the room the thing will be looked at in, and the ordering of media changes: a print at 320:1 in daylight beats a display at 137:1 in the same room, and the display’s thousand-to-one specification was measured in a darkened laboratory.

Who found it, and when #

The dynamic range of reflective media has been known since the first photographic prints, and the number has hardly moved: a glossy silver print reaches about a hundred to one under ordinary viewing and rather more measured, and modern inkjet on baryta stock reaches a few hundred. Four hundred years of printing technology have not moved a printed black by a factor of two, because the limit is the surface rather than the colorant.

Black point compensation is much more recent and its history is unusually specific: it was introduced by Adobe in the late 1990s as a fix for photographs that came out with blocked shadows, was not part of the ICC specification, and existed for years as a checkbox whose behaviour differed between applications. It was standardised by the ICC in 2010 — a rare case of a workaround being adopted into the specification it was working around, and the reason it is still a switch rather than part of an intent.

Where the ladder goes next #

This rung sits on the halftone, because a black is a full-coverage patch and the ink limit is a constraint on coverages, and on how bright is white, which is the emissive side of the same question about the ends of a range.

Beside it, the fourth ink is not for colour is where the depth this essay measures comes from, and why it takes four inks to reach it.

Above, the choice made here in one dimension is made in three: no mapping preserves everything is the same clip-or-compress decision applied to the whole solid, with both costs measured.