Colour Science & Perception
what the eye settles, and what it cannot
Concept

The Yule–Nielsen exponent — where it appears

The exponent accounting for light that enters a sheet under bare paper and leaves under a dot, and which measures the paper. The exponent is fitted rather than derived, which makes it a description of a particular paper rather than a constant of the process.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A halftone tint, its four regions, and what they average to. At 40% and 30% coverage the sheet is a mosaic of 4 fully-inked regions, not a mixture of anything. Their areas are the product of the coverages — Demichel's rule, which holds because the screens are rotated to make it hold — and the patch's reflectance is the area-weighted average of theirs, raised to the Yule–Nielsen exponent n = 1.8. Averaging the regions' CIELAB coordinates instead, which is what mixing means to almost everybody, lands ΔE00 = 0.76 away.

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.

applied · Delivery Two mechanisms, one ramp, and the patch that separates them. A cyan ramp printed by a press with 10 per cent mechanical gain and a Yule–Nielsen exponent of 2.4. Fitting a mechanical gain at n = 1.0 gives 23 per cent and fitting one at n = 2.4 gives 10 per cent; both reproduce the ramp to under 0.66 of a lightness unit, and the curves lie on top of one another. The two-ink overprint below was in neither fit, and there they are ΔE00 = 3.20 apart.

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.

applied · Delivery What a halftone measures, against what it looks like. A 50 per cent screen, measured by an aperture that averages the patch and seen by an eye that blurs it first and compresses afterwards. At a coarse ruling the two disagree by ΔE00 11.1, and the patch looks 14.3 lightness units darker than it measures — the average of a concave function is below the function of the average, which is Jensen's inequality and not an illusion. The gap falls under a unit above 30 cycles per degree. That is a viewing distance, and the correction a press applies for dot gain has no distance in it anywhere.

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.

applied · Delivery An orange ink's tints on three papers: which way the hue turns. The hue of each tint of an orange ink, from the solid to a tenth coverage, against the solid on the same paper, in degrees of Oklab hue: on a coated sheet, an unbrightened uncoated sheet and a newsprint. Solid lines are read against daylight's white, as an instrument reads them; dashed lines against the paper's own white, as a reader adapted to the page. At a tenth coverage, read against daylight, the coated sheet's tint has turned -8.7 degrees and the newsprint's 21.8; read against each paper's white, -8.7 and -1.1.

Newsprint turns a tint with its colour, not its gain

A halftone tint turns its hue the way a mixture of light does, by less, because optical dot gain carries it part of the way towards a paint tint. The straight line through a coated sheet's gain predicted that an uncoated sheet's larger gain would carry the orange past the crossing at a factor of 3.2, so that the same ink would turn opposite ways on two papers. It does turn opposite ways — on newsprint the orange's pale tints swing 13 degrees one way where a coated sheet's swing 8 the other. But the gain is not what does it. The road towards paint bends and stops at 60 to 70 per cent of the way, the orange needs a factor of 5.4 to cross, and newsprint's reversal comes almost entirely from the paper being yellow. Read against the paper's own white, as a reader looking at the page is adapted, it goes away.

brain · Appearance

Named alongside it

The objects these essays reach for when they reach for this one.

HalftoneProcess inksSubstrateQuality controlTone reproductionAdditive mixtureArea coverageChromatic adaptationContrast sensitivityDemichel's areasDot gainHue

All concepts