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

Diffusion length — where it appears

How far light travels sideways inside a scattering material before absorption ends it, computed from the absorption and reduced scattering coefficients. It runs from a fifth of a millimetre in coated paper to fourteen in candle wax, and every aperture result is that length divided by a hole.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

How much light comes back at each distance from where it went in. The diffuse reflectance kernel of 3 materials at 550 nanometres, computed from the dipole approximation to the diffusion equation. Both axes are logarithmic. The horizontal axis is the distance from the point the light entered, in millimetres; the vertical is how much comes back out per unit area there. Each curve's own diffusion length is marked with a tick. Coated paper returns almost everything within a fifth of a millimetre; marble is still returning light at ten. The reflectance the model wants is the whole of each curve, integrated over the plane, and what an instrument reads is only the part inside its aperture.

A surface has a kernel

Light that enters a translucent material does not come back where it went in. It scatters some thousands of times and leaves a few millimetres away, so what the surface has is not a reflectance but a function of distance — and the reflectance the model wants is that function's integral over the whole plane, which no instrument ever collects.

scene · Scene The share of a sample's reflectance an aperture recovers, by how wide it is. Six materials, and the fraction of each one's true reflectance that a measurement recovers through an aperture of the stated radius. The horizontal axis is logarithmic in millimetres; the vertical is a share, so 1.0 is the whole of it. The dashed line is a 4-millimetre radius, which is about what a hand-held spectrophotometer has. At that aperture coated paper reads 98 per cent of its own reflectance and candle wax reads 48. Every curve approaches one from below and none of them reaches it: the kernel's tail is what is being cut, and it falls as one over the aperture rather than exponentially.

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.

applied · Delivery Where a sample's colour goes as the aperture closes. The a and b of three translucent materials as the measuring aperture narrows from forty millimetres to one. Each track starts at the open circle, which is the colour the model says the sample has, and ends at the filled one. The axes cross at the neutral point. pale marble passes through neutral at a radius of 5.32 millimetres and comes out on the other side; candle wax passes through neutral at a radius of 7.07 millimetres and comes out on the other side; skin passes through neutral at a radius of 0.76 millimetres and comes out on the other side. Nothing about the sample changed: the aperture is a filter with a colour of its own, and the colour is decided by how the sample scatters rather than by what it absorbs.

The hue the hole decides

A piece of pale marble measured through a wide aperture is faintly yellow. Measured through a narrow one it is faintly blue, and between the two there is an aperture at which it is exactly neutral. Nothing about the stone changes; the aperture is a filter with a colour, and what decides that colour is the size of the particles rather than the pigment between them.

scene · Scene Two slabs with one reflectance, and two colours through an aperture. Two constructed media whose bulk reflectance agrees at every wavelength to fifteen figures, and whose diffusion lengths differ by a factor of four. The upper curve is that shared reflectance — both slabs lie on it exactly. The two patches on the right are what a 4 millimetre radius returns from each, and they are 6.3 ΔE₀₀ apart. This is a metamerism with no observer in it: the two samples are the same colour to anybody under any light, and the instrument separates them because it is measuring a kernel through a hole rather than measuring a reflectance.

A pair the aperture separates

Two constructed slabs with the same reflectance at every wavelength, to fifteen figures — the same colour to any observer under any light — and 6.25 ΔE₀₀ apart when measured through a four-millimetre aperture. It is a metamerism with no observer in it, no illuminant in it, and no spectral difference to construct it from.

matching · Gamut What is read at each distance from the edge of a lit region. Three materials under a half-plane of light, with the boundary at the centre of the horizontal axis and the lit side on the right. The vertical axis is the radiance leaving the surface as a share of what it leaves far inside the lit region. On the unlit side the sample is emitting light while receiving none, so the ratio the model calls a reflectance has a zero denominator there. The distance over which the curve runs from a tenth to nine tenths is 0.21 millimetres on coated paper and 5.1 on pale marble — which is the width of the neighbourhood a point's colour is decided by.

Two blurs before the eye's own

A translucent object arrives at the eye already blurred, by a kernel that is a property of the material rather than of the optics. On every material in this collection's table that blur is coarser at ordinary reading distance than the finest detail the eye can resolve — so the softness of marble or skin or wax is not a failure of vision, it is the object.

eye · Cones

Named alongside it

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

Subsurface scatteringTranslucencyApertureChromaInter-instrument agreementMarginalisationMeasurement conditionPoint spread functionScatteringAbsorptionAcuityAssertion

All concepts