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

Most of this diagram is a lie, and it is not the diagram's fault.

The chromaticity horseshoe is the canonical illustration of colour science, and nearly every printed copy is filled edge to edge with colour it cannot actually show. A screen reaches a triangle inside it. Everything beyond that triangle — including the whole spectral boundary, the pure wavelengths the diagram exists to place — has been quietly clipped to something reachable, and the caption never says so. These are essays about colour with the arithmetic done and the failures marked: every swatch computed from a spectrum through a named observer, and everything the display cannot reach admitting it.

The CIE 1931 chromaticity diagram with its unreachable region marked. The spectral locus encloses every chromaticity a human eye can see. Cells inside the sRGB triangle are drawn in their own colour; the 85 per cent outside it are hatched, because no value this display accepts is the colour belonging there.
Fig. 1 The CIE 1931 chromaticity diagram with the honest part separated from the dishonest part. Inside the triangle the colours are correct — computed from chromaticity through to sRGB and verified in gamut. Outside it they are hatched, because no value this display can accept is the colour that belongs at those coordinates. The hatching covers about two thirds of this diagram’s area — a fraction of the CIE 1931 plane rather than a property of the eye, since a different set of coordinates gives anything from 62 to 92 per cent. Counting stimuli instead: 92 per cent of this collection’s constructed surfaces are reachable, and none of the pure wavelengths is.

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469 essays across 9 fields

Two identical grey patches on different surrounds. Both inner squares are #818181. The one on the dark field looks lighter. The values are checked to be equal before the figure is drawn, so the claim is a fact about the drawing rather than a promise. What the brain does

These two patches are identical

It is the most repeated and least checkable sentence in visual perception, because the whole point is that it does not look true. Every instance here is computed, and checked before the figure is drawn.

7 figures Three colour-difference formulae, disagreeing. ΔE76, ΔE94 and ΔE2000 for the same 9 pairs of colours. The largest disagreement between ΔE76 and ΔE2000 here is 26.6 units — larger than the threshold usually quoted for a just-noticeable difference, so the choice of formula can decide whether two colours count as matching. Difference and uniformity

How far apart are two colours

ΔE is meant to be a distance with the property that the same number means the same perceived difference everywhere. Three successive formulae have tried, they disagree with each other by more than a just-noticeable difference, and the disagreement decides real matching questions.

6 figures A spectrum, weighted three ways, and the three numbers left over. The illuminant D65 above; below, the same spectrum multiplied by each matching function. The area under each product is one coordinate of XYZ. Everything else about the spectrum — its shape, its structure, all its remaining degrees of freedom — is discarded here. What the eye does

Three numbers

A spectrum has as many degrees of freedom as anyone cares to give it. The eye reports three. Everything colour science can do, and every way it fails, follows from that one collapse.

8 figures Four standard illuminants, and how little they have in common. Spectral power distributions for A, D50, D65, E, on one scale. Illuminant A rises steeply toward the red; the daylight illuminants carry the atmosphere's absorption structure; E is flat by definition. All four are ordinarily called white. What light is

A spectrum is not a colour

What arrives at the eye is a function of wavelength. What the eye reports is three numbers. Keeping the two apart is the single most useful habit in the subject, and almost every confusion in applied colour comes from letting them merge.

7 figures The CIE 1931 colour-matching functions. The three functions that turn a spectrum into three numbers. They are all positive, which is why XYZ exists — the RGB functions they were derived from are not. ȳ is by construction the luminous efficiency function, which is why luminance comes out of Y. Where the model breaks

Seventeen observers in 1931

The standard observer that governs every colour specification in industrial use is an average over seventeen young British men, measured with equipment from the 1920s. It is known to be wrong in the blue, the correction has existed since 1951, and it has never been adopted.

7 figures The CIE 1931 chromaticity diagram with its unreachable region marked. The spectral locus encloses every chromaticity a human eye can see. Cells inside the sRGB triangle are drawn in their own colour; the 85 per cent outside it are hatched, because no value this display accepts is the colour belonging there. Matching and measuring

Most of this diagram cannot be shown

The chromaticity horseshoe is the canonical illustration of colour science, and nearly every printed copy is filled edge to edge with colours the page cannot produce. The honest version marks them, and the marking covers most of the picture.

8 figures A spectrum after 2 bounces off the same surface. The lamp's spectrum at the top, then the same spectrum multiplied by a reflectance peaking at 530 nm once for each bounce. Interreflection is elementwise multiplication, so light that reaches the eye by the long way round carries ρ raised to the number of surfaces it met. Each row's swatch is drawn at fixed luminance so only the chromaticity changes, and the distance from the D65 white point, printed at the right, rises from 0.000 to 0.235. The spectrum narrows every time, which is why a room painted in one colour is more saturated in its corners than on its walls. What a scene does

A bounce is a multiplication

Colorimetry multiplies an illuminant by a reflectance once and integrates. A surface in a room is lit by every other surface the lamp reached first, so the spectrum arriving at the eye has been multiplied several times — and the second multiplication is where the whole apparatus of matching starts to come apart.

8 figures A camera's spectral sensitivities, after the infrared-cut filter. Silicon quantum efficiency times the colour-filter dye times the infrared-cut filter, per channel, on a grid running to 1100 nm rather than to 780. With the filter removed, 68 per cent of the area under the three curves lies beyond the visible band, and all three curves are the same curve out there. What a camera does

A camera is a fourth observer

The 1931 functions, the 1964 functions and a person's own cones are three sets of three curves that collapse a spectrum onto three numbers. A camera is a fourth, built from silicon and dye rather than from pigment and neural wiring, and it agrees with none of them.

5 figures 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. What it takes to deliver it

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.

7 figures

All 9 fields · every essay · what's new

How deep it goes

9 ladders, and what stands on each

rungs 1–25

Appearance

These two patches are identical, and 52 arguments that stand on it.

53 essays rungs 1–18

Cones

Three numbers, and 52 arguments that stand on it.

53 essays rungs 1–20

Metric

How far apart are two colours, and 52 arguments that stand on it.

53 essays rungs 1–23

Capture

A camera is a fourth observer, and 51 arguments that stand on it.

52 essays rungs 1–23

Delivery

A halftone is not a mixture, and 51 arguments that stand on it.

52 essays rungs 1–24

Gamut

Most of this diagram cannot be shown, and 51 arguments that stand on it.

52 essays rungs 1–21

Scene

A bounce is a multiplication, and 51 arguments that stand on it.

52 essays rungs 1–20

Light

A spectrum is not a colour, and 50 arguments that stand on it.

51 essays rungs 1–19

Limits

Seventeen observers in 1931, and 50 arguments that stand on it.

51 essays

All 9 ladders · the claims this site tested

Threads running through

themes, not chapters

Say which colour

A swatch is a set of coordinates in a space, under an observer, on a display with a gamut. Every colour drawn here carries all four, because a hex code on its own does not identify a colour at all.

167 essays

Outside the gamut

Most colours a human can see cannot be shown on this page. The usual response is to clip them silently and print the picture anyway. The response here is to mark them and say how far out they are.

55 essays

Identical, and checked

"These two patches are the same colour" is the most repeated and least checkable sentence in perception, because the whole point is that it does not look true. Every instance here is checked by computation.

44 essays

Three numbers

An infinite-dimensional spectrum is projected onto three cone responses, and everything colour science can do — and every way it fails — follows from that single collapse.

207 essays

Matching is not appearance

CIE XYZ predicts when two lights will match under identical viewing conditions. It was never a model of how anything looks, and most of the confusion in applied colour comes from using it as one.

136 essays

Computed, not quoted

Every swatch begins as a spectral power distribution and is carried through the colour-matching functions as it is drawn. None is a hex code recalled from a table.

463 essays

The instrument is the reader

This is the one subject where the page is displayed on the apparatus under discussion, and the reader's own eye is the measuring device. Several figures here are experiments rather than illustrations.

258 essays