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

The illuminant is half the answer

An object has a reflectance, not a colour. The colour appears when a specified light falls on it, which is why two surfaces can match in a shop and clash outside, and why every serious matching standard names the light.
14 min read 6 figures Say which colourComputed, not quotedMatching is not appearance

The question “what colour is this?” has no answer until a light is named. That sounds like a technicality and it is the source of an entire class of expensive industrial problem.

One reflectance, two illuminants, two coloursA reflectance peaking near 610 nm, and the colours it produces under D65 and A. The object has not changed. The light has, and colour is a property of the pair.400450500550600650700wavelength / nmunder D650.490, 0.417under A0.561, 0.413reflectance is a fraction, 0 to 1CIE 1931 2° observer
Fig. 1 One reflectance under daylight and under tungsten. The surface is identical in both; the chromaticities are substantially different. Colour is a property of the pair, and naming only one of them leaves the question unanswered.

The arithmetic

The light reaching the eye from a surface is the illuminant multiplied by the reflectance, wavelength by wavelength, and it is that product which gets integrated against the matching functions.

XYZ=∫E(λ) R(λ) xˉyˉzˉ(λ) dλ\mathrm{XYZ} = \int E(\lambda)\,R(\lambda)\,\bar{x}\bar{y}\bar{z}(\lambda)\,\mathrm{d}\lambda

Nothing subtle happens here. The reflectance RR belongs to the object and is fixed; the illuminant EE belongs to the situation and is not; and the result depends on both. Changing EE changes the answer, and there is no reason for two surfaces that agreed under one EE to agree under another.

Why the shorthand usually works

Ordinary language treats colour as a property of objects, and gets away with it for two reasons.

Everyday illuminants are broadly similar in the ways that matter. Daylight, tungsten and most artificial lighting are smooth and broad; they differ in overall slope more than in structure. Reflectances are also mostly smooth. A product of two smooth functions is not very sensitive to moderate changes in either.

The visual system discounts the illuminant so effectively that most people never notice it changing. Walking from a sunlit street into a tungsten-lit room is a large change in the stimulus and a small change in the experience.

Both hold well enough that “the red car” is a perfectly good phrase. Both break down under specific conditions, and the breakdowns are where the money goes.

Where it fails: structure in the lamp

The failures cluster around lamps whose spectra have structure.

A tungsten filament is thermal and smooth — Planck’s law gives the whole curve from one temperature. A fluorescent tube is not: it emits a few narrow mercury lines on a broad phosphor background. A white LED is a blue semiconductor peak plus a phosphor hump, with a characteristic dip between them.

Those spikes and dips are invisible when looking at the lamp, because the eye integrates and integration smooths. They become very visible when the light falls on a surface, because the surface multiplies before the eye integrates. A reflectance peaking in an LED’s dip returns much less light than its daylight appearance would suggest, and a reflectance peaking on a mercury line returns much more.

This is the mechanism behind a common experience: a room looks fine until something specific in it looks wrong — skin, wood, a particular fabric. The lamp’s white point is correct and its spectrum has a hole exactly where that surface reflects.

Four standard illuminants, and how little they have in commonSpectral power distributions for A, 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.400450500550600650700wavelength / nmA0.448, 0.407D650.313, 0.329E0.333, 0.333normalised to 100 at 560 nmCIE 1931 2° observer
Fig. 2 Three illuminants with quite different shapes. Their chromaticities differ far less than their spectra do, because the collapse to three numbers has already discarded most of what distinguishes them — and it is precisely the discarded structure that decides how they render surfaces.

The matching problem

The sharp version is illuminant metamerism: two surfaces matching under one light and not another.

A metameric pair under D65 and under AThe same two reflectances under two lights. Under D65 they match to ΔE00 = 6.2e-14. Under A they are ΔE00 = 13.8 apart, which is a plainly visible difference. Neither surface changed; the illuminant did.400450500550600650700wavelength / nmunder D65ΔE00 6.2e-14under AΔE00 13.8same surfaces, different lightCIE 1931 2° observer
Fig. 3 Two reflectances that match to arithmetic noise under daylight and are ΔE₀₀ 11 apart under tungsten. Neither surface changed. The light did.

Every industry that matches colour has had to confront this, and the responses are consistent:

Name the illuminant in the standard. Textile, paint and plastics standards all specify the illuminant, often several, and a match may be required to hold under all of them.

Prefer matches built from the same colorants. Two formulations using the same pigments in different proportions match under every light, because their reflectances differ by a scaling rather than in shape. A match achieved with different pigments — a metameric match — is regarded as inferior even when the colour difference under the reference light is smaller.

Use viewing booths. A standardised enclosure with several switchable illuminants, so a sample can be checked under each.

The automotive industry has the hardest version of the problem, since adjacent body panels made from different materials — painted steel, moulded plastic, a repaired section — must match across daylight, garage lighting and street lighting, at large size, sharing an edge, which is the most sensitive comparison there is.

Colour rendering, and why the index is unsatisfactory

The natural thing to want is a number saying how faithfully a lamp renders colours. The standard one is the colour rendering index, and it is widely used and widely criticised.

It works by computing the colour shift of eight standard samples between the test lamp and a reference — a blackbody or daylight at the same correlated colour temperature — and averaging. A perfect score is 100.

The criticisms are substantial:

The samples are unsaturated. The eight are moderate pastels, and lamps with poor rendering of saturated colours can still score well. Saturated reds are the usual casualty, since red reflectances are exactly the ones sensitive to structure at the long-wavelength end.

Averaging hides failures. A lamp rendering seven samples perfectly and one terribly averages well, and the one is what will be noticed.

The reference changes with the lamp. Each lamp is compared against a reference at its own correlated colour temperature, so the index measures faithfulness to a moving target rather than to any absolute standard.

It can be optimised against. A lamp designed to score well on eight known samples can do so without rendering anything else well, and there is a commercial incentive to do exactly that.

Newer measures — TM-30 in particular — use many more samples and report fidelity and gamut separately rather than collapsing to one number. The underlying difficulty does not go away: rendering quality is a many-dimensional property and any single number discards most of it.

The other half nobody quotes

There is a second quantity that matters as much as colour temperature and is almost never printed: the distance from the Planckian locus, called Duv or tint.

Two lamps sharing a correlated colour temperature can sit on opposite sides of the locus, one faintly green and one faintly pink. They look plainly different beside each other and carry identical labels. Fluorescent lamps are frequently green-shifted, and the shift is what makes some rooms feel subtly unpleasant in a way the temperature rating does not predict.

The measurement chain, and where the illuminant enters

It is worth tracing exactly where the light enters the calculation, because the position determines what can and cannot be separated later.

A spectrophotometer measuring a surface supplies its own light source and reports reflectance — a curve between zero and one, a property of the surface alone. That is the measurement worth storing, because it is illuminant-independent.

A colorimeter, by contrast, reports XYZ under some illuminant, which has already folded the light into the answer. The reflectance cannot be recovered from it, because three numbers do not determine a spectrum.

So a colour specified as XYZ or Lab is specified under an illuminant, and converting it to another illuminant requires either the original reflectance — which is gone — or an approximation. Chromatic adaptation transforms do the approximation, and they are approximations precisely because the information needed to do it exactly was discarded at measurement time.

A spectrum, weighted three ways, and the three numbers left overThe 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.D65 spectrum400450500550600650700wavelength / nmx̄ → 95.04ȳ → 100.00z̄ → 108.90the area under each product is one coordinateCIE 1931 2° observer
Fig. 4 The step where the illuminant becomes irrecoverable. Once the product of reflectance and illuminant has been integrated to three numbers, nothing distinguishes a bright surface under dim light from a dim surface under bright light, and no later calculation can separate them.

This is the practical argument for storing spectra rather than colorimetry wherever it is affordable. A reflectance can be rendered under any illuminant afterwards; a Lab value cannot.

How much structure matters

The size of the effect depends on how much structure the lamp has, and the range is large.

Blackbody spectra from Planck's law, 2000 to 10000 KEach curve is computed from Planck's law and normalised to its own peak. The peak moves toward shorter wavelengths as temperature rises. Only two of these radiators peak inside the visible band at all — a 2000 K source peaks at 1449 nm, far into the infrared, and merely rises toward the red across everything shown here.400450500550600650700wavelength / nm2000 K3000 K6500 Keach normalised to its own peakCIE 1931 2° observer
Fig. 5 Thermal sources, the smooth extreme. A blackbody has no structure at all — one parameter fixes the entire curve — so two blackbodies at different temperatures render surfaces differently but predictably, and nothing surprising happens to any particular surface.

At the other extreme, a low-pressure sodium lamp emits essentially one wavelength. Under it every surface returns a scaled version of the same spectrum, so all surfaces differ only in brightness and colour vision fails almost completely. There is nothing pathological about the lamp; the information simply is not present in the reflected light, and no amount of adaptation recovers it.

Fluorescent and LED sources sit between the two, which is the awkward region: enough structure to cause surprises, not so little that the failure is obvious. A surface whose reflectance peaks in an LED’s phosphor dip is genuinely darker under that lamp than its daylight appearance predicts, and the effect is specific to that surface rather than a general shift the eye can discount.

The rule that follows

Every serious colour specification names its illuminant, and the reason is now stateable in one line: a colour is a property of a surface, a light and an observer, and naming fewer than three leaves the specification incomplete.

This site follows the same rule in its figures. Every swatch derived from a reflectance names the illuminant it was computed under, and every figure names its observer, because a chromaticity quoted without both is a number without a referent.

What was computed here

Every figure on this page computes the product of a reflectance and an illuminant, integrates it, and converts the result — nothing is a quoted swatch.

The illuminants themselves are computed or reconstructed rather than tabulated as chromaticities. Illuminant A comes from Planck’s law at 2856 K and lands at (0.4475,0.4074)(0.4475, 0.4074) against a published (0.4476,0.4074)(0.4476, 0.4074); D65 is reconstructed from the CIE daylight basis and lands exactly on (0.3127,0.3290)(0.3127, 0.3290).

The metameric pair in the illuminant-metamerism figure is verified to match under D65 to ΔE₀₀ below 0.4, verified to differ spectrally by more than five per cent, verified to be inside the display gamut so that neither patch has been clipped into agreement, and verified to come apart under illuminant A by more than one ΔE unit. All four checks run on every build, and the gate confirms each still rejects when handed a case that should fail.

The reflectances used in these figures are idealised smooth curves rather than measured ones. Real reflectances carry more structure, which makes the illuminant effects larger rather than smaller — so the figures understate the practical problem rather than exaggerating it.

What to store, and why it matters

A practical consequence follows from where the illuminant enters the calculation.

A reflectance is illuminant-independent and can be rendered under any light afterwards. A colorimetric value — XYZ, Lab, a hex code — has an illuminant baked into it and cannot be un-baked, because three numbers do not determine a spectrum.

So a colour archive storing Lab values has committed to an illuminant permanently, and an archive storing spectra has not. Museums, textile archives and paint manufacturers increasingly store spectra for exactly this reason: the question “what will this look like under the lighting installed next decade” is answerable from a reflectance and unanswerable from a Lab value.

The same logic applies at a smaller scale to any colour specification intended to outlive its context.

The extreme case

A light with no spectral variety carries no information about surfaces, and no amount of adaptation recovers what was never there.

Every pure wavelength, and the fact that none of them can be displayedMonochromatic stimuli from 460 to 620 nm. All 9 are outside the sRGB gamut, so all are hatched; the number under each is how far outside, as a percentage of the channel range. A swatch captioned with a wavelength is never that wavelength.460−1374480−201500−95520−65540−28560−8580−7600−96620−187all hatched — none is reachablenumber is the gamut miss, %CIE 1931 2° observer
Fig. 6 The extreme of spectral structure: single wavelengths. A light like this carries almost no information about the surfaces it falls on, which is why sodium lighting destroys colour vision rather than merely tinting it.

The summary is one sentence and it is the sentence this field keeps having to repeat. A colour is a property of a surface, a light and an observer together. Naming fewer than three leaves the statement incomplete, and the incompleteness is not pedantic — it is why matches fail, why proofs disagree with presses, and why two people can look at the same wall under different lamps and honestly disagree about what colour it is.

There is a corollary worth drawing out for anyone specifying colour. A specification naming only a colour value has named a stimulus under an unstated light. A specification naming a reflectance and an illuminant has named something reproducible. The extra effort is small and the difference shows up whenever the specification outlives the room it was written in — which, for anything printed, manufactured or archived, is essentially always.

This is also why colour standards read as fussy to outsiders. The apparent pedantry about viewing booths, illuminant codes and observer angles is what makes a match verifiable by two parties who never meet.

A last practical note on where this bites hardest. The industries that care most about it are the ones where a customer compares two objects in a place the manufacturer does not control: paint against a sample card in a hallway, a replacement panel against the rest of a car in a street, a garment against a bag under shop lighting and then under daylight. In each case the comparison is side by side, at large size, sharing an edge — the most sensitive arrangement available — and under a light nobody specified.

That combination is why the tolerances in those industries are far tighter than any general-purpose threshold would suggest, and why matching by pigment rather than by measurement is preferred wherever it can be arranged.

What the pictures cannot show

The swatches are the stimuli, not the appearances. What an observer standing in a tungsten-lit room perceives is much closer to the daylight swatch than to the tungsten one, because adaptation discounts most of the difference. Placing the two side by side on one screen defeats that adaptation and exaggerates the effect considerably.

The exaggeration is deliberate and is the only way to show the stimulus difference at all — but a reader concluding that objects change colour dramatically between rooms is drawing a stronger conclusion than the figure supports.

The reflectances used are also idealised smooth curves rather than measured ones. Real reflectances have more structure, which makes the effects larger rather than smaller, so the figures understate the practical problem.

Who found it, and when

Dyers knew about illuminant metamerism long before it was named; matching batches under different lights is an old and practical difficulty. Ostwald gave it a name around 1900.

The CIE’s standard illuminants were adopted in stages through the twentieth century, and the colour rendering index was introduced in 1965 and revised in 1974. Its inadequacies have been documented essentially since, and TM-30 was published by the Illuminating Engineering Society in 2015 as a replacement. Adoption has been slow, for the usual reason that the older number is embedded in regulations and product labelling.

Where this goes next

The mechanism in full is two spectra, one colour. The reason lamps have the spectra they do is blackbody and the colour of temperature. And the reason none of this is as noticeable as the arithmetic suggests is constancy is the default.

Where this goes next

400450500550600650700wavelength / nmA0.448, 0.407D500.346, 0.358D650.313, 0.329E0.333, 0.333normalised to 100 at 560 nmCIE 1931 2° observer 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. 400450500550600650700wavelength / nmthe two coloursΔE00 = 6.2e-14spectra differ by 92%reflectances, under D65CIE 1931 2° observer Two spectra, one colour Metamerism is usually described and almost never demonstrated. It does not have to be — the metameric black space is enormous, so a matching pair can be constructed to order, verified, and then made to come apart by changing the light. 400450500550600650700wavelength / nm2000 K3000 K4000 K6500 K10000 Keach normalised to its own peakCIE 1931 2° observer Blackbody and the colour of temperature Heat something and it glows, in a colour fixed by its temperature alone. Planck's law gives the whole spectrum from one number, and the Planckian locus is the only curve in colour science derived from physics rather than from measurements of people.