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.

A physicist describing light gives a spectral power distribution: how much energy arrives at each wavelength. It is a function, it has as much structure as the source happens to give it, and it is a complete description of the light as far as colour is concerned.

A colour is three numbers. The gap between those two statements is where most of this subject lives.

Four standard illuminants, and how little they have in commonSpectral 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.400450500550600650700wavelength / nmA0.448, 0.407D500.346, 0.358D650.313, 0.329E0.333, 0.333normalised to 100 at 560 nmCIE 1931 2° observer
Fig. 1 Four standard illuminants on one scale. Illuminant A climbs steeply toward the red; the daylight illuminants carry the atmosphere’s absorption structure; E is flat by definition and is not a real light at all. All four are routinely described as white.

Those four curves have almost nothing in common as functions. Every one of them would be called white by somebody sitting under it, and the chips beside them show the chromaticities differ substantially. Both facts are true, and reconciling them is a matter of adaptation rather than of physics.

The three things that have spectra

Illuminants are sources. A tungsten filament, the sky, a fluorescent tube, an LED. The relevant curve is emitted power against wavelength, and the shapes are wildly different — a tungsten lamp is a smooth thermal curve, a fluorescent tube is a few narrow spikes on a broad background, an LED is a blue peak plus a phosphor hump.

Reflectances are surfaces. The relevant curve is the fraction of light returned at each wavelength, so it lies between zero and one and has no units. A surface has a reflectance whether or not anything is illuminating it, which is the sense in which a property of the object exists independent of the light.

Transmittances are filters, and behave like reflectances multiplicatively.

The light reaching the eye from an object is the product of the illuminant and the reflectance, wavelength by wavelength. That product is what gets integrated.

One reflectance, two illuminants, two coloursA reflectance peaking near 550 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 D650.339, 0.501under A0.419, 0.515reflectance is a fraction, 0 to 1CIE 1931 2° observer
Fig. 2 A reflectance peaking in the green, and the colours it produces under daylight and under tungsten. The surface has not changed between the two swatches. The light has, and colour is a property of the pair rather than of either alone.

Why “the colour of an object” is a compression

An object does not have a colour. It has a reflectance, and a colour arises when a specified light falls on it and a specified observer looks.

This is not pedantry — it is the source of a genuine class of industrial problem. Two surfaces can match under one illuminant and not another, which means “these two are the same colour” is an incomplete sentence until the light is named. Paint, textile, print and automotive industries all specify the illuminant in their matching standards precisely because leaving it out makes the specification meaningless.

The everyday compression works because daylight and indoor lighting are broadly similar in the ways that matter, and because the visual system discounts the illuminant so effectively that most people never notice it changing. Both of those hold well enough, most of the time, that the shorthand is harmless — until it is not.

What a spectrum is not

Three tempting misreadings, all common:

A spectrum is not a set of colours. A drawing of the visible spectrum as a rainbow strip is a drawing of the colours of single wavelengths, which is a different object from a spectral power distribution. The rainbow strip has one dimension of wavelength; a power distribution has a value at each wavelength, and a graph of it is not coloured.

5 spectra, one colourOne base reflectance in the heavy line and 4 constructed partners, every one of which produces the same XYZ under D65. The metameric black space is infinite-dimensional, so this is a sample of the family rather than the family.400450500550600650700wavelength / nmall of themthis colour5 spectra drawnCIE 1931 2° observer
Fig. 3 Five spectra that are one colour. The heavy line is a base reflectance and the others are constructed partners, every one producing identical XYZ under D65. This is the ordinary situation rather than a contrived one — the family is infinite-dimensional and these are four samples from it.

A spectrum is not recoverable from a colour. The mapping loses almost everything. Given three numbers there is a seventy-eight-dimensional family of spectra that produce them, and nothing in the three numbers indicates which one arrived. Devices that claim to measure “spectral colour” from an RGB camera are estimating, using strong assumptions about what real reflectances look like.

A spectrum does not tell anyone what something looks like. It fixes the stimulus and nothing else. Appearance depends on the surround, the adaptation state and the viewing conditions, and the distinction is worth keeping sharp.

The one honest thing to say about “white”

White is not a spectrum. Illuminant E, the flat one in the hero figure, is the only spectrum with any claim to being neutral by construction, and it is not a real light and does not look particularly white under normal conditions.

What “white” means in practice is whatever the visual system has adapted to. A room lit by tungsten looks white-ish after a few minutes even though its spectrum is dramatically red-weighted, and a photograph taken in that room without correction looks orange precisely because the camera did not adapt. The white point is a property of the observer’s state rather than of the light.

Colour science handles this by carrying a white point explicitly through every calculation. CIELAB, CIELUV and Oklab are all defined relative to one, and a Lab value without a stated white point is incomplete in the same way a temperature without units is.

Where the standard illuminants come from

They are a mixture of physics and committee, and the mixture is worth knowing.

Illuminant A is a definition: a Planckian radiator at 2856 K. Because it is a blackbody, it is computed from Planck’s law rather than tabulated, and everything about it follows from one temperature.

The D series — D50, D65, D75 — are daylight, and daylight is not a blackbody. Sunlight passes through an atmosphere that absorbs at specific wavelengths, and the resulting curve has structure no thermal source has. The CIE handles this with three tabulated basis functions reconstructed at a chosen correlated colour temperature, which is why D65 is a genuine measurement-derived object rather than a formula.

Illuminant E is flat, exists to make the arithmetic transparent, and corresponds to nothing.

D65 is the white point sRGB assumes, which makes it the white point of essentially every image on the web, whether or not anything in the production chain was ever near daylight.

The shapes real sources have

The four standards in the hero figure are idealisations. Real light is messier, and the mess matters.

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. 4 Thermal sources computed from Planck’s law. These are the smooth case — a single parameter fixes the whole curve, and nothing about the spectrum has structure. Almost nothing in a modern room emits like this.

A tungsten filament is genuinely thermal and genuinely smooth, which is why illuminant A can be defined as a temperature. Nearly everything else in current use is not. A fluorescent tube emits a handful of narrow mercury lines sitting on a broad phosphor background. A white LED is a blue semiconductor peak plus a wide 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 everything. They become visible the moment the light falls on a surface, because the surface multiplies before the eye integrates — a reflectance with a peak sitting in the LED’s dip returns much less light than its appearance under daylight would suggest.

This is the mechanism behind the common experience of a room looking 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 where that surface reflects.

The colour of a thing, and the colour of the light from a thing

There is a distinction in ordinary language that colour science has to make sharp, and it comes up whenever anyone tries to write down what was measured.

Reflectance belongs to the object. It is a curve between zero and one, it does not change when the lamp changes, and it is what a spectrophotometer measures by supplying its own known light source.

The stimulus is the product of that reflectance with whatever is actually illuminating the object. It changes constantly and is what the eye receives.

The appearance is what the observer experiences, and depends on the stimulus, the surround, the adaptation state and several other things. It is a third quantity again, and no amount of spectral measurement determines it.

Most everyday statements about colour slide between all three. “This paint is blue” is a claim about reflectance; “the wall looks blue” is a claim about appearance; and the sentence that gets people into trouble is “the paint matches”, which needs to specify which of the three is being asserted and under what light.

A constant-lightness hue circle at chroma 0.12, with the unreachable arcs hatchedThirty-six hues at one lightness and one chroma. 35 of 36 are inside the sRGB gamut; the rest are hatched. The gaps are not evenly spaced, because the gamut is a triangle in a space where a constant-chroma circle is a circle.chroma 0.12, lightness 0.735 of 36 reachablehatched arcs cannot be shownsRGB
Fig. 5 A reminder of what happens between stimulus and page. Even after the spectrum has been reduced to three numbers, a good proportion of those numbers cannot be delivered by this display — the hatched arcs are hues that exist and cannot be shown here.

Radiometry, photometry, colorimetry

Three words that sound interchangeable and name three different measurements. Confusing them is the commonest error in lighting specifications.

Radiometry measures energy. Watts per square metre per nanometre, no reference to any observer. A radiometric quantity is a fact about the light.

Photometry weights the spectrum by the eye’s sensitivity to brightness — the luminous efficiency function, which is also the yˉ\bar{y} matching function. Lumens, lux and candelas are radiometric quantities filtered through one curve. A photometric quantity is a fact about light and a standard observer, and carries no information about colour at all: two lights of identical lumen output can be any colours whatever.

Colorimetry weights the spectrum three ways instead of one, giving XYZ. This is where colour begins, and Y is exactly the photometric quantity, which is why luminance falls out of a colorimetric calculation for free.

The CIE 1931 colour-matching functionsThe 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.400450500550600650700wavelength / nmȳȳ is the luminous efficiency functionCIE 1931 2° observer
Fig. 6 The three weighting functions of colorimetry. The middle one, yˉ\bar{y}, is by construction the luminous efficiency function, so photometry is the middle row of this system used alone.

The practical consequence: a lamp specified only in lumens has been specified photometrically, and nothing has been said about its colour or about how it will render surfaces. A lamp specified in lumens plus a correlated colour temperature has had two of the three colorimetric dimensions pinned and the third left free, which is why two lamps meeting the same specification can still differ visibly.

The infrared and ultraviolet are not colours

A spectral power distribution extends indefinitely in both directions, and colour occupies only the part the cones respond to — roughly 380 to 780 nm, with the edges soft rather than sharp.

Energy outside that band contributes nothing to colour, however much of it there is. A tungsten lamp radiates most of its output in the infrared and none of it affects the lamp’s chromaticity. This is why the curves on this site are truncated at 380 and 780 without apology: everything omitted is irrelevant to the question being asked, though very relevant to questions about heat.

There is one qualification worth making. Ultraviolet can affect colour indirectly, through fluorescence — a material absorbing in the ultraviolet and re-emitting in the visible. Optical brighteners in paper and detergent work exactly this way, converting invisible ultraviolet into visible blue to make white look whiter than white. A fluorescent sample cannot be characterised by a reflectance at all, since its output at one wavelength depends on the input at another, and the whole reflectance-times-illuminant model quietly fails for it.

What was computed here

Every curve on this page is either computed from a physical law or reconstructed from the CIE basis functions, and then checked against a published landmark.

Illuminant A comes from Planck’s law at 2856 K and its chromaticity 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 daylight basis and lands at (0.3127,0.3290)(0.3127, 0.3290) exactly. D50 lands at (0.3457,0.3585)(0.3457, 0.3585), also exact. Illuminant E lands at one third, one third to 2×1062 \times 10^{-6}.

That last check earned its place during construction. The daylight basis functions are published by the CIE from 300 nm, and this site samples from 380 nm; an early version computed an index offset against 300 and read the wrong part of the table. The result was a perfectly smooth, entirely plausible daylight spectrum whose white point sat at (0.3251,0.3278)(0.3251, 0.3278) — wrong in the third decimal, and invisible in the picture. Only the assertion against the published white point caught it.

The habit this essay is arguing for

One sentence: keep the spectrum, the stimulus and the appearance apart, and say which is meant.

Almost every confusion in applied colour is a slide between them. “The paint is blue” is about reflectance; “the wall looks blue” is about appearance; “the paint matches” needs to say which, and under what light, for whom.

Why the distinction is worth the effort

Because the collapse is irreversible, and everything downstream inherits it.

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. 7 The step that makes the distinction irreversible. The curve above becomes the three areas below, and no later calculation recovers what was discarded.

There is one further reason the habit is worth the effort. Storing a spectrum keeps every future question answerable; storing a colour answers one question permanently and forecloses the rest. An archive of reflectances can be rendered under a lighting standard nobody has written yet. An archive of Lab values cannot, because the illuminant was folded in at measurement time and cannot be extracted afterwards.

What the pictures cannot show

The swatches beside each illuminant are what a perfect white reflector would look like under that light to an unadapted observer. Nobody is unadapted. A reader sitting under a tungsten lamp is adapted to it, and the tungsten swatch on their screen will look considerably more orange to them than the room does.

There is no way to fix this within the figure. The comparison being drawn is between illuminants, and the reader’s own illuminant is a fourth one, uncontrolled and unknown.

The curves also stop at 380 and 780 nm. Real sources emit outside that range and real surfaces reflect there, and none of it contributes to colour — but the truncation means these are not complete descriptions of the light, only of the part the eye can respond to.

Who found it, and when

Newton separated white light into a spectrum with a prism in 1666 and, crucially, recombined it, establishing that the colours were components rather than modifications. The idea that colour is a property of light rather than of objects dates from that work.

Quantitative spectroradiometry arrived much later, and the CIE’s standard illuminants were adopted in stages through the twentieth century — A, B and C in 1931, the D series added in 1964 after Judd, MacAdam and Wyszecki analysed several hundred measured daylight spectra and extracted the three basis functions still used today.

Where this goes next

The thermal sources have their own logic, taken up in blackbody and the colour of temperature. The dependence of object colour on the light is the illuminant is half the answer. And the collapse from a curve to three numbers is three numbers, which is where the rest of the site starts.