The sun is not one illuminant

The sun is very nearly a blackbody at about 5800 K. Daylight is not, and the gap between those two statements is where every practical question about daylight lives.

What reaches a surface outdoors has been through the atmosphere, which scatters short wavelengths preferentially, absorbs in bands where water and ozone live, and contributes its own scattered light from the whole sky. Add cloud, which is a broadband scatterer, and the time of day, which changes the path length through all of it, and the result is not one spectrum and is not the spectrum of any hot object.

Three basis functions #

The CIE’s answer, adopted in 1964, is a reconstruction rather than a table. Measured daylight spectra from several studies were decomposed by principal component analysis, and it turned out that three components account for essentially all the variation: a mean spectrum $S_0$, and two eigenvectors $S_1$ and $S_2$.

Any daylight illuminant is then

$$S(\lambda) = S_0(\lambda) + M_1 S_1(\lambda) + M_2 S_2(\lambda)$$

with $M_1$ and $M_2$ determined by the desired chromaticity, which is itself determined by a single parameter: the correlated colour temperature.

So the whole D-series is one number wide. D50, D55, D65 and D75 are not four separate standards; they are four points on a curve, and the curve is generated by two polynomials in $1/T$ that give the chromaticity and a pair of linear relations that give $M_1$ and $M_2$ from it.

That is a much stronger claim than a table would be. It says daylight varies along essentially one dimension, and that the first eigenvector — which is broadly a blue-to-yellow tilt — captures the overwhelming majority of what changes between a clear noon and an overcast afternoon.

Three members of the same list are worth drawing on their own, because they are three different kinds of object wearing one word.

The second is not a daylight at all, and it is defined by a different kind of statement: a formula for a hot body rather than a fit to a set of measured skies.

Where this site nearly got it wrong #

The reconstruction is implemented here rather than tabulated, and there is a comment in the code that is worth surfacing because the failure it records is the kind that produces a perfectly plausible wrong answer.

The CIE publishes the $S_0$, $S_1$, $S_2$ tables from 300 nm. This site’s wavelength grid starts at 380 nm. The first implementation computed an index into the basis arrays by subtracting 300 rather than using the arrays as already aligned to the site’s own grid — and read the wrong part of each array.

The result was a smooth, entirely plausible daylight spectrum. It looked like daylight. It plotted like daylight. Its chromaticity came out at (0.3251, 0.3278), which is close enough to D65’s (0.3127, 0.3290) that no figure would have looked wrong, and only assertD65 noticed, because it compares the computed chromaticity against the published one to a tolerance tighter than eyeballing.

That assertion is the reason this essay can quote any number at all. The comment in the code now says, in effect, do not reintroduce a wavelength-to-index calculation here.

The daylight locus is not the Planckian locus #

A blackbody’s chromaticity traces a curve across the diagram as its temperature rises — the Planckian locus. Daylight’s chromaticity traces a different curve, and the two are close without touching.

Daylight sits above the Planckian locus, on the green side, at essentially every temperature. The reason is atmospheric: preferential scattering of short wavelengths adds blue, and the absorption bands remove power unevenly, and neither of those is anything a hot object does.

This is why correlated colour temperature alone does not specify a white. CCT is the temperature of the blackbody whose chromaticity is nearest to the light in question, on a chart where “nearest” has a specific and slightly arbitrary definition. Two lights with the same CCT can sit on opposite sides of the Planckian locus and look visibly different — one greenish, one pinkish — and the number does not distinguish them.

The second coordinate is Duv: the signed distance from the Planckian locus, measured perpendicular to it in a uniform chromaticity diagram. A specification giving CCT without Duv has given one coordinate of a two-dimensional quantity, and this is one of the commonest omissions in lighting specification.

Setting them together makes the taxonomy visible, and it is not the taxonomy the names suggest. A is a definition — a blackbody at 2856 K, computed from Planck’s law, and any tungsten lamp resembling it does so by approximation. E is a fiction, equal power at every wavelength, included because it makes the chromaticity of the observer itself visible by landing at exactly one third, one third. The D-series is a fit to measurements, and is the only one of the three that is an empirical claim about the world.

That difference in kind matters when a specification names one. Asking a laboratory for illuminant A is asking for a temperature. Asking for D65 is asking for a spectrum nobody can build exactly, and the honest response is a simulator plus a statement of how well it matches — which is why D65 simulators are graded rather than certified.

How far to one side, and whether it varies #

Systematically to one side is a direction, and the distance turns out to be nearly a constant.

Computing the Duv of the reconstructed daylight illuminant at each temperature — the signed distance from the Planckian locus, which is what the second coordinate exists to record:

The offset is +0.0030, give or take a tenth of that, across a factor of six in temperature. It peaks at 5500 K and is smallest at the bottom of the range, and the whole variation is 22 per cent — so the daylight locus is not merely on one side of the Planckian one. It runs a nearly constant distance from it.

Two checks arrive with the table. The blackbody’s own Duv computes as machine zero at every temperature, which is what being a locus means. And the recovered correlated temperature matches the nominal one to within twenty kelvin at the worst point, out of twenty-five thousand — so the reconstruction and the temperature it was asked for agree, which a fit of three basis functions to a one-parameter family had no obligation to do.

The size is worth its own sentence. A Duv of 0.003 sits inside the ±0.006 a white-point specification usually allows and is about three times what an instrument can resolve. Daylight is off the Planckian locus by an amount that passes every tolerance and is measurable by anybody who looks.

D50 is the other daylight illuminant in daily use, and putting it beside D65 in the same construction is what makes the phrase “a daylight illuminant” mean something specific.

What D65 is and is not #

D65 is the white point of sRGB, of Rec. 2020, of Display P3, and of almost every display standard written since the 1990s. It is worth being precise about what has been standardised.

It is not the spectrum. Specifications pin D65 by its chromaticity, (0.3127, 0.3290), not by its spectral power distribution. That makes the standard well-defined and quietly freezes in a choice of observer, since a chromaticity is a spectrum integrated against colour-matching functions and somebody had to pick which. This is the choice the whole site keeps arriving at.

Its temperature is not 6500 K. The D-series formula was written when the second radiation constant $c_2$ had a slightly different accepted value, and when the constant was revised the CIE chose to keep the chromaticities fixed rather than the temperatures. So D65’s actual correlated colour temperature is about 6504 K, which is why this site’s code asks for daylight(6504) and not daylight(6500).

There is no D65 lamp. D65 is a computed spectrum; light sources sold as D65 simulators approximate it, and how well they do is measured by a metamerism index rather than by a difference, because two spectra can match under one observer and separate under another.

What the reconstruction cannot do #

The D-series covers 4000 K to 25000 K and refuses outside it. That is a real limit rather than a coding convenience: the polynomials are fits over that range and produce nonsense beyond it, and a function that silently extrapolated would return a smooth curve for a 2000 K “daylight” that does not exist.

It also cannot produce the two things that most affect real daylight and are not on its one dimension. The infrared and ultraviolet are outside this site’s 380–780 nm range entirely, which matters because ultraviolet is what excites optical brighteners — so every fluorescence number on this site is a declared floor rather than a measurement, and the D-series is one of the reasons.

And it cannot produce direct sunlight separately from skylight. Real outdoor illumination is a mixture of a nearly-Planckian direct beam and a strongly blue diffuse component, in a ratio that depends on cloud, and the D-series is a fit to the mixture. A surface in shadow is lit almost entirely by the second component and is much bluer than any D-series illuminant, which is why shadows photograph blue and why white balance struggles outdoors in a way it does not indoors.

That mismatch is the practical limit of the D-series as a model of illumination in general. It is a basis for daylight, fitted to daylight, and its three components span a space containing only smooth broadband spectra. An artificial source with narrow emission lines is not merely outside the fitted temperature range; it is outside the space, and projecting it onto the three basis functions produces a daylight illuminant of some temperature that shares its chromaticity and none of its structure.

That projection is exactly what a correlated colour temperature does. Quoting a CCT for a fluorescent tube is reporting which member of the daylight family it is nearest to in chromaticity, while saying nothing about the structure that decides which surfaces it flatters.

The comparison is the useful one for anybody choosing a lamp. Daylight is not efficient: it is a broadband spectrum with power spread across the whole band and well beyond it, and its luminous efficacy of radiation is a little over 200 lumens per watt against a ceiling of 683. Every artificial source that beats it does so by being less like it, and what that costs is measured elsewhere on this ladder. Daylight’s reputation for rendering colour well is not a reputation for efficiency; the two are in opposition, and daylight is at the wrong end of the trade.

Illuminant A is the useful contrast, because it is the one standard illuminant that is not a daylight reconstruction at all.

What “correlated” is doing in the name #

The word is load-bearing and is almost always read as filler.

A colour temperature proper belongs only to a Planckian radiator, and it is the temperature of that radiator. Illuminant A has a colour temperature of 2856 K, full stop, because illuminant A is defined as a blackbody at 2856 K.

A correlated colour temperature belongs to anything else, and it is the temperature of the blackbody whose chromaticity is nearest — where “nearest” is measured in a particular uniform chromaticity diagram, perpendicular to the locus, by a convention that has itself changed over the years. It is a projection of a two-dimensional quantity onto a one-dimensional family, and the information discarded by the projection is exactly the Duv.

Two consequences follow that specifications routinely get wrong. A CCT is only meaningful within a bounded distance of the locus — beyond about |Duv| = 0.05 the nearest-blackbody construction stops corresponding to anything anybody would call a colour temperature, and standards say so. And a CCT is not a temperature of anything: an LED with a CCT of 3000 K contains nothing at 3000 K, and its junction is at something under 400 K.

What was computed, and how #

Every daylight spectrum on this site is generated from the three basis functions, and three assertions guard the generator.

The basis tables are the right length. They must have exactly one entry per wavelength on the site’s grid, checked at call time, which is what makes the index-offset bug impossible to reintroduce silently.

Reconstructing D65 returns the published D65 chromaticity, to 10⁻³. This is the assertion that caught the offset bug and it is the reason the tolerance is tight rather than generous.

The normalisation is at 560 nm, by CIE convention, and the reconstruction is scaled to 100 there — which matters because relative spectral power distributions are only defined up to a scale and comparing two normalised differently is comparing nothing.

The correlated colour temperature computation is separate, searches a temperature range for the nearest Planckian chromaticity, and is asserted to recover the temperature of a blackbody handed to it — which is the check that the “nearest” search and the locus agree with each other.

The limiting case is the illuminant that has no shape at all, and it is worth drawing because it is the one whose white is exactly where the arithmetic puts it.

What one dimension buys, and what it hides #

The claim that daylight is one-dimensional is the interesting one and deserves examination rather than acceptance.

It buys enormous practical convenience. A single number specifies a daylight illuminant, so a specification can say “D50 viewing conditions” and be unambiguous; a viewing booth can offer four settings and cover the range; and a white-balance algorithm can search a one-parameter family rather than a space of spectra, which is why illuminant estimation is tractable at all outdoors.

What it hides is that the one dimension is a fit to a sample. The 622 spectra were measured at three northern-hemisphere sites at temperate latitudes, mostly in daytime, mostly under conditions somebody was willing to go outside in. Daylight at high latitude near sunset, or through heavy haze, or under a forest canopy — which is filtered by chlorophyll and is emphatically not on the locus — is daylight, and is not in the family.

The forest case is the sharpest. Light under a green canopy has had a large bite taken out of it by chlorophyll absorption, its chromaticity is well off both loci, and its correlated colour temperature is a projection that discards the very structure that makes it what it is. Anyone whose ancestors spent time under trees was looking at an illuminant the D-series does not describe.

Who found it, and when #

The principal-component analysis of daylight is Judd, MacAdam and Wyszecki, 1964, working on 622 measured spectra from Ottawa, Rochester and Enfield. The finding that three components suffice is the substantive result and it has held up: later and much larger measurement campaigns have found small improvements and no fourth dimension worth standardising.

The CIE adopted the D-series the same year, alongside the 1964 ten-degree observer — the two arrived together, which is a coincidence of timing and not a connection, though it does mean the standards defining large-field colorimetry and defining daylight are the same vintage.

Duv as a formal quantity is much more recent, standardised by ANSI in the 2000s for solid-state lighting, essentially because LEDs made it easy to build sources that sat well off the Planckian locus and the existing CCT-only specifications could not describe them. Before LEDs, most artificial sources were either thermal, and therefore on the locus by construction, or fluorescent and grouped by tightly-specified phosphor blends.

What the picture cannot show #

The locus figure draws two curves on a chromaticity diagram, and the diagram’s unreachable region is hatched as everywhere on this site. The hatching matters less here than usual — both loci run through the middle of the diagram, well inside any display gamut, so a reader can actually see the colours in question, which is rare on these pages.

What cannot be shown is the thing the essay is about. A reader looking at a D65 patch on a screen is not seeing D65; they are seeing a metamer of it produced by three primaries, under whatever the room’s actual illumination is, adapted to whatever their visual system has settled on. The spectral difference between real daylight and its display metamer is enormous — one is smooth and continuous, the other is three narrow peaks — and no figure on a screen can convey it, because the screen is the thing doing the substituting.

That is the site’s founding difficulty arriving in its purest form. An essay about the spectrum of daylight, illustrated on an apparatus whose entire method is to replace spectra with triples.

Where this goes next #

Downward, the colour of temperature is where Planck’s law and the locus are set out, and a lamp is not a blackbody is the same distinction made for artificial sources.

The thread worth following is the second coordinate. Duv exists because one number was not enough, and the same shape of problem — a scalar standing in for something that has more than one dimension — recurs everywhere in this subject: a colour temperature without a Duv, a tolerance without a shape, a gamut coverage without a volume. In each case the scalar is not wrong; it is a projection, and the projection is only safe while everything being compared lies in the plane it projects along. LEDs broke that for colour temperature in the 2000s, wide-gamut displays broke it for coverage in the 2010s, and the pattern is that the scalar survives exactly as long as the technology that made it adequate.