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

The D-series daylight illuminants — where it appears

The CIE's daylight illuminants, reconstructed from three tabulated basis functions rather than measured. The basis is published from 300 nanometres, so the series carries a defined ultraviolet content — which is what makes a measurement of a fluorescent sample specifiable.

Named by 8 essays across 3 fields — each of them below, with the objects they name alongside it.

Colour temperature, and the number nobody quotes beside it. The Planckian locus in the 1960 UCS diagram — the only diagram on which correlated colour temperature is well defined — with four sources and the perpendicular from each to its nearest point. The temperature is where the foot of the perpendicular lands; Duv is how long the perpendicular is. halophosphate sits 0.0246 off the locus at 4513 K, which is a visible green cast that its colour temperature does not mention.

The sun is not one illuminant

Daylight is not a blackbody and is not one spectrum. It is a one-parameter family reconstructed from three measured basis functions, its chromaticities lie on a curve that is near the Planckian locus and not on it, and the difference is the reason a colour temperature needs a second number beside it.

light · Light A camera's spectral sensitivities, with the filter removed. Silicon quantum efficiency times the colour-filter dye times nothing else, 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.

The grid outside every figure

Every figure here is computed on 380 to 780 nanometres, which is exactly right for an eye and insufficient for a sensor. This field met the first subject the grid cannot hold, and the decision was not to widen it — because widening it honestly is impossible.

imaging · Capture D65, and a source built to have its chromaticity and nothing else. The smooth curve is the CIE's daylight reconstruction at 6504 K. The other is five Gaussian emission bands whose weights were solved so that the two agree in chromaticity to 8.5e-10 — closer than any instrument could tell them apart when looking at the lamps. Three numbers were matched and seventy-eight were not, and everything either source falls on will report the difference.

There is no D65 lamp

D65 is standardised by three numbers, and three numbers do not pin a spectrum. A source built to hit them exactly — matched to a part in a billion, with a third of the visible band nearly empty — separates pairs that D65 says are identical by up to eight and a half units of colour difference.

light · Light The same census, sorted by where the change of light came from. Each row is a change of illumination. The pale bar is how far it moves an ordinary surface for an observer who does not adapt; the solid bar at its left end is what is left after the observer has applied the one gain adaptation gives them, which is the ratio of the two whites in the CAT16 basis and is not fitted to anything. Sorted by where the change came from. The two kinds of light that existed before electricity sit at the top and leave the smallest share of themselves behind; the discharge lamps are worse, and the worst of them is d65 to a triphosphor tube at 33 per cent.

Which lamp changes are free

The changes of light that existed before electricity commute with one another to a couple of parts in a thousand, so one set of axes handles all of them. The lights the lighting industry invented do not, and the worst pair in the census is seventy-six times further from commuting than the best.

light · Light Six functions of wavelength, and the six different places they stop. Every table this collection integrates against, drawn over the range the body that published it defined it on. The scale is logarithmic so that the ultraviolet and the near infrared both fit. The bottom row is the range used here before the infrared band was added, and it is the intersection of the two rows that matter for an eye looking at a reflector — which is the right answer only while everything in the integral is being multiplied together. The daylight basis runs 80 nanometres further down than that intersection, and it was published that way because the ultraviolet in daylight is what makes a brightened sheet of paper glow. The analytic row is drawn to the edge of the plot because it has no edge: Planck's law is a formula and is exact at every wavelength, which is why illuminant A needs no table at all.

The tables do not stop together

This collection integrates from 380 to 780 nanometres, and decided once, in writing, that the range could not honestly be widened. The argument was correct at the long end and wrong at the short one — the CIE publishes the daylight basis from 300 nanometres, and publishes it from there for exactly the reason it matters.

light · Light What a sheet of glass takes out of the band a brightener eats. The transmittance of four glazings across the short-wave band, with the brightener's own absorption shaded underneath. The overlap between a curve and the shading is what the sheet behind that glass has to work with. Ordinary window glass stops below about 310 nanometres and leaves most of the band; laminated glass has a plastic interlayer that was put there to hold the sheet together in a crash and happens to absorb almost to 380; a filter sold to protect a print removes the band entirely. The curves are logistic edges at stated wavelengths rather than measurements of particular products.

The window is part of the light

A viewing condition here has always been a spectrum and a geometry. For anything fluorescent it needs a third thing — the transmittance of whatever the daylight came through — because ordinary window glass, a laminated windscreen and a museum filter remove three quite different parts of the band a brightener eats, and the sheet is a different colour behind each.

scene · Scene How short of determining the light a photograph is, as the scene grows. Each cell is the number of unknowns left over after every equation the image supplies: three sensors, a three-dimensional illuminant, and reflectances confined to a linear model of the dimension on the left. At one and two dimensions more surfaces close the gap. At three the gap never closes, because each further surface adds three equations and three unknowns; at four it widens. The count is arithmetic and has no algorithm in it.

An image does not determine the light

A photograph of a scene under one illuminant gives three numbers per surface and asks for the illuminant plus three numbers per surface. The count closes only if reflectances lie in a two-dimensional model, and no number of surfaces helps — at three dimensions the alternative scenes can be written down, and they reproduce every sensor response exactly.

scene · Scene Six functions of wavelength, and the six different places they stop. Every table this collection integrates against, drawn over the range the body that published it defined it on. The scale is logarithmic so that the ultraviolet and the near infrared both fit. The bottom row is the range used here before the infrared band was added, and it is the intersection of the two rows that matter for an eye looking at a reflector — which is the right answer only while everything in the integral is being multiplied together. The daylight basis runs 80 nanometres further down than that intersection, and it was published that way because the ultraviolet in daylight is what makes a brightened sheet of paper glow. The analytic row is drawn to the edge of the plot because it has no edge: Planck's law is a formula and is exact at every wavelength, which is why illuminant A needs no table at all.

The grid is a range, not an index

Three of the four departures in this round restore an argument the model dropped. The fourth does not — the 380-to-780-nanometre grid is the range of the one argument the model kept, chosen in the first weeks and never revisited. It costs 6.70 ΔE₀₀ on a coated printing paper, it is the cheapest of the four to fix, and it is the one still unfixed.

light · Light

Named alongside it

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

IlluminantPlanck's lawStandard observerFluorescenceOptical brightenersReflectanceSpectral power distributionUltravioletAssertionColour constancyCorrelated colour temperatureIntegration

All concepts