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

Planck's law — where it appears

The spectral radiance of a blackbody at a stated temperature, from which the colour of anything glowing hot follows. It is a formula rather than a table, so it extends exactly to any wavelength — which is why illuminant A needs no tabulated values at all.

Named by 11 essays across 3 fields — each of them below, with the objects they name alongside it.

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.

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.

light · Light Blackbody spectra from Planck's law, 2000 to 10000 K. Each 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.

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.

light · Light Luminous efficacy of a monochromatic source, under the 2° observer. Lumens per watt against wavelength. The curve is the luminous efficiency function scaled by 683, which is what luminous efficacy of radiation is — the 1979 redefinition of the candela fixed 555 nm at exactly 683 lm/W and everything else follows. Marked at 450 nm (26 lm/W), 500 nm (221 lm/W), 555 nm (683 lm/W), 600 nm (431 lm/W), 650 nm (73 lm/W). Under this observer the peak reaches 683 lm/W.

What a lamp cannot give back

Six hundred and eighty-three lumens per watt is not a measurement of anything. It is the definition of the candela, it is a ceiling no white light can approach, and the distance between a lamp and that ceiling is mostly the price of being able to see what colour things are.

light · Light 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 The two components of daylight, computed from one radiator and one scattering law. A 5800 K radiator through the atmosphere at air mass 1. The direct beam is the radiator times e^{−τm}; the sky is what that extinction removed, so the two are complements and neither needs its own model. The sky is steeply blue because τ ∝ λ⁻⁴, and a surface in shadow is lit by that component alone. Open ground and shadowed ground therefore sit under two illuminants differing by ΔE00 = 21.4 — which is why a photograph of snow has blue shadows and why no single white balance fixes both halves of it.

A shadow has its own illuminant

Outdoors there are two lights, not one. The direct beam is a radiator reddened by the atmosphere; the sky is precisely the power that reddening removed. A shadow is lit by the second alone, so shadowed ground and sunlit ground sit under illuminants 21 units of ΔE apart — before any surface, any eye or any opinion is involved.

scene · Scene The blue channel, as the three things multiplied to make it. Silicon's quantum efficiency, the colour-filter dye's transmittance, and their product. The dye is the only stage carrying any colour information and it is clear above about 800 nm — transmittance 0.92 at 900 nm against 0.06 at 550.

Silicon sees past the visible

A sensor's response ends at 1107 nanometres because that is the band gap, and the colour-filter dyes have stopped absorbing three hundred nanometres before it. So all three channels measure the same thing over the last third of the range, and every published sensitivity plot is drawn after the component that hides it.

imaging · Capture How much of what an unfiltered sensor records is invisible. The share of a camera's raw signal coming from beyond 780 nm, against the colour temperature of the lamp, for one surface with a near-infrared reflectance of 0.62. Without the filter it runs from 98 per cent at 2000 K to 51 at 9000; with it, under five per cent everywhere.

The filter that makes colour possible

An infrared-cut filter is not a refinement on a colour camera. Removing it collapses the separation between the three channels by a factor of nearly nine under tungsten, and the component that keeps colour photography working is the one nobody photographs.

imaging · Capture 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 Dimmed to a fiftieth, three ways. Switching a lamp on and off faster than anyone can see scales the spectrum and changes nothing else, so its colour temperature is a horizontal line and its chromaticity moves by 7.3e-14 ΔE00 — exactly, to floating point. Reducing the drive current moves the die's peak and cools the junction, which moves the mixture: ΔE00 3.5 across the range. A filament has no spectrum of its own to move; it is a blackbody at whatever temperature the power leaves it at, and it falls 1672 K. Three methods, one instruction, three colours.

Three ways to dim a lamp

"Dimmed to ten per cent" names three different colours. Switching the lamp on and off faster than anybody can see changes the chromaticity by nothing at all — exactly, to floating point. Reducing the current moves it a few units. Reducing the power to a filament moves it eighteen hundred kelvin down the Planckian locus, and stays on the locus exactly the whole way.

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

Named alongside it

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

IlluminantCorrelated colour temperatureSpectral power distributionStandard observerThe D-series daylight illuminantsSpectral sensitivityInfraredReflectanceSiliconThermal radiationWhite pointAssertion

All concepts