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

Planckian locus — where it appears

The path a blackbody's chromaticity traces as its temperature rises, which is the reference every colour temperature is quoted against. A lamp is rarely on it, so a temperature alone is an incomplete description of what the lamp looks like.

Named by 11 essays across 2 fields — each of them below, with the objects they name alongside it.

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 triphosphor fluorescent — three narrow phosphors plus the mercury lines, and the white it produces. The spectral power distribution of a triphosphor source, normalised to its own peak, and the colour a perfect white reflector takes under it: chromaticity (0.3379, 0.3389), correlated colour temperature 5258 K at Duv -0.0035. The white looks ordinary. The spectrum producing it does not.

A lamp is not a blackbody

A fluorescent tube puts a third of its light into four mercury lines. A white LED is a blue spike with a hole beside it. Both are sold by a colour temperature, and a colour temperature says nothing about either.

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 Mixtures of 2700 K and 6500 K, on the diagram colour temperature is defined on. Both sources are Planckian radiators, so both sit exactly on the locus. Every mixture of them lies on the straight line between them, because mixing is addition and chromaticity is a projection of it — and the locus is curved, so the line is a chord. The equal mixture sits -0.0064 off the locus at a correlated colour temperature of 3953 K: a light that is measurably pink, specified by a number that says nothing about it.

Two lamps do not average

Light adds, band by band, and every number a lamp is sold by is a projection of the sum rather than a sum of the projections. Two radiators sitting exactly on the Planckian locus mix into a light that is measurably pink; two poor lamps mix into a better one than either.

light · Light Three ways to dim a lamp, and only one of them is free. What an adapted observer is left with, as the same lamp is taken down to one per cent by each of the three methods. Duty-cycle dimming lies exactly on zero at every depth: it scales the spectrum, a scaling is a gain in every basis, and adaptation removes all of it. Current dimming moves the pump and the phosphor apart and leaves 0.15 at a tenth. A filament follows the Planckian locus, which is the largest chromaticity change of the three and leaves 3.63 — the ordering by chromaticity and the ordering by what a person sees are not the same ordering.

Only one dimmer is invisible

An earlier essay separated the three ways to dim a lamp by the chromaticity each arrives at. Asked instead what an adapted observer is left with, the ordering is different and one method comes out at exactly zero — a duty cycle is a scaling, a scaling is a gain in every basis, and adaptation removes all of it at every depth.

light · Light A phosphor grid's camera error is a V about the locus. Forty-eight white LEDs varied in pump, converter share and red phosphor (circles, shaded by red phosphor) and the census's forty-four (squares), placed by how far each white sits from the Planckian locus and by the camera's mean colour error under it. Across the grid the error rises away from the locus on both sides — correlated 0.68 with the distance on the green side and -0.64 on the pink — and is lowest near it. Every one of the census's LEDs sits on the green side, from 0.007 to 0.034.

LEDs varied in their phosphors fall off every line

The merged smooth family estimates a camera's colour error from an ambient-light sensor's departures to ±0.127, and five new white LEDs, varied in their phosphors where the census's forty-four vary their pump, missed by ±0.196 because the family's line had learned almost nothing about the sensor's 640 nm channel. Rebuilt on forty-eight LEDs varied in pump, converter and red phosphor, the line learns it: its 640 nm weight goes from −0.13 to −0.74, most of the way to the −0.85 the new LEDs implied. The prediction was that the new LEDs would then land within ±0.13. They miss by ±0.229, worse than before, crossing to the other side of the line, and the census's own held-out error more than doubles, to ±0.294. No pool of LEDs restores it, and no line in the sensor's departures reads the grid's own LEDs better than ±0.29. Across the grid the camera's error is a V about the Planckian locus, rising away from it on the green side and on the pink — and every one of the census's LEDs sat on the green side.

imaging · Capture The curve holds inside the bin and fails outside it. Four error lines learned on eighty-nine white LEDs at a Duv of nought and ±0.003, each read at those three values with every LED left out and at ±0.0015 and ±0.006 on 119 LEDs none of them was fitted on. The slope and curve per temperature reads ±0.045 and ±0.043 inside the bin and ±0.153 and ±0.161 at twice its edge, where a slope per temperature alone reads ±0.093 and ±0.110.

The bin's curve holds between its points and breaks beyond them

A camera's colour error under a white LED was read from an ambient sensor across a manufacturing bin by a line with a slope and a curve in Duv for each colour temperature, fitted at three Duv values — on the locus and 0.003 either side — and reading the LEDs beside the locus within ±0.056 and ±0.048 ΔE₀₀. A curve through three points passes through them whatever happens between them. The prediction was that 119 new LEDs built at ±0.0015 are read within ±0.06, and those at ±0.006 worse than ±0.10. Both halves hold: ±0.045 and ±0.043 inside, ±0.153 and ±0.161 outside. But the error's own mean course stays on its parabola within 0.02 out to ±0.006. The line's bend is not the error's: it is the gap the line leaves between the locus LEDs and the bin's edges, and a gap spent as a curvature quadruples at twice the distance.

imaging · Capture With the level placed, the line bends as the error does. At each temperature, the curvature in Duv of the camera error's mean course through nought and ±0.003, beside the curvature each slope-and-curve line implies, averaged over the three pumps. At 2,700 K the course bends by +7,916, the line without a level by +2,803 and the line with one by +8,198; at 4,000 K the course bends by +2,196, the line without a level by +14,591 and the line with one by +2,195; at 6,500 K the course bends by +363, the line without a level by −13,349 and the line with one by +445.

A level for each temperature lets the curve be the error's

An error line with a slope and a curve in Duv for each colour temperature read white LEDs inside a manufacturing bin within ±0.045 ΔE₀₀ and LEDs at twice the bin's edge only within ±0.16, though the camera's own error stays on its parabola there. Its curve was borrowed: the line's shared terms could not place each temperature's level, and the square of the Duv absorbed the gap. The prediction was that one more number a pump, the square of the mireds, brings the locus LEDs within ±0.05 and those at ±0.006 within ±0.08. It brings the locus to ±0.025 — three times better than the locus-only line that started this run of essays — and the outer LEDs to ±0.049 and ±0.058. The curvature the line now implies at each temperature is the error's own within a fifth; what it leaves is the warm whites' scatter at the bin's edges.

imaging · Capture The red phosphor bends nothing and tilts the warm whites. The 2,700 K LEDs' residual at each Duv under the eleven-term line, with the square of the Duv times the estimated red phosphor added, and with the Duv times the estimated red added instead. The bend term leaves ±0.006 at ±0.068 and ±0.088, against ±0.069 and ±0.087; the slope term takes them to ±0.046 and ±0.067.

The red phosphor tilts the warm whites and bends nothing

An error line with a level, a slope and a curve in Duv for each colour temperature reads white LEDs at 4,000 and 6,500 K within ±0.04 ΔE₀₀ across and beyond a manufacturing bin, but warm whites at twice the bin's edge only within ±0.087. The prediction was that the red phosphor sets a warm white's bend, so that one term more a pump — the square of the Duv times the estimated red — brings them within ±0.05. It moves them by a thousandth. The red phosphor enters the slope instead: the Duv times the red takes them to ±0.046 below the locus and ±0.067 above. And the rest points upstream. The first stage reads a warm white's red phosphor squeezed toward the middle of its range, the warm misses follow that misreading times the Duv at r = 0.79, and given the red each LED was built with the warm whites come within ±0.05 — though the same substitution doubles the error at 4,000 K.

imaging · Capture The squeeze belongs to the temperature, not the Duv. For the 2,700 K LEDs at a Duv of ±0.003 and ±0.006, the first stage's mean estimate of the red phosphor against the red each was built with, by three first stages; the dashed line is a perfect reading. With one Duv term, no red and a full red are read at 0.13 and 0.80; with the Duv times the departure and the mireds at 0.14 and 0.80; with a level and a departure slope for each temperature at 0.02 and 1.01.

The line had already undone the squeeze

An ambient sensor's first stage reads a 2,700 K white LED's red phosphor squeezed about a third toward the middle of its range, and the camera-error line's warm misses outside the bin follow that misreading times the Duv. The prediction was that giving the first stage the Duv times its 600 nm departure and times the mireds would undo the squeeze. It changes nothing: the squeeze belongs to the temperature, and a level and a departure slope for each temperature read the warm red four times better, within ±0.035. But the eleven-term error line does not move — no warm LED by more than 0.006 — because at one temperature a squeeze is a rescaling its red and red-times-mireds terms had already undone. Only the red-slope line, whose one coefficient a pump spans three temperatures, gains: to ±0.034 below the locus, within 0.002 of the red known. And the cold whites pay for it.

imaging · Capture Split between two estimates, the line keeps both ends. The warm whites at ±0.006 and the cold whites at −0.003, read by the red-slope line on the squeezed red, on the un-squeezed red, and split — the eleven terms on the squeezed estimate, the red slope on the un-squeezed. The split line reads the warm whites at ±0.034 and ±0.057 and the cold at ±0.025; the squeezed line reads them at ±0.046, ±0.067 and ±0.021, the un-squeezed at ±0.034, ±0.057 and ±0.040.

Two estimates of one red each read their own end

Two first stages read a white LED's red phosphor from an ambient sensor: one squeezes the warm whites' red a third toward the middle, the other reads it four times better, and a camera-error line with a red slope prefers the first for cold whites and the second for warm. The prediction was that a line handed both — the eleven-term line on the squeezed estimate, the red slope on the faithful one — keeps each end's gain. It does, within 0.004 at the cold end. But the second estimate is not needed: the squeezed red alone, its red slope multiplied by the mireds, reads every LED within a ten-thousandth of the split line. And the two estimates' difference is worth a term of its own. Added to the line, it reads the cold whites within ±0.016 at every Duv and on the locus within a thousandth, and moves the warm whites and the middle by nothing.

imaging · Capture

Named alongside it

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

Held-out validationWhite LEDCamera rawCorrelated colour temperatureDuvOverfittingLinear modelIlluminantSpectral power distributionThermal radiationChromatic adaptationColour rendering

All concepts