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

Every essay — page 44

Page 44 of 54, continuing through the fields in the same order.

What light is What the eye does Matching and measuring Difference and uniformity What the brain does What a scene does What a camera does Where the model breaks What it takes to deliver it

SeriesObserversNamed objectsRefutationsSearch

What a camera does

A camera is three functions of wavelength collapsing a spectrum onto three numbers, which is what an eye is — and they are different three functions. Everything a photograph can and cannot establish about colour follows from that, and from the fact that silicon sees three hundred nanometres past where anybody is looking.

How wrong a camera profile is, and who it is wrong for. A colour matrix fitted against the 1931 observer, evaluated four ways. Its residual against that observer is ΔE00 0.92 — the Luther failure, which is a property of the sensor and is the honest measurement of the camera. Against a person drawn from a population of 160, the worst-off twentieth report 3.35. And a camera with no spectral error whatever, reporting the standard observer's own tristimulus values exactly, would leave 3.47. The camera is not the problem. It was fitted to somebody who does not exist, and so is the standard it was fitted against.

Fitted to an eye nobody has

A camera profile's residual against the observer it was fitted to is under a unit, and that is the number everybody quotes. Against a person drawn from a population it is 3.35 at the ninety-fifth percentile — and a camera with no spectral error whatever, reporting the standard observer's tristimulus values exactly, would carry 3.47. The camera is not the problem.

7 figures The same flicker, written across the frame. A rolling shutter exposes each row of the sensor at a different moment, so a lamp that flickers above fusion is recorded as bands. There are 1.7 of them here — the readout time times the lamp's frequency, which is a camera setting and not a property of the light — spanning 2.37 stops. Held at matched luminance the lightest band and the darkest are still ΔE00 5.40 apart in colour, because the two drive currents are two spectra and the shutter caught one of each.

The shutter samples the lamp

A lamp switched between two drive currents at a hundred hertz is one steady colour to a person and two spectra to a camera. A thousandth-of-a-second exposure catches whichever phase the shutter opened at — two and a third stops of exposure and five units of colour, decided by nothing but timing — and a rolling shutter writes the difference across the frame as bands.

6 figures The basis a camera balances in is a different basis for every light. A camera's white balance is a per-channel gain on raw values, which is a von Kries adaptation in whatever basis the filter dyes give it. That basis is not a property of the dyes alone: it is the dyes and the light in the room, and it moves when the light does. Each bar is how far the basis has turned, in degrees, from where it sits under D65. A sensor satisfying the Luther condition would have a bar of exactly zero on every row, because for such a sensor the light cancels — which is the one property nobody buys a sensor for.

A camera balances in another basis

White balance is a per-channel gain on raw values, which makes it a von Kries adaptation in whatever axes the filter dyes happen to give. Those axes are not a property of the dyes alone — they move with the light, by up to seventeen degrees across the adaptation census — and the sensor for which they would not move is the one that adapts worst of all.

6 figures Two lamps of the same colour, and one sheet that is two colours under them. The same brightened sheet under a xenon flash, the same flash behind its cover glass, and a phosphor-converted white LED of nearly the same chromaticity. Each patch is computed relative to its own lamp's white, which is what a perfect white balance does — so everything a camera can see and correct has already been removed. What is left is ΔE00 11.8 between the first and the last, against 3.2 between the two lamps themselves. The LED has no emission below 380 nanometres at all, because its pump die is at 450, so the sheet simply does not fluoresce under it and nothing in the photograph records why.

A camera cannot record the excitation

Two lamps of nearly the same chromaticity, one with ultraviolet and one with none, put a brightened sheet twelve units apart after a perfect white balance. Nothing in the camera measured the difference — the filter stack removed the band before the sensor saw it — so the correction that would fix the picture needs a quantity the file does not contain.

7 figures The lamps the four conditions shine, where they differ. The short-wave half of what each measurement condition puts on the sample, plotted to 560 nanometres because past that the three are indistinguishable in shape. M₁ is D50 with its ultraviolet; M₂ is the same lamp behind a cut filter at 400 nanometres, and at 360 it is 0.0 per cent of what M₁ delivers; M₀ is a tungsten lamp, which has some ultraviolet, has less than daylight, and is not specified at all by the standard — so two M₀ instruments need not agree with each other. M₃ is not plotted because its lamp is M₂'s; what makes it a fourth condition is a polariser.

The lamp that stopped emitting ultraviolet

A blue-pumped white LED has a die at 450 nanometres and emits nothing shorter. Between about 2005 and 2020 that lamp replaced almost every other indoor source, which removed the excitation supply from a great many rooms — so brightened materials stopped glowing indoors without a single one of them being reformulated.

6 figures What a camera matrix reports on its own chart, and what it delivers off it. The same camera fitted on charts of increasing chromatic range. The left bar of each pair is the mean error on the chart the matrix was fitted to, which is the number a profile comes with; the right bar is the error on a saturated set it never saw. At the thinnest chart the fit reports 0.19 ΔE00 and delivers 1.65, a factor of 8.6. The gap closes as the chart widens, and it closes because the chart improves rather than because the camera does.

The chart decides the profile

A camera's colour matrix is nine numbers fitted to a set of patches somebody chose, and the number that comes with it is the error on those patches. On a chart with no chromatic range that number is 0.19 ΔE00 and the matrix delivers 1.65 — and a second matrix, indistinguishable on the chart, delivers 2.03.

7 figures A camera matrix fitted under each light, used under each light. Mean ΔE00 over the same surfaces, with the matrix fitted under the row's light and the scene under the column's. The diagonal is what a profile's data sheet quotes and is between 1.0 and 1.2 everywhere. Off it the numbers rise steeply: the matrix fitted under illuminant A reports 1.17 there and delivers 9.34 under a 9000 K daylight, a factor of 8.0. Nothing about the camera changes between cells.

A matrix is fitted under one light

A camera's colour matrix is nine numbers determined by a chart photographed under a particular illuminant, and the error it quotes is the error under that illuminant. Fitted under a tungsten lamp and used under a cold sky it delivers eight times as much — and the two-matrix scheme every real profile uses turns out not to be a compromise at all.

7 figures The dyes a camera has, and the dyes an adaptation basis would want. Three sensor sensitivities drawn twice: faintly, the silicon-and-filter-array set this collection models, and boldly, three Gaussian dyes chosen to make the inverse of their own response matrix a good basis for a white-balance gain. The designed dyes sit at 610, 542, 449 nm with widths of 35, 26, 30 nm — narrower and further apart than the real ones, which is what sharpening looks like when a search rather than a committee does it. They leave 0.97 ΔE00 against the real sensor's 1.62, and they are held within 0.28 of the Luther condition so that the result is still a camera.

A sensor designed for its inverse

A camera's white balance is a gain in a basis made from its own dyes and the light in the room. Choose the dyes for that basis instead of for cost and quantum efficiency, hold the sensor within a stated distance of the Luther condition, and the design reaches the best adaptation figure any basis achieves — and then the room moves it.

5 figures Four cameras that all satisfy the Luther condition exactly. Four sensors whose sensitivities are linear combinations of the colour-matching functions — the theoretical ideal, satisfying the condition to machine precision, each with an adaptation basis that does not move when the light does. They differ only in which linear combination, which the condition does not constrain, and they leave 2.46, 0.97, 1.65, 2.37 ΔE00 after a white balance. The best of them reaches 0.974, which is the best any basis at all achieves. Being a perfect colorimeter costs nothing in adaptation; what costs is the mixing matrix, and the control measured here carries one nobody chose.

The condition chooses no axes

It has long been said here that a sensor satisfying the Luther condition exactly adapts worse than a silicon one, and offered a reason — that its channels are the matching functions, and a gain on those is the oldest mistake in the subject. The measurement was of one sensor. The condition leaves the axes entirely free.

5 figures Which of a camera's three dyes each direction moves. A grid with one column per direction — stiffest on the left, flattest on the right — and one row per parameter of a camera's three dyes. Each cell's bar length is that parameter's share of that direction, so a column with one long bar is a direction that moves one thing. The stiffest column is dominated by blue centre, at a weight of 0.96. The flattest column is spread across blue width, red width, green width — a combination rather than any single number, which is why a specification listing one tolerance per parameter cannot express it.

Where a camera is blind to itself

A colour filter array is six numbers — three dye centres and three bandwidths — and how well the resulting sensor adapts is far more sensitive to some combinations than to others. The stiffest direction is almost entirely where the blue dye sits. The flattest is all three bandwidths at once, and the design can move twenty-five times further along it for the same cost.

8 figures A camera's dye widths are free under one requirement and not under another. Three panels, one per dye. In each, a pair of bars per requirement: how far that dye's centre wavelength and its bandwidth can move before the requirement gets five per cent worse. Under the adaptation objective — the one the previous round measured — every width has far more room than its centre, which is the finding that put a tolerance budget on the centres. Throughput and the colour matrix's noise gain, the two requirements that objective was said to be silent about, reach the edge of the search in every direction and hold nothing. What tightens the widths is the Luther residual, which was in the model already. The bottom pair in each panel is what survives all four.

The widths were free because nothing else was asked

A camera's three dye bandwidths carry almost all of the flattest direction of the adaptation objective, so that objective says a tolerance budget belongs on the centre wavelengths. The two requirements it was said to be silent about turn out not to bind either — and the one that does was in the model already.

7 figures What a camera's dye 1 is allowed to be, under four requirements. The plane a colour-filter dye is designed in: its centre wavelength across, its bandwidth up, both in nanometres, so the two axes are comparable and the shapes mean something. Four outlines, one per requirement, each the set of dyes within five per cent of the designed one on that requirement; the shaded region is where all four hold. Two of the four — throughput and the colour matrix's noise gain — reach the edge of the search in every direction and are invisible as boundaries. The intersection is ±6.8 nanometres of centre and ±13.3 of width, against the adaptation objective's own ±20.6 in width alone.

Two tolerances do not meet in a tolerance

A specification lists requirements separately and a manufacturer has to satisfy them together. Where two long thin regions cross at an angle, what is left is much smaller than either, its longest direction is neither of theirs, and no list of tolerances describes it.

6 figures