Capture — the series
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A camera is a fourth observer
The 1931 functions, the 1964 functions and a person's own cones are three sets of three curves that collapse a spectrum onto three numbers. A camera is a fourth, built from silicon and dye rather than from pigment and neural wiring, and it agrees with none of them.
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Raw is not a picture
A raw file is three integrals per site and a list of decisions nobody has taken yet. Every one of those decisions has a defensible answer and none of them has a correct one, which is why two converters open the same file and disagree.
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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.
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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.
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Luther said when it would work
There is an exact condition under which a fixed three-by-three matrix converts camera raw to XYZ correctly for every spectrum in existence. It was stated in 1927, it is a theorem rather than a guideline, and no camera ever built satisfies it.
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A grey edge arrives coloured
A sensor site measures one channel and the other two are interpolated from neighbours that sat somewhere else. Across a black-and-white step that reconstruction gives an achromatic scene a chroma of 144 per cent of its own local mean, and nothing in the scene or the sensor was coloured.
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Most things are pale in the infrared
A spectrophotometer stops at 780 nanometres and a black cotton shirt reflecting five per cent of visible light reflects more than half the near infrared. The measurement everybody has and the quantity a camera integrates are different quantities, and nothing in the first says so.
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The camera has its own metamers
Two surfaces a camera records as identical can be plainly different to a person, and two a person cannot tell apart can be recorded as different. Both pairs are constructed rather than found, from one projection, used for both.
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A camera profile is a fit
Since no matrix is exact, the one a manufacturer ships is a least-squares compromise over a set of surfaces somebody chose. Fitted on desaturated patches it is excellent on desaturated patches — and the sample set is a hidden argument to every camera profile in existence.
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A blown highlight turns
An exposure that clips nothing changes no hue at all. Once one channel reaches the ceiling the recorded hue rotates by as much as sixty-seven degrees, with nothing in the scene having changed colour — and every response a converter can make to that is an invention.
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No matrix is right everywhere
The best three-by-three this sensor admits, fitted and tested on the same twenty-four surfaces, leaves a worst case of ΔE00 2.85. A control sensor built to satisfy Luther's condition reaches ten to the minus seven under the identical computation, which is what makes the first number a measurement.
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The highlight is the white balance
Every estimator a camera uses is an assumption about the scene wearing the costume of a measurement. The specular component of a glossy surface is not — it carries the illuminant to within a third of a degree on a scene where averaging is fifty times worse, and it does so without knowing what colour the paint underneath is.
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Correcting colour costs noise
The matrix that turns a sensor's raw into XYZ has large off-diagonal terms of both signs, because that is what correcting a sensor which fails Luther's condition requires. Differences of large numbers are where noise grows, and the full correction amplifies photon noise by 1.66 times.
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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.
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A photograph is not a measurement
A photograph is a measurement made by an instrument whose kernel nobody published, under an illuminant nobody recorded, corrected by a matrix fitted to somebody else's surfaces, with two thirds of every pixel invented. It supports relative claims well and absolute ones badly, and it is used for the second.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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A chart decides what a camera scores
A camera profile's reported error changes by a factor of five when the test chart's saturation changes, with the camera and its matrix untouched. The elasticity is 0.67 — the same figure, to two per cent, that an entirely unrelated measurement over an entirely unrelated set of surfaces gives.
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The coincidence was a mechanism
Two sensitivities from two libraries with no shared code came out two per cent apart, and the claim made about them was that they share a mechanism rather than a number. That claim has a colour-difference formula inside it, so it can be tested by changing the formula — and both curves move together across the whole menu, from 0.5 to 1.15.
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A pixel has an aperture too
A camera photographing a translucent object has the same two discs a spectrophotometer has — one lit, one looked at — and gets them the other way round. Its illumination covers the whole scene, so the flat colour of a translucent surface comes out exactly right at any magnification, and the error moves entirely into the edges.
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The objective nobody chose
Every camera profile here, and as far as can be told everywhere, is a linear least-squares solve in tristimulus space. That is an objective and it is on nobody's menu — it weights an error by how bright the patch is. Refitting the same matrix to minimise a real colour-difference formula improves the fit in all six, and moves the matrix, which means different pixels rather than a different report.
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The chart was measured, not photographed
A camera profile is fitted so that the camera's response maps onto the chart's tristimulus values, and those values came out of a spectrophotometer. So the profile's target carries the instrument's departures and the camera does not — a mildly translucent chart read through a four-millimetre aperture supplies targets 2.55 ΔE₀₀ from the truth, which is twice the profile's own fitting error.
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The chart was measured by an observer too
A camera profile is fitted so that the camera's numbers reproduce the chart's measured tristimulus values. Those values were computed through the 1931 observer, so the fit inherits every departure in this round — and the fit's own residual, at 0.19 ΔE₀₀ on the chart, is fifteen times smaller than the term it cannot see.
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A sensor has no lens
A camera is a fourth observer and it is the only one with none of the six arguments this round measured. It does not age, it has no macular pigment, its response does not broaden with density and its peaks do not vary — so it is perfectly reproducible and is not any of the observers it is fitted to reproduce.
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The order is not in the documentation
A raw converter performs a white balance, a colour matrix, a tone curve and a clip, and every account of the process lists them in that order without saying the order decides anything. Exchanging the first two moves the picture by nine colour differences at the mean and thirteen at the worst patch. The twenty-four arrangements collapse into five outcomes running out to sixty-five, and nothing a converter ships says which of them it is.
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One step has no choice
Four of a raw converter's operations can be arranged twenty-four ways. The reconstruction cannot be arranged at all — a colour matrix needs three numbers and a mosaic site has one, so filling in the mosaic is forced to the front by arithmetic rather than by convention. What is not forced is whether it happens in linear light or after the curve, and that decision costs 5.8 colour differences at an ordinary edge and nothing at all four sites away from it.
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A contrast control is three controls
A tone curve is a function of one number at a time and knows nothing about hue. Applied to each channel separately it rotates a hue circle by up to seventeen degrees, raises chroma by a factor of 1.27 at ordinary strength, and lifts lightness — so a photographer who moves a contrast slider has moved three things and the interface names one of them. All three scale with the curve's strength, monotonically, and the hue rotation depends on which hue it is.
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A stop is not a stop afterwards
Doubling the light is exactly a factor of two in raw values and in tristimulus values, which is the one thing about exposure everybody is sure of. A stop taken after the tone curve is a factor of something else, and matching the two on an eighteen per cent grey leaves the rest of the frame between three and four colour differences apart at the mean and up to eleven at the worst patch. The gain that matches one stop is 2.47 rather than 2.
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Two converters and one highlight
The clip is the only step in a raw pipeline that destroys information rather than moving it, and it is the step whose position varies most between converters. Below the sensor's ceiling its position changes nothing at all, exactly. Above it, clipping at the sensor and clipping after the matrix land twenty-one colour differences and seventy-eight degrees of hue apart, and which hues are affected is a property of the camera's own dyes.
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The corner of the frame has another filter
A camera's infrared-cut filter is an interference stack, and light crossing it at an angle sees its edge moved towards the blue — from 665 nm at the centre of a frame to 646 at twenty-five degrees. The corner's red channel loses a tenth of its response under daylight and a sixth under tungsten. A grey-card gain map makes the corner exactly right under the lamp it was made under; under a tungsten lamp the same grey is 2.6 colour differences wrong, under a white LED 4.2, and even under its own lamp the coloured patches are not corrected, because a moved edge is not a gain.
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A black level is multiplied by the balance
Every raw value carries a pedestal that is subtracted before anything else, and a white balance is then a different gain in each channel. Subtracting a constant and multiplying by one commute only when the constant is zero or the gains are equal. So a pedestal left three thousandths of white too high becomes 2.4 colour differences in a two per cent grey, most of it chroma, in the colour the lamp starves — and pushing that shadow four stops in editing makes it 8.9. An offset in proportion to the lamp's own white is the exception, and it is exactly grey.
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Clipped noise does not average away
Noise on a raw reading is as likely to fall below the true value as above it, which is why averaging an area removes it. A converter that sets negative readings to zero keeps the upper half and throws the lower away, and the mean of what is left is the signal plus a pedestal. With no black level error anywhere, a half per cent grey under a tungsten lamp comes out 1.04 colour differences off at high gain, 8.98 after a four-stop push — and a blur that removes every trace of the noise leaves the tint where it was.
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A corner is corrected by one row
A grey-card gain map makes the corner of a frame exactly right on grey and leaves coloured patches 1.86 colour differences wrong at twenty-five degrees. A three-by-three matrix fitted at that position halves it — and six of its nine numbers do nothing, because the moved filter edge is in one channel. The three that matter rebuild the lost red from green and blue, they carry to another lamp better than a gain map in eleven cases of twelve, and in the twelfth, a row fitted under tungsten and used in daylight, they leave the grey 9.2 off.
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Two matrices do not reach a white LED
A camera profile's two matrices, blended by the scene's colour temperature, are as good as a matrix fitted anywhere along daylight. Under a white LED or a fluorescent tube the same blend leaves colours twice as far off as a matrix fitted under that lamp, and no weight inside the profile's range repairs it. What decides it is not how far the lamp sits from the Planckian locus — a triphosphor tube sits nearly on it and fares worst — but whether its spectrum has lines in it, which a white balance reading cannot see.
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Filling in a highlight is a claim about the surface
A converter that rebuilds a clipped channel has to say what the highlight was. A matt surface over-exposed keeps its own colour, and filling the lost channel from that colour is exact. A glossy highlight is the surface's colour plus a reflection of the lamp, and the same fill leaves it 7.6 colour differences too colourful — while a fill that solves for surface and lamp is exact. Neither works once two channels are clipped, and a tungsten lamp keeps a highlight in the one-channel band more than twice as long as daylight does.
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Flicker sorts lamps the wrong way
A camera cannot see a spectral line in its own white, so the essay on the two-matrix profile named the classifiers a device might have instead, and the first of them was flicker. Flicker is measurable, and it measures the wrong thing. It sorts lamps by how their power is delivered while the matrix needs them sorted by how their spectrum is shaped, and the two are independent: a white LED on a constant driver is perfectly steady and strongly structured, and it is what most indoor photographs are lit by.
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The converter can choose except where it matters
A converter rebuilding a clipped highlight has to say whether the surface was matt and over-exposed or glossy and carrying a reflection, and the evidence is whether its raw chromaticity slides towards the lamp's on the way up. Read through the sensor's own noise, the slide is clear on most of the chart from the few tens of pixels a specular highlight holds — and on the surfaces where it takes half a frame, confusing the two models costs more than the median. A ratio cannot see a common scale, and an exposure supplies one.
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Four places to clamp are two pipelines
The essay on clipped noise ended on a procedure: a black frame and a dim grey card at a high amplification would place each raw converter's clamp. A procedure is a claim that a measurement identifies something, and this one identifies less than it looks. A clamp at zero commutes with the white balance and with the tone curve and not with the colour matrix, so the four positions are two pipelines — and the measurement separates them, on a card at half a per cent of white rather than on the black frame.
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One row for every lamp costs the lamps that lose least
A corner correction fitted under one lamp is right under that lamp and can be badly wrong under another, so a converter unsure of its lamp was offered a single row fitted under several at once. Pooled over four lamps, one row holds every lamp's corner between 1.33 and 1.56 colour differences — no lamp worse than a grey-card map, and none near the 4.91 a wrong row can leave. The price falls on the white LED and the fluorescent tube, which it leaves four times worse than their own rows, because they lose the least red at the corner and the pooled row is built to repair the lamps that lose the most. Two rows, one per class of lamp, keep almost all of both.
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Two lamps decide what one lamp could not
Under one lamp a handful of surfaces cannot tell a glossy highlight from a matt over-exposure without most of a frame, because there the two differ by a scale a ratio cannot see. In a room lit evenly by a 3000 K lamp and daylight, every surface on the chart is decided from ten pixels. A body can sit at one lamp's white, not at two, and the rescue holds only while the second lamp carries a fifth of the light and its white sits far enough from the first.
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Two sensors disagree about deep red, not lines
A phone's ambient-light sensor and its camera read the same lamp differently, and the difference sorts fourteen lamps into smooth and structured without a single mistake — where flicker made five. It is not reading their lines. Almost all of it comes from the sensor's clear channel collecting deep red the camera's infrared cut throws away, so daylight with its far red trimmed is called structured and a white LED with a far-red emitter is called smooth.
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A narrow channel has to be read on its own
An ambient sensor with a clear channel tells structured lamps from smooth ones by reading deep red, and one without it reads structure but breaks at one per cent of calibration error. A narrow fourth channel between the camera's peaks was proposed to have both. Pooled into the sensor's disagreement with the camera, it reads structure and breaks at one and a quarter per cent — no better than the design it was meant to rescue. Read on its own, as its departure from what the camera predicts for it, a channel at 450 nm holds to four per cent, the clear channel's figure, and far red does not move it.