A camera cannot record the excitation

A camera is three functions of wavelength collapsing a spectrum onto three numbers, which is what an eye is. Where the analogy has always held on this site — since a camera became a fourth observer — is that both are integrators: whatever arrives is weighted and summed, and what is lost is lost the same way for both.

For a fluorescent sample the analogy breaks in a specific place. The eye’s short-wave limit is a filter it cannot remove and does not need to. The camera’s is a filter somebody chose, for a good reason, and the consequence is that the camera cannot measure a quantity its own picture depends on.

Read as a pair rather than as three patches, the same measurement is sharper: the two lamps agree under the condition that takes the excitation away and disagree under the one that supplies it.

The claim #

White balance is a diagonal matrix on three numbers, and the difference between a lamp with ultraviolet and one without is an addition in a fixed direction. A diagonal cannot produce an addition, and the camera has no measurement of the addition’s size — so the correction is not merely unavailable, its input does not exist.

• A xenon flash supplies 65 per cent of a brightener’s excitation from below 380 nanometres. A phosphor-converted white LED supplies none, because its pump die is at 450.
• The two are nearly the same colour: their white points are 0.0034 apart in chromaticity, which any white balance absorbs without comment.
• The sheet under them is ΔE00 11.84 apart after each is referred to its own lamp’s white — b* at −11.7 under the flash and +0.6 under the LED.
• The camera’s own filter stack removes the band before the sensor, deliberately: ultraviolet focuses at a different distance and would be a blur added to every channel.
• So a raw file records the emission and not the excitation, and the field that would let a converter correct for it is not missing from the metadata by oversight — nothing in the camera measured it.

Why the filter is there #

Silicon is sensitive well into the ultraviolet — the band gap sets the long edge at 1107 nanometres and the short edge is a matter of how much of the light gets through whatever is in front. Left alone, a bare sensor would record from about 200 nanometres.

It is never left alone, and there are three reasons stacked in front of it.

The lens glass absorbs. Ordinary optical glass has the same short-wave edge as any other silicate — around 300 to 350 nanometres depending on the formulation, and multi-element lenses stack the effect. A camera with a dozen glass elements is opaque below about 350 before any coating is applied.

The ultraviolet-and-infrared cut filter removes what is left. Every colour camera has one, bonded over the sensor, and it is specified to pass roughly 400 to 680 nanometres. The infrared half of its job is famous — silicon sees three hundred nanometres past where anybody is looking — and the ultraviolet half is not discussed because nothing seems to depend on it.

And the optics could not focus it anyway. Refractive index rises steeply towards short wavelengths, so ultraviolet light focuses well in front of the visible image; without the filter it would arrive as a veiling haze rather than as detail. That is the same longitudinal chromatic aberration the eye has, and it is the reason the eye’s own filter is not a loss either.

So the filter is right. Nothing here argues for removing it. What follows is only that a correct engineering decision has an information consequence that nobody carried forward.

What white balance can and cannot do #

White balance is a per-channel gain on raw values. It is a von Kries adaptation in whatever axes the dyes happen to give, and its whole job is to divide out the illuminant.

For a reflecting scene that is exactly right. Change the lamp and every raw value scales by the same three factors — approximately, and exactly on a three-dimensional set of surfaces — so three numbers recover the scene.

For a scene with a brightened sheet in it, changing from a lamp with ultraviolet to one without does two things at once. The multiplicative part is small: the two lamps are nearly the same colour, so the gains barely move. The additive part is not: one lamp makes the sheet glow and the other does not, and the glow is a fixed amount of blue added to the sheet’s radiance and to nothing else in the scene.

A diagonal matrix scales; it does not add. Applying any gain to the LED photograph scales the sheet and everything around it together, which is precisely wrong — the sheet needs more blue and the wall behind it does not.

The measurement makes the size of the mismatch explicit. The two lamps’ white points are ΔE00 3.25 apart in the sense of a perfect diffuser under each. The sheet is 11.84 apart. The camera has removed the first, correctly, and what remains is three and a half times what it removed.

What the diagonal can and cannot move #

That a diagonal cannot produce an addition is exactly right, and it is easy to read as saying a gain does nothing here. It does something. It moves the error.

The gain that maps the LED sheet onto the flash sheet, applied after a perfect white balance, is 1.045, 1.007 and 1.212 on X, Y and Z. It fixes the sheet to zero, by construction: three numbers against three numbers. What it does to everything else is the measurement.

A perfect neutral goes from exactly right to 11.70 ΔE00 wrong. The two lamps agree about a flat reflectance to the last digit — that is what referring each to its own white means — so all 11.70 units of that are manufactured by the correction. The sheet’s own error was 11.84. A diagonal in this situation does not reduce the error in the frame; it transfers nearly all of it onto the surfaces that were right.

Across this collection’s hundred and twenty natural reflectances the same thing happens without exception. The median difference between the two lamps rises from 1.56 to 6.74 ΔE00 and the worst from 3.40 to 12.61, and every one of the hundred and twenty is worse afterwards. Not a single surface benefits from the correction that fixes the paper.

That is a stronger statement than the algebraic one, and it is what the algebra is for. A diagonal cannot add, so it cannot fix the sheet without changing everything; and because the sheet’s error is very nearly the whole of what a neutral then acquires, the accounting is close to a conservation. There is a fixed quantity of wrongness in the frame, and the gain decides only where it sits.

What the balance leaves on ordinary surfaces #

One number in that comparison deserves separating out, because it is not about fluorescence at all. Before any sheet-fixing gain, after a perfect white balance, those hundred and twenty ordinary reflectances still differ between the two lamps by a median of 1.56 ΔE00, and by as much as 3.40.

That is the ordinary residual of a white balance, and it is there because the two lamps are the same colour and not the same spectrum. A chromaticity distance of 0.0034 says the whites match. It says nothing about whether a diagonal removes the change on anything that is not white, and between a phosphor-converted LED and daylight it does not.

So the headline comparison — 11.84 against the 3.25 the camera removed — sits on a floor that is not zero. The fluorescent difference is what a balance cannot touch. A unit and a half on an ordinary surface is what it merely fails to, which is the older problem this one is stacked on.

The decomposition also says which direction the fluorescent part points. Of the 13.70 units the sheet moves in plain CIELAB distance, 89.5 per cent is b* — from −11.66 under the flash to +0.61 under the LED — with 6.10 in a* and a quarter of a unit in lightness. The difference is very nearly a pure blue-yellow displacement, which is what a fixed emission band added to a fixed reflectance has to produce, and it is why the failure reads as a white balance that cannot be set rather than as an exposure or a cast.

What a correction would need #

The interesting question is not whether current cameras can do it but what would be required, because the answer says how far outside the design the problem sits.

The correction is a subtraction with a coefficient. Take the emission direction in the camera’s own space — a fixed vector, since the emission profile does not depend on the light — and subtract a multiple of it from every pixel showing the fluorescent material. The multiple is the excitation the lamp supplied.

Two things are needed and the camera has neither.

The scalar. How much excitation the lamp supplied is a property of the lamp below 400 nanometres, and the camera has no channel there. It cannot be inferred from the visible spectrum either: the two lamps in this essay differ in excitation by a factor of infinity and in visible chromaticity by 0.0034, so no function of the three raw channels can distinguish them.

The mask. Which pixels are fluorescing is not knowable from three numbers per pixel. A brightened sheet and a slightly blue non-fluorescent one produce the same triple, which is why a photograph is not a measurement of anything the sheet is.

So the correction needs a fourth measurement — a channel below 400 nanometres, on the camera or on the lamp — and a fourth measurement is a design change rather than a firmware one. A raw file’s illuminant metadata could carry it if anything measured it, which is the shape of the gap: not a missing field but a missing sensor.

The one route that exists is the flash. A camera that supplies its own light knows what that light is, and a xenon tube’s ultraviolet output is a manufacturing property rather than a scene unknown. A camera firing its own flash could in principle carry the scalar; a camera photographing a room cannot.

What it looks like in a photograph #

The effect is one photographers meet constantly and diagnose as something else.

White fabric photographs differently under flash and under room light. A wedding dress, a white shirt, a laboratory coat — under a xenon flash they are markedly bluer than under an LED panel of the same colour temperature, and a retoucher pulling the blue out of one will find the other is now yellow — a correction that costs noise as well as accuracy.

Paper photographs differently from how it looked. A document photographed indoors under LED lighting reads warmer than it appeared to a person who was standing next to a window while looking at it — because the person had daylight and the camera had none.

And the failure is not repeatable across lighting kit. Two sets of continuous LED panels of the same nominal colour temperature can differ slightly in the deep blue, and a fluorescent tube has short-wave mercury lines that a phosphor-converted LED does not, so the same subject on two shoots is a different colour and every white balance target in the frame says the lighting was identical.

The characteristic signature is that it affects only some materials. A skin tone, a wall, a piece of wood behave identically under the two lamps; the white goods, the paper and the fabric do not. A correction that fixes the sheet breaks everything else, which is what makes the problem look like an impossible white balance rather than like a missing measurement.

That is the lamp’s side of the arrangement. The sheet’s side is a pair of pictures: what leaves it when the excitation is supplied, and what leaves it when it is not.

What the flash could do, and what it does #

The one case where the missing quantity is knowable is worth following, because it shows how narrow the opening is.

A camera firing its own flash supplies the light. The tube’s ultraviolet output is a manufacturing property rather than a scene unknown, and the geometry — how much of the scene is lit by the flash rather than by ambient — is something the camera can estimate by comparing a pre-flash exposure with an ambient one, which it already does for metering.

So in principle a flash exposure carries the scalar the correction needs. In practice it does not, for two reasons that are both about the rest of the frame. The scene is rarely lit by the flash alone, so the excitation reaching any given surface is a mixture of a known quantity and an unknown one in an unknown proportion. And the correction still needs the mask — which pixels are fluorescing — and nothing in three channels supplies it.

The result is that the one situation where the camera knows its own light is also a situation where it cannot use the knowledge. That is a fair description of most partial information in an imaging pipeline: a quantity that is known for part of the signal and unknown for the rest is often worth less than a quantity that is unknown throughout, because applying it selectively requires exactly the segmentation that is missing.

What was computed, and how #

Three lamps: a xenon flash modelled as D65 on the wide grid, the same flash behind an ordinary glass cover, and a phosphor-converted white LED from this collection’s own lamp model with its conversion set to land near daylight chromaticity — 6350 K against D65’s 6504, and 0.0034 away in chromaticity.

The LED’s zero below 380 nanometres is not an approximation. A blue-pumped white LED has a die at about 450 and emits nothing shorter; that is the single most consequential difference between the light of 2005 and the light of now, and it is a hard zero rather than a small number.

Each sheet is evaluated under its own lamp and referred to that lamp’s perfect diffuser, which is what a perfect white balance does. So the comparison is after the camera has removed everything it can see.

The assertion is a ratio. The sheet must move further between the two lamps than the whites the camera balances on do, by at least a factor of three. That is written as a comparison rather than as a threshold because the claim is about what survives the correction, not about how large the raw difference is.

Where the model stops #

The flash is modelled as daylight. A xenon arc’s visible spectrum is close to daylight and its ultraviolet is genuinely rich — xenon arcs are the standard source in weathering cabinets for that reason — but a real flash tube has an envelope with its own transmittance and often a deliberate ultraviolet-absorbing coating, which would reduce the effect.

The lens and filter are not modelled at all. This essay asserts that the camera sees nothing below 400 nanometres and does not compute what a real stack passes. A camera with a modified filter — astronomical conversions exist, and they are sold for exactly this reason — would see some of it, and what it would then report is a different calculation.

And there is no scene. A single patch under three lamps is not a photograph. What a photograph does with a fluorescent object next to non-fluorescent ones, through an automatic white balance estimating the illuminant from the whole frame, is a harder question and the answer would be worse rather than better.

Who found it, and when #

That cameras cut the ultraviolet is as old as colour film, which had the same problem and solved it with the same filter; the yellow “haze” filters sold for landscape photography from the 1930s onwards are ultraviolet absorbers, and they were sold on sharpness rather than on colour.

That brightened materials photograph unpredictably is common working knowledge in product and fashion photography, where the standard advice is to test the actual fabric under the actual lighting. That advice is correct and is a way of saying that the quantity is not predictable from anything recorded.

The structural statement — that white balance is a diagonal and the difference is an addition — follows directly from the earlier result about what a gain can remove, applied to a case those essays explicitly set aside. Its finding was that a fluorescent surface is not a change of light and not a matrix on tristimulus values; this is what that means for a device whose only correction is a matrix.

The generalisation #

The pattern is a sensor whose designers removed a band for a good reason, in a system that later needed the band as an input.

The removal was correct on its own terms and remains correct: an ultraviolet-transparent camera would produce blurred, hazier images and gain nothing for the overwhelming majority of subjects. What changed is that the correction pipeline downstream grew sophisticated enough to want a quantity the front end had discarded.

The diagnostic is worth stating because it applies to any measurement chain. When a correction cannot be computed, ask whether its input was lost or was never acquired. A lost input can sometimes be recovered from redundancy elsewhere in the signal. An input that was filtered out at the aperture cannot be, by any amount of processing, and the distinction decides whether the fix is an algorithm or a component.

Where the ladder goes next #

If the quantity depends on the lamp and the lamps have changed, then the supply itself is the story: the lamp that stopped emitting ultraviolet is a change to the world’s lighting that happened in twenty years and moved every brightened material’s appearance without anybody reformulating one.

The other direction is the sheet rather than the camera. A brightened white is not a reflectance at all, which is why no device that assumes reflectances — a camera, a profile, a proof — has a place to put it.