The filter that makes colour possible

A component list for a camera puts the sensor first, then the lens, then a long way down a piece of coated glass called the infrared-cut filter. It sounds like a refinement, in the category of anti-reflection coatings and dust shields.

It is not. Take it out and the camera stops being a colour camera.

The share depends on what is being photographed as well as on the lamp, and both dependences are steep.

A strongly coloured surface with a bright tail is the worse case and the commoner one, since most dyed fabric and all vegetation is exactly that.

Two more readings say that the filter is not solving a problem confined to hot lamps or to exotic surfaces.

The claim #

Removing the infrared-cut filter reduces a camera’s colour separation by a factor of 8.8 under a tungsten lamp. The filter is not improving colour reproduction; it is the component that makes there be any.

The number is the mean channel spread — how far the three raw values sit from their own mean, relative to it — over eight saturated surfaces under a 2856 K lamp. With the filter, 1.045. Without, 0.119.

Why the loss is so complete #

The mechanism was set out in the previous rung and is worth restating in one sentence, because the size of the effect follows from it directly.

Past about 800 nanometres the three colour-filter dyes are transparent, so all three channels receive the same infrared signal. Adding an equal amount to each of three numbers is the operation that most efficiently destroys the ratios between them, and colour is nothing but those ratios.

The arithmetic is unkind. If the three visible readings are $v_R, v_G, v_B$ and the common infrared term is $c$, the recorded triple is $(v_R + c,\ v_G + c,\ v_B + c)$ and the spread about the mean is unchanged in absolute terms while the mean itself has grown by $c$. So the relative spread — the thing that determines chromaticity — falls as

$$\frac{\sigma}{\mu + c}$$

and since $c$ under tungsten is several times the whole visible signal, the fall is not gentle.

The lamp decides how bad it is #

This is the half of the finding that stops it being a fact about cameras and makes it a fact about photography.

The size of $c$ depends on how much power the source emits past 780 nanometres, and thermal sources differ enormously in that. A tungsten filament at 2856 K has its Planck peak at 1015 nanometres — outside the visible band by more than the band is wide — so almost everything it emits is invisible. A 6500 K daylight source peaks at 446 nanometres, inside the band, and its infrared tail is proportionally far smaller.

Measured on the same surfaces with the same uncut sensor: the channel spread is 0.289 at 6500 K against 0.119 at 2856 K. Removing the filter costs less than half as much under daylight as under tungsten.

The practical form of this: a filterless camera is worst exactly where photography is hardest anyway. Indoors, under incandescent light, at night — the conditions where the signal is already scarce — is where the invisible fraction is largest. Outdoors at noon it is a lesser problem, and a sunlit scene is the case a naive test would use.

The factor of nine and the invisible share are one number #

The essay derives the mechanism as σ/(μ + c) and then never applies it to its own two figures, which is a pity, because the algebra turns the collapse factor into a share.

If the filter’s contribution is to remove a term c common to all three channels, then the ratio of the filtered spread to the unfiltered one is (μ + c)/μ. So a factor of 8.78 means c is 7.78 times the visible signal, and the invisible part is 88.6 per cent of what an uncut sensor collects under tungsten.

At 6500 K the same arithmetic on the same numbers gives a factor of 3.62, so c is 2.62 times the visible part and the invisible share is 72.3 per cent.

Those are the two curves the hero figure plots, arrived at from the channel-spread measurement rather than from the integral, and they agree with it — which is the check the two figures make on each other and neither states. It also gives the collapse factor a form worth carrying: the factor is one over one minus the invisible share, so it goes to infinity as the share approaches one and is a hyperbola rather than anything gentle. Halving the invisible share from 88.6 to 44 per cent would take the factor from 8.8 to 1.8, which is the whole of what the filter has to achieve.

Half is nearly right, and by one point #

No thermal radiator gets half its power into the visible band at any temperature is a strong claim about every temperature at once, and it is true — narrowly.

The visible share of a blackbody’s total radiated power rises to a maximum of 49.04 per cent at 6,913 K and falls away either side: 1.7 per cent at 2,000 K, 10.5 at 2,856, 41.0 at 5,000, 48.7 at 6,500, and back to 40.5 by 10,000. So the claim clears by one percentage point at its tightest, and the temperature where it is tightest is a little above daylight.

The Wien peaks check exactly at both ends of the essay’s own comparison: 1,015 nanometres at 2,856 K and 446 at 6,500. And the maximum-visible-fraction temperature has its peak at 419 nanometres — inside the band, near its short end, which is where a radiator has to put its peak to get the most of its power into a four-hundred-nanometre window whose long side is bounded and whose short side is not.

A few per cent is a different quantity #

The same figure’s caption says a tungsten filament manages a few per cent, and the blackbody share at 2,856 K is 10.5 per cent — an order of magnitude rather than a few, and a real filament’s emissivity favours the visible, so the true figure is higher still.

A few per cent is the luminous efficacy of radiation divided by its ideal, which is a different quantity and the one everybody has in mind. Weighting the same blackbody by the luminous efficiency function gives 16.4 lm/W at 2,856 K, which is 2.4 per cent of the 683 lm/W a perfectly efficient source would reach. At 6,500 K it is 95.4 lm/W, or 14.0 per cent.

The two quantities differ by a factor of four and answer different questions. The radiant share is what the infrared-cut filter is fighting, because a photon at 900 nanometres reaches the sensor whatever the eye thinks of it. The luminous share is what a lighting engineer pays for. Quoting the second in a figure about the first understates the filter’s job by four times, and the direction matters: the filter has more to remove than the caption implies, not less.

It is worth noticing that both quantities peak in nearly the same place — 6,913 K for the radiant share and 6,628 for the luminous one — and that neither peak is where anybody builds a lamp. A thermal source optimised for either would be bluer than daylight and would still throw away half of everything it emitted, which is the argument for every non-thermal source there is.

What the filter costs #

A filter that removed exactly the invisible band and nothing else would be free, and no such filter exists. A dielectric stack has a shoulder, and the shoulder is in the deep red.

So the deepest reds a camera records are attenuated by the component that makes the rest of the picture possible. Move the filter’s cut-off further out to recover them and more infrared leaks in; move it in and the reds go. The choice is a design parameter and manufacturers place it differently, which is one of the several reasons two cameras disagree about a saturated red.

The consequence is visible in the direction one would expect. A deep red flower, a brake light, a red garment under tungsten — these are the subjects that come out of different cameras looking least alike, and part of the reason is that the three shoulders are at three different wavelengths.

There is also an angular cost. A dielectric interference filter’s passband shifts towards shorter wavelengths as the angle of incidence increases, so a ray arriving at the corner of a wide-angle lens meets a slightly bluer cut-off than one arriving at the centre. On fast wide lenses this produces a measurable colour shift across the frame, and it is corrected — like almost everything else in the pipeline — by a lookup table fitted afterwards.

A surface with a lower infrared reflectance is the favourable case, and it is worth knowing whether the share falls with it proportionally.

What survives the filter, and what does not #

The filter removes a common-mode signal, and it is worth being precise about what that leaves, because “the camera is fine now” is not quite the conclusion.

What the filter fixes is chromatic collapse. Once the invisible term is gone, the three channels are again measuring three different things and the ratios between them mean something. That is the whole of what it buys, and it is enough for colour photography to exist.

What it does not fix is that the three things are the wrong three things. A perfectly filtered camera still has sensitivities that are not a linear combination of the colour-matching functions, and so still fails Luther’s condition, and so still has surfaces it gets measurably wrong. The infrared problem and the Luther problem are independent: solving the first completely leaves the second exactly where it was.

Keeping the two apart matters because they are fixed by different components and confusing them leads to the wrong repair. A camera rendering foliage badly under tungsten may be leaking infrared, in which case the filter is at fault and no matrix will help. The same camera rendering a saturated blue badly in daylight is failing Luther, in which case the filter is irrelevant and a better-fitted matrix will help a little.

Two channels, one measurement, and the reason it is invisible #

There is a reason the filter’s contribution is so easy to overlook even by people who know the sensor responds past the visible, and it is worth naming.

The infrared signal does not look like contamination. It is smooth, it is stable, it is proportional to exposure, and it changes with the scene in all the ways a real signal does — a brighter surface gives more of it, a darker one less. Nothing about a filterless camera’s output has the texture of an artefact. It has the texture of a photograph of a slightly different world.

That is the general shape of the most dangerous kind of measurement error, and this site has met it before. A purity calculation that came out a ten-thousandth of its true value clamped every sample to fully saturated and drew nine identical patches under nine different captions. A white point off by four orders of magnitude reported a perfect white balance across a scene it had just drawn as strongly coloured. In every case the arithmetic was working and the answer was wrong, and nothing about the output announced it.

A contaminating signal that behaves like the signal is not caught by looking at the output. It is caught by a control — the same measurement with one component removed — which is why the figures here draw the filtered and unfiltered sensor together rather than either alone.

What the filter is not #

Three things it gets confused with, each worth separating.

It is not an ultraviolet filter. Silicon’s blue response falls away for reasons of absorption depth rather than of the band gap, and the lens is usually absorbing most of the ultraviolet anyway. The two filters are separate components solving separate problems, and are sometimes combined in one piece of glass, which is where the confusion starts.

It is not what makes a camera unable to see in the dark. Removing it does not turn a camera into a night-vision device. The near infrared it admits is reflected light and needs a source: a filterless camera in a dark room sees nothing at all unless something is illuminating the room at 850 or 940 nanometres, which is exactly what a security camera’s ring of emitters is doing. Thermal emission from a room-temperature object is around 10 micrometres, nine times further out, where silicon is entirely transparent.

And it is not an anti-aliasing filter. Many cameras have one of those too — a birefringent layer that blurs the image slightly to keep scene detail below the mosaic’s sampling limit, which is a defence against a completely different colour artefact. The two are stacked together in front of the sensor and are routinely spoken of as one part.

Four temperatures is the sweep a specification would tabulate, and it spans warm interior light to overcast daylight.

Where the model stops #

The sensor is a model. Its dye leak, its filter shoulder and its silicon curve are stated shapes with the right physics at both ends, not a measurement of any particular camera. The factor of 8.8 would be a different number for a real sensor. What would not change is the sign and the order of magnitude, because both follow from the dyes converging rather than from where exactly they converge.

The infrared tail of the surface is doing a great deal of work and is deferred. Everything above assumes surfaces reflect substantially in the near infrared, which they do, and the assumption is an essay of its own because it is the least obvious part of the argument and the one that reverses the conclusion if it is got wrong. A first draft of the library’s own assertion extended every reflectance with a tail of zero — a surface that absorbs the entire near infrared perfectly — and reported that removing the filter cost 16 per cent rather than a factor of nine. The arithmetic was correct and the material does not exist.

And nothing here is about the sensor’s own thermal signal. Dark current rises steeply with temperature and is a genuine problem in long exposures. It is not what an infrared-cut filter addresses, because it is generated in the silicon rather than arriving through the lens.

A very reflective surface in the infrared is the worst case for an unfiltered sensor, and it is commoner than it sounds.

The generalisation #

The instructive part of this is not the filter but what its absence from the discussion says.

A component whose entire function is to remove a signal is invisible in every plot of what the instrument does, because those plots are drawn downstream of it. Every published camera sensitivity curve is measured through the filter, so the filter’s contribution appears as an absence — the curves simply end. Nothing in the picture indicates that a component is holding them there, and nothing indicates what would happen if it stopped.

That shape recurs. A lock-in amplifier’s reference, a spectrophotometer’s order-sorting filter, the ocular media in the eye’s own short-wavelength response: in each case a subtractive element defines the measurement, and in each case the specification quotes the result rather than the element. The general protection is to ask what the instrument would report with each component removed, one at a time, which is a question a model can answer and a datasheet usually cannot.

It also suggests where to look for surprises in any three-channel system: not at the wavelengths where the channels differ, which is where all the design attention goes, but at the wavelengths where they stop differing while still responding.

Narrowing the sweep to the temperatures a camera is actually pointed at is the reading a specification would be written from.

Where to put the cut-off, and why nobody agrees #

The one free parameter is the wavelength at which the filter turns over, and there is no correct value.

Push it out towards 700 nanometres and the deepest reds survive. A red at 660 nanometres is still substantially transmitted, saturated reds are recorded with their full chroma, and the cost is that more of the lamp’s near-infrared tail arrives with them. Under daylight that cost is small; under tungsten it is not, and it is not evenly distributed either — it lands hardest on exactly the saturated surfaces the wider filter was meant to protect.

Pull it in towards 630 and the infrared is gone completely, at the price of cutting into the visible band. The red channel loses its long tail, red surfaces record darker and less saturated than they are, and the correction has to come from the matrix — which means amplifying a smaller number, which means amplifying noise with it.

So the parameter trades three quantities against each other: infrared rejection, red fidelity, and red-channel noise. Every camera maker resolves it differently, none of them publishes the curve, and the resulting disagreements between two bodies photographing one red object are among the largest in ordinary practice.

The general point is that the filter is not a switch but a curve, and a curve has a shape as well as a position. A steeper transition would let the cut-off sit further out with the same rejection, which is exactly what more dielectric layers buy and exactly what they cost money for. The component that is invisible in every discussion of colour reproduction turns out to have its own three-way design trade-off, resolved commercially, and reported to nobody.

Who noticed, and when #

The problem arrived with the sensors. Photographic emulsions needed sensitivity to be added at the long end — dye sensitisation from 1873 onwards — so infrared contamination was never a default hazard for film; an ordinary panchromatic emulsion simply stops before it becomes one.

Solid-state sensors had the opposite default from the first colour designs of the nineteen-seventies, and the filter was in front of them from the beginning. It has almost no literature because it was never a discovery: anybody who built an uncut colour sensor saw the result immediately and put glass in front of it.

The interesting modern development is the deliberate removal. Astronomical imaging, forensic and art-conservation photography, agricultural remote sensing and infrared-illuminated security cameras all strip the filter on purpose, and a small industry converts consumer cameras for the purpose. Those conversions are the clearest available demonstration of everything above, because the same body with the same lens produces the two pictures.

Where the ladder goes next #

Downward, this rung sits on silicon sees past the visible, which supplies the mechanism, and on a lamp is not a blackbody, which is where the source’s spectrum stops being a temperature.

Upward, most things are pale in the infrared supplies the third factor in the product and is the essay this one keeps deferring to. Beyond that the field leaves the infrared entirely: Luther’s condition is about the visible band and holds even for a perfectly filtered camera, which is the point of it.