Most things are pale in the infrared

The previous two essays established that a camera responds three hundred nanometres past where anybody is looking, and that all three of its channels respond identically out there. Both are facts about the instrument.

They would be harmless if the world were dark in the near infrared. It is not. It is brighter out there than it is in the visible, and by a lot.

Which lamp the four surfaces are photographed under decides how far apart the camera puts them, and the lamp is the argument nobody records.

Two more readings say where in the range the separation is largest and how little of a tail it takes to produce one.

The claim #

Most coloured surfaces stop absorbing somewhere past 700 nanometres and are highly reflective in the near infrared, and no measurement anybody routinely has says so — a spectrophotometer’s range ends at 780 or 700 nanometres and a camera’s does not.

The word that carries the weight is most. This is not a curiosity about a few odd materials; it is close to a general property of organic colorants, and the exceptions are worth naming precisely because there are few of them.

Why the world is pale out there #

The mechanism is the same one that made the colour-filter dyes give up, arriving from the other direction.

A pigment or a dye is coloured because it has an electronic transition whose energy lies in the visible band: it absorbs the photons matching that transition and reflects the rest, and which photons it absorbs is what its colour is. Those transitions are typically between 1.7 and 3.2 electronvolts, which is 390 to 730 nanometres, which is the visible band — this is not a coincidence but very nearly a definition, since a material with no transitions there is colourless.

Below about 1.7 electronvolts there is generally nothing for a photon to do. The molecule has no accessible transition, so it does not absorb, so the light is either scattered back or transmitted to whatever is underneath. And what is underneath — cotton fibre, paper, skin, cellulose, paint binder — is usually a strong diffuse scatterer.

So a dyed material in the near infrared is largely the undyed substrate. Black cotton is cotton. A black car’s paint is often carbon black, which is one of the genuine exceptions and stays dark; a black dyed fabric is not.

What this looks like #

The consequences are the standard demonstrations of infrared photography and every one of them is this argument.

Foliage is white. Chlorophyll absorbs strongly in the red — that is why leaves are green — and stops absorbing over about forty nanometres between 680 and 720, jumping from a reflectance near 0.05 to one near 0.5. The step is called the red edge, it is one of the sharpest spectral features in nature, and it is the basis of essentially all vegetation remote sensing. A leaf photographed through a sensor that sees past it is brilliant.

Dark fabric is pale. A shirt at five per cent visible reflectance may be at fifty or sixty in the near infrared, and it therefore records as a mid grey rather than as black.

Skin is waxy and flattens out. Haemoglobin and melanin both stop absorbing, so the variation that carries skin’s colour and much of its structure disappears, and what is left is subsurface scattering, which is strong and uniform.

Some blacks stay black. Carbon black, magnetite, and most inorganic dark pigments absorb by mechanisms that do not stop at the band edge, so printing ink and tyre rubber and a matte-black instrument housing stay dark. This is the property that makes it possible to read a printed page through a paint layer in art conservation and to distinguish two inks that match to the eye.

The size of it, measured #

The library’s own assertion is the cleanest statement available. Take eight saturated surfaces, give them a near-infrared reflectance of 0.62 — the middle of the range real dyed materials occupy — and photograph them under a 2856 K lamp with an uncut sensor. The mean channel spread is 0.119, against 1.045 with the filter fitted: a factor of 8.8.

Now run the same computation with the surfaces’ infrared reflectance set to zero, and the factor falls to 1.16.

That reversal happened in this library, and it is the finding this essay exists to record. The first version of the assertion extended every reflectance with a tail of zero — the obvious thing to write, since the site’s grid ends at 780 and there was no data past it — and reported that removing the filter cost about sixteen per cent. The curves were smooth, the numbers were plausible, and the conclusion was the opposite of what the physics gives.

Nothing about the calculation was wrong. It was a correct calculation about a perfect near-infrared absorber, which is a material nobody has ever made a shirt out of.

The measurement nobody has #

A spectrophotometer of the kind this site has already described reports reflectance from 360 or 380 nanometres to 700 or 780. That is the range the colour-matching functions are non-zero over, so it is the right range for every colorimetric purpose, and instruments are built to it because extending further costs money for no colorimetric benefit.

The result is that the standard measurement of a surface contains no information about the quantity a camera is partly integrating. A colour tolerance in a contract names an illuminant, an observer and a limit; the reflectance data behind it stops at 780; and two coatings certified identical may differ by a factor of two out where a camera can see. If the coatings are ever photographed under tungsten with an ageing or damaged filter, they will not match.

This is the same shape as the gap a corner opens in a metameric match — a specification with no field for the quantity that actually decides the case — arriving from a different direction. There, the missing field was geometry. Here it is a range.

Two surfaces, one certificate #

It is worth working the consequence through on a case that is not hypothetical, because the failure is a supply-chain failure rather than a photographic one.

A manufacturer specifies a black trim panel. Two suppliers deliver, both measured on the same instrument under the same illuminant against the same standard, both inside a ΔE00 of 0.8, both certified. One is pigmented with carbon black; the other is a dyed polymer over a pale filler.

To the eye, under any illuminant, they match — carbon black and the dyed polymer are both flat and dark across the whole visible band, so this is not even a metameric match but a plain one. Under a spectrophotometer they match. In the near infrared one is at 0.04 and the other at 0.55.

That difference is invisible until something looks past 780 nanometres, and several things now do routinely: a driver-monitoring camera behind a windscreen, a proximity sensor, a lidar return, a machine-vision inspection rig with infrared illumination. Each of them sees two panels that the specification says are the same colour and the instrument says are the same colour, and reports them as wildly different.

The specification has no field for the quantity that decides the case, which is the same structural failure this site has already recorded twice: a colour tolerance has no field for geometry, and a colour rendering index has no field for how saturated the surfaces are. Here the missing field is a wavelength range.

The three are worth putting together because they are the same shape and have the same cause. A standard fixes the quantities that mattered when it was written, and every one of them is silent about the quantity that matters in an application invented afterwards. The silence is not an oversight; it is what a standard is.

How large the reversal was, in the unit it happened in #

The two numbers that record the error are quoted in different units, and converting them says how close the first version came.

The corrected computation makes the filter worth a spread ratio of 8.8, which is an increase of 778 per cent. The version with a tail of zero made it worth 1.16, an increase of 16 per cent. As factors the two look eight apart; as the quantity actually being reported — how much the filter buys — they are a factor of 49 apart. The first version did not underestimate the effect. It reported a different order of magnitude and read as a reasonable engineering margin.

That is the property that let it stand. A result of 16 per cent invites a sentence about a minor correction; a result of 778 per cent invites somebody to check the arithmetic. The wrong answer was the one that looked like it needed no defending, and the tail of zero was invisible precisely because it produced a number nobody would query.

The lamp does most of it #

The mechanism is stated here as a property of surfaces, and the surfaces are only half of it. The other half is the 2856 K lamp, and it is the larger half.

A blackbody at 2856 K emits 1.89 times as much power between 780 and 1100 nanometres as it does across the whole visible band. Before any reflectance is applied at all, roughly 65 per cent of what a bare silicon sensor collects from that lamp is light nobody can see. Apply a visible reflectance of 0.3 and a near-infrared tail of 0.62, and the invisible share of a flat-response channel is about 80 per cent: four fifths of the signal, carrying no colour information, added equally to all three channels. A factor of 8.8 in channel spread is what that does, and it is not surprising once the fraction is written down.

The failure is therefore a tungsten failure, and the temperature dependence is steep:

Under daylight the same uncut sensor collects two and a half times less of the invisible band, which is why an infrared leak is a defect that shows itself indoors under incandescent light and hides outdoors. It also sharpens the trim-panel case: the driver-monitoring camera behind a windscreen usually works with its own near-infrared illuminator, which is the tungsten column pushed further still, while the same two panels photographed in daylight would differ by much less.

Both halves have to be large for the effect to be large, and that is the same either-factor structure this collection keeps finding: a bright infrared band with dark surfaces costs nothing, and pale surfaces under a source with no infrared cost nothing either. Extending the reflectance with a tail of zero set one of the two factors to zero, which is why the answer collapsed rather than merely shifting.

A halogen lamp sits between the tungsten case and daylight, and it is the lamp most studio work is actually done under.

Where the model stops #

The tail used throughout is a stated parameter and not a measurement. extendSurface takes the reflectance at 780, ramps it smoothly to a stated value by 900 nanometres, and holds it there. Real reflectance curves in the near infrared are not flat: they have water absorption bands around 970 and 1200 nanometres, and cellulose, protein and lipid all have identifiable features that are the basis of near-infrared spectroscopy as an analytical technique. The model is right about the level and says nothing about the structure.

The site has no data out there and this essay does not pretend otherwise. Every infrared number here is computed from a constructed surface under an analytic Planck source, because those are the only two things that can be extended honestly: the D-series daylight illuminants are defined by three basis functions tabulated to 780 and there is no defensible continuation of them. Anything requiring a real illuminant past the visible band is outside what this collection can compute, and the methodological consequences of that get their own essay.

And “most” is doing real work. Inorganic pigments, carbon blacks and metals behave differently, and the exceptions are exactly what makes infrared imaging useful in conservation and forensics — if everything went pale there would be no contrast to photograph.

Two tails rather than four is the comparison a reader can hold in their head, and the middle of the range is where most real surfaces sit.

The generalisation #

The transferable claim is about the relationship between an instrument’s range and the range of the thing it is used to reason about.

A measurement truncated at the edge of one application’s needs becomes silently wrong when it is used for another, and the truncation is invisible in the data. A reflectance file stopping at 780 nanometres does not carry a flag saying this surface may do anything at all past here. It looks complete. It is complete for the purpose it was made for and for no other, and nothing in the file distinguishes the two cases.

The general protection is not to extend every measurement to every range, which is unaffordable. It is to make the extension explicit and parameterised wherever a truncated measurement is used outside its range, so that the assumption is a number somebody chose rather than a zero nobody noticed. That is why extendSurface takes its tail as a stated argument and refuses a value outside $[0,1]$, and why every figure in this essay names the tail it used.

The stronger version of the lesson is the one the failed assertion taught. The default extension of a truncated measurement is zero, zero is a physical claim, and it is usually the most extreme claim available. A tail of zero here asserts a perfect absorber; in a different context it asserts a perfect vacuum, an infinitely stiff support, or a signal that stops. Whatever it asserts, it is rarely the neutral choice it appears to be.

A very cool lamp is the case where the infrared should matter least, and it is the one that says how much of the effect is the lamp.

Why the eye is not missing anything #

A reader who has followed the last three essays might reasonably conclude that human vision is missing a large and informative part of the world, and it is worth resisting that reading, because the trade is not obviously a loss.

The near infrared is bright, and it is bright uniformly. That is exactly the property that makes it useless for telling things apart. If almost every organic surface is between 0.4 and 0.8 out there, a hypothetical fourth cone peaking at 900 nanometres would receive a large signal carrying very little discriminative information — a channel with a high mean and a low variance, which is the worst arrangement available for a detector working in ratios.

That argument can be given a number, and the number is 2.9. Take the near infrared as reflectances spread over 0.4 to 0.8 and the visible band as spread over 0.02 to 0.90. The infrared band’s coefficient of variation is 0.19 against the visible band’s 0.55, and its Michelson contrast is 0.33 against 0.96 — the same ratio of 2.9 twice, which is not a coincidence, since for a spread of that shape the coefficient of variation is the Michelson contrast divided by √3. A fourth cone out there would work at a third of the contrast the existing three work at, while receiving more light than any of them.

Where infrared is informative is precisely where it is not uniform: the red edge, the water bands, the inorganic pigments. Those are the features remote sensing and conservation imaging exploit, and every one of them is exploited with a narrow band chosen for the purpose rather than with a broad channel.

There is also a straightforward physical objection to seeing further out. Thermal emission from the eye’s own tissue rises steeply with wavelength, and a detector at body temperature responding at two or three micrometres would be swamped by its own housing. That constraint is real for infrared astronomy, which cools its detectors to liquid-nitrogen temperatures for exactly this reason, and it sets a hard limit on how far any warm biological detector can usefully see.

So the honest summary is not that the eye is blind to something important. It is that the eye’s band is where the information is, and a camera’s band is wider than the information, which is the whole argument of this trio in one sentence.

Who noticed, and when #

Infrared photography is older than most people expect. Robert Williams Wood published infrared and ultraviolet landscape photographs in 1910, and the white foliage in them — the effect that came to be called the Wood effect after him — was the first widely seen demonstration of the red edge, several decades before anybody had a spectroradiometer to explain it with.

Military reconnaissance made it systematic. Infrared-sensitive film in the nineteen-thirties and forties distinguished live vegetation from cut branches and painted canvas used as camouflage: both are green to the eye, only one has chlorophyll, and only one is bright past 700 nanometres. That is a metameric pair broken by a range rather than by an illuminant, and it is the same argument this essay makes about a camera.

The measurement caught up in the nineteen-seventies with satellite multispectral imaging, which turned the red edge into an index — the normalised difference vegetation index, a ratio of a near-infrared band to a red one — and made it the most widely computed spectral quantity on the planet. The colour-science literature and the remote-sensing literature have been describing the same absorption edge from opposite sides ever since, and mostly not citing each other.

Where the ladder goes next #

Downward, this rung sits on the filter that makes colour possible, which needs this essay to be true for its own number to hold, and on what the instrument reports, which is where an instrument’s range first became a subject here.

Upward, the infrared thread ends and two others begin. The grid outside every figure is the methodological consequence — what a collection built on a 380–780 grid should do when it meets a field the grid cannot hold. And Luther’s condition leaves the infrared behind entirely, because it is a statement about the visible band that holds for a perfectly filtered camera.