Optical pyrometry

How can you read the temperature of molten steel without ever touching it?

A thermometer works by contact. You put it in the thing, wait for it to come to the same temperature, and read what happened to it. Now consider a ladle of steel at sixteen hundred degrees Celsius. There is no probe you can leave in it that will survive, and anything that did survive would take long enough to equilibrate that the melt would have moved on.

Yet steelmakers read that temperature routinely, from across the shop floor, through the air, to within a few degrees. Whatever they are doing is not measuring temperature. It is measuring something else and inferring temperature from it — and the whole craft turns out to live in the gap between those two sentences.

Start with what the steel is sending you. Everything above absolute zero radiates, and the amount and colour of that radiation depend on temperature. For an ideal emitter — a blackbody — Planck's law gives the full spectrum from the temperature alone, and Wien's displacement law summarises it: the wavelength of peak emission times the temperature is a constant, about 2.9 millimetres times a kelvin. At 1800 K the peak sits near 1.6 micrometres, in the near infrared, which is why hot steel glows orange rather than blue.

So there is a proxy: brightness at some wavelength, which for a blackbody maps one-to-one onto temperature. Point a calibrated detector, read the radiance, invert Planck's law. That is a pyrometer, and the earliest practical one — the disappearing-filament instrument of around 1901 — did it beautifully by eye. You look at the target through a telescope with a tungsten lamp filament superimposed on the image, and turn up the lamp current until the filament vanishes against the glow. When it disappears, the two brightnesses match, and the lamp current has been calibrated against temperature. The observer never judges an absolute brightness, only whether two brightnesses are equal, which the eye does far better.

Now the objection, and it is the important one. Steel is not a blackbody. Real surfaces emit only a fraction of the ideal, and that fraction — the emissivity — depends on the material, its finish, its oxidation state and the wavelength. A surface with an emissivity of 0.4 sends you the radiance of a much cooler blackbody. Which way does the error go?

Too cold, always. The proxy is systematically biased downward, and the size of the bias depends on a quantity you do not know and which changes as the metal skins over or the surface is stirred. So the naive reading is not a temperature at all; it is a brightness temperature, meaning the temperature a perfect emitter would need to look that bright.

Can we do better than guessing the emissivity? Here is the elegant move. Take the radiance at two nearby wavelengths and form their ratio. Each measurement carries a factor of the emissivity at its own wavelength, but if those two emissivities are equal — if the surface is grey over that small span — the factor appears in the numerator and the denominator and cancels. What survives is a ratio that depends only on temperature.

That is two-colour, or ratio, pyrometry, and it is a general pattern worth naming. When a proxy is contaminated by an unknown factor, you may not need to measure the contaminant: you may be able to arrange two measurements that share it and take a quantity in which it drops out. The confound is not estimated. It is cancelled.

Several refinements, in order of how often they bite.

Ratio pyrometry only cancels emissivity for a grey body. Materials whose emissivity varies steeply with wavelength — many oxides, and glass, which is nearly transparent in the visible and strongly emitting in the mid-infrared — break the cancellation, and the two-colour reading can then be worse than a single-band reading with a well-chosen emissivity value. The technique trades an unknown constant for an assumption about a slope.

There is also a way to make the emissivity problem disappear physically rather than mathematically. A small hole into a large isothermal cavity behaves as an almost perfect blackbody: radiation entering is reflected many times inside and has little chance of finding its way back out, so the hole emits as if the emissivity were one. This is why pyrometers are aimed down a bore, into a tundish, or at a hole in a furnace wall wherever geometry allows — the cavity supplies the ideal emitter that the bare surface refuses to be.

The path from target to instrument matters too. Water vapour and carbon dioxide absorb strongly in particular infrared bands, and dust, steam or a dirty window attenuate the signal. Uniform attenuation is exactly the confound a two-colour ratio survives; wavelength-selective attenuation, such as a water-vapour band sitting on one channel, is exactly the one it does not. Choosing the pair of wavelengths is therefore about dodging absorption bands as much as about sensitivity.

Finally, be clear about what is measured even when everything works. A pyrometer reads a surface, and reads it now. The interior of a billet may be hundreds of degrees from its skin, and a reflective metal surface can bounce radiation from a hotter object elsewhere in the furnace straight into your instrument, reading high for reasons that have nothing to do with its own temperature.

• Multi-wavelength pyrometry, which fits an emissivity model across several bands rather than assuming greyness across two.
• How thermal imaging cameras handle the same problem across a scene, and what an emissivity setting actually does.
• Cavity radiators as calibration standards, and how the temperature scale is realised at high temperatures.

Every term the collection defines is gathered in the glossary.