### The Butler's Name is Emissivity

We got a new toy in the lab recently — a thermal sensor, aka an IR thermometer, which uses the incoming radiation profile to sense the temperature of a remote object. It’s useful because it does not require physical contact. (I wasn’t there the day it arrived, and rumour has it that it “saw” some things that cannot be unseen as it was “tested” using quasi-calibrated biological standards of temperature at 37ºC )

So how does it work?

All objects will emit electromagnetic radiation; the ideal is a blackbody which emits according to

$$P = Aepsilon{sigma}T^4$$

A is the area, sigma is a constant, T is temperature, and epsilon is the emissivity, which is 1 for a blackbody

If we look at an object about the size of a 2L soda bottle (roughly 4 cm radius, 33 cm tall), we find that at 300K, it emits about 7.5 Watts of power. Because the blackbody spectrum is a continuum, this represents a wide spectrum of wavelengths, which will have a peak in the infrared, somewhere around 10 microns. In thermal equilibrium its temperature will not be changing, which means it’s also absorbing 7.5 Watts from its surroundings (ignoring conduction and convection losses, which should be small) If the object is not in thermal equilibrium, it wither radiates more power and cools down, or absorbs extra radiative energy and heats up.

But that’s if it’s a perfect blackbody. If it isn’t — the emissivity is less than 1 — some of the incoming radiation is reflected. If less radiative power is absorbed, it has to have a lower temperature to be in equilibrium (or, at the same temperature, it radiates a lower power). So at a given emissivity, one could measure the radiation profile, and values at a few wavelengths will indicate the shape of the blackbody curve and will tell you the temperature.

I did this, though with a 12 oz (355 ml) can instead of a 2L bottle. You can see the dot of the built-in laser pointer showing that the sensor is pointed at the can.

Whoa! This is a can right out of my fridge, and is obviously not at 61ºF. What’s going on? Well, the emissivity did it. An aluminum can, even with some coloring, is nowhere near a blackbody. Depending on the particulars of how much oxidation and level of polishing, the emissivity of aluminum can range from about 0.2 to below 0.1. The thermometer’s spec sheet says it assumes a value of 0.95, so there’s quite a discrepancy. This means the sensor is getting a mix of radiation from the can (below 40ºF) and from the surrounding room-temperature items (and a little from me, sitting less than a meter away), and this skews the results.

What if we cut down on the reflections? I encased the can in a single sheet of paper.

OK, that’s significantly better. The paper is in good contact with the can and the can might be slightly warmer than in the first shot, as it’s been sitting at room temperature or been handled by a warm-blooded creature, so the surface temperature may have gone up a little. Cooling the paper down to the can’s surface temperature probably had a negligible effect.

That’s lower, though not dramatically (and probably not significant in terms of instrument sensitivity), though the same caveats apply — the can can only have warmed between shots. I didn’t return it to the fridge, and I was handling it.

There’s a cautionary tale here — you want to trust your instruments, but you have to know what is actually being measured to ensure you don’t let systematic errors into your results.

1. Anonymous Coward on July 18th, 2011

Do you know how these things work? I don’t, and I’m surprised that the emissivity screws up the reading by such a small amount. Obviously it’s not just reading total power irradiated, as a factor of 10 change in emissivity would give a factor of ~2 change in temperature (in Kelvin, thanks to the T^4 dependence).

Is there some clever trick that reduces the sensitivity to the emissivity?

2. swansont on July 18th, 2011

I’m guessing the total power to which the sensor is responsive is measured and the calibration of the sensor material is factored in. I suspect it’s a Germanium sensor, since that goes a little deeper into the IR than Silicon, and power at wavelengths shorter than a micron is negligible — the spectrum moves up sharply at about 1.6 – 1.7 microns near room temperature.

In a band between 1 and 2 microns (the low end cutoff doesn’t matter very much), blackbody power triples between 270K and 280K and roughly doubles in the next two 10K increments. That seems dynamic enough to be useful, and also seems to jibe with the magnitude of error I saw.

3. Anonymous Coward on July 18th, 2011

Ah – I wasn’t thinking about the frequency band. I like your guess as to what’s going on.

4. drew on July 18th, 2011

Check out Kirchoff’s law of thermal radiation…emissivity is equal to the absorptivity, which put another way is (1-reflectivity). So the fraction of what gets emitted and what gets reflected are complements of each other.

In practice, what you see with an IR sensor is always some weighted average of the thermal temperature of the surface and its surrounding environment. It should never indicate a temperature cooler than both of them because some amount of radiation is ‘lost’.