Thanks. If I understand this properly, it is the calculated combined in band emissivity of the bolometer and alumina.
This I have a minor disagreement with, and my opinion is corroborated by experiments using the Optris software:
The bolometer response is modified by the internal camera software, so that the sub-black body bolometer emissivity curve reports as a blackbody when viewing a true blackbody. This is the primary camera calibration. So the two curves, in my opinion, should not be combined. There will be a camera-specific adjustment that levels the raw (micro) bolometer response. Since there cannot be an emissivity > 1, and a blackbody will have a straight line at 1 across the wavelengths, the adjustment to the integrated in band bolometer response can be estimated.
I skipped this step, and instead assumed that camera bolometer reported a blackbody when it saw one (or else the camera would not work very well, even if the object emissivity was not a perfect greybody), and using radiant power matching, mathematically very closely (within 5 C) matched the results achieved with IR camera footage on real hot objects with good calibration (thermocouples, calibrated emissivity paint, and dual frequency pyrometers). In general, if I recall correctly, I ended up about 20 C less than Clarke. Still respectably close enough that both methods were ending up essentially in the same place, although my method ended up closer to the Optris software results (which were not exactly the same as the Lugano reactor, obviously).
This is an interesting point. The first thing I'd say is that the difference, as you point out, as not at all in the grand scheme of things significant. As such perhaps TC would have been well advised to make no correction at all, and not open up this can of worms.
The second thing is that I think TC was at least partly correct on this one matter: although it is not simple to see why.
The camera sofware will (true) compensate so that black bodies have the correct temperature. However the only thing they have to go by is the integrated response from the bolometer (it is a single frequency detector - unlike some IR cameras that measure two distinct frequencies - using different filters, or different sensors - and therefore can do better).
So the integral of the bolometer reponse and the material grey-body response is needed: it gives the camera output. This is then compared with the bolometer response integrated over a BB spectrum curve _at the estimated temperature_. So, in fact, TC is partly correct, but to be more precise an extra correction is needed where the bolometer output is interpreted as a BB signal of a given temperature integrated over the bolometer response and the temperature adjusted to match the output. It is not (I think) correct that this second correction is correctly made simply by leaving out the BB component of the bolometer response - even though it might be approximated by that. It would be interesting to see.
Paradigmnoia's suggestion will give a close approximation to the actual response, because the two effects cancel. But, maybe, it will still be significantly incorrect. What I will give to P however is that given the two simple options, I think on balance I'd choose not to do the BB weighting at all than to do it just once, as TC does.
One additional reason why over-elaboration here does not much help is that TC only had available a guessed approximation to the bolometer response. Specific sensors are likely to depart from this a bit, and Optris do not (AFAIK) give precise info. Aty least if they do, TC does not reference this, but rather he references Bob Higgins's generic IR bolometer response curve.