Hey JimM, this is a message from tomas123 with a lot of information that may be useful for you.
Yeah, I'm aware of the tomas123 posts on this subject. I was just trying to answer the question from the OP vitorpaes, about where the R1, R2, B, F, O parameters came from. In the Minkina and Dudzik references, they actually only mention R, B, and F. But they also mention Global Gain and Global Offset. In the tomas123 and Phil Harvey (ExifTool) rendition, I think R2 = Global Gain and O = Global Offset. However, does that mean R = R1 or R = R1/R2 ? I haven't been able to resolve this.
In other posts from tomas123, he references a total of 15 parameters in the FLIR metadata that you use in order to calculate temperature when accounting for emissivity, reflected temperature, and atmospheric losses. He also posted a spreadsheet where he has all of the calculations, and he shows for a 16-pixel test image that he gets the same temperature values (to about 5 decimal places) as FLIR tools for object distances of 0 meters and 100 meters. So, although I can't completely resolve the equations above, the proof is in the pudding on the tomas123 temperature calculations. In looking at scraps of information from FLIR documents, there is not consistency in how to calculate temperatures. It might be that things changed over the years, or there might be alternative methods for calculating temperatures, or different methods for different cameras.