## 6 Results of Uncertainty Simulations for Multiple Cases of Use of Radiation Thermometry  
Through years of activity as a calibration laboratory and in terms of academic activities, the measurement uncertainty of radiation thermometry was required (however unknown) in multiple cases of RT use. Four cases of radiation thermometry use were found of interest for future measurement activities and considered in this investigation. An appropriate instrument for each use is selected based on the operating temperature range and standard practice. Case 1: Measurement Uncertainty of a Reference Radiation Thermometer with No Atmospheric Compensation in High Temperature Calibration Using a Laboratory Black Body Calibrator  
Case 1 is the temperature measurement uncertainty of the laboratory black body calibration device. The usual emissivity of the laboratory cavity calibrators is 0.998 \(\pm\) 0.002 (bounds). While laboratory calibrations are required for all radiation thermometers, our high temperature reference standard, Heitronics KT19.01 II, is simulated in this case as a reference thermometer, contributing to the uncertainty of the reference temperature data in calibrations of thermometers by comparison. While calibrations by comparison with a radiation thermometer reference are typically performed above 1000 \({}^{\circ}\)C, the full range of the thermometer is simulated in this case. The nominal focal distance of this thermometer is 733 mm and the best achievable uncertainty of distance is considered. As no atmospheric correction is used by Heitronics KT19.01, the uncertainties of atmospheric conditions account for the change in conditions between the calibration of a reference thermometer and the use of this thermometer as a reference in laboratory calibrations. All influence parameters are listed in Table 8 with their partial contributions to the measurement uncertainty at 1000 \({}^{\circ}\)C. The Monte Carlo simulated combined standard measurement uncertainty at 1000 \({}^{\circ}\)C accounted for 1.72 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Measured** & **Parameter** & **Input** & **Simulated** & **Reported** & **Simulation** \\
**Temp.** & & **Deviation** & **Deviation** & **Deviation** & **Mismatch** \\ \hline \(-\)50 \({}^{\circ}\)C & Emissivity & 0.95 \(\rightarrow\) 0.99 & 14 \({}^{\circ}\)C & 13.3 \({}^{\circ}\)C & 5.3\% \\ \hline
500 \({}^{\circ}\)C & Emissivity & 0.95 \(\rightarrow\) 0.99 & 4.8 \({}^{\circ}\)C & 5.1 \({}^{\circ}\)C & \(-\)5.9\% \\ \hline \(-\)50 \({}^{\circ}\)C & Reflection & 20 \(\pm\) 5 \({}^{\circ}\)C & 0.133 \({}^{\circ}\)C & 0.12 \({}^{\circ}\)C & 10.8\% \\ \hline
500 \({}^{\circ}\)C & Reflection & 20 \(\pm\) 5 \({}^{\circ}\)C & 0.012 \({}^{\circ}\)C & 0.012 \({}^{\circ}\)C & 0\% \\ \hline \(-\)50 \({}^{\circ}\)C & Reflection & 20 \(\pm\) 5 \({}^{\circ}\)C & 0.69 \({}^{\circ}\)C & 0.63 \({}^{\circ}\)C & 9.5\% \\ \hline
500 \({}^{\circ}\)C & Reflection & 20 \(\pm\) 5 \({}^{\circ}\)C & 0.06 \({}^{\circ}\)C & 0.06 \({}^{\circ}\)C & 0\% \\ \hline \end{tabular}
\end{table} 
Table 7: Measurement uncertainty simulation results for examples from literature, compared to reported values for a radiation thermometer, operating in 8–14 \(\upmu\)m spectral range. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **Value with Standard** & **Probability** & **Standard Uncertainty** \\  & **Uncertainty** & **Distribution** & **Contributions at 1000 \({}^{\circ}\)C** \\ \hline Relative humidity & (40 \(\pm\) 10)\% RH & Uniform & 1.50 \({}^{\circ}\)C \\ Air temperature & (23 \(\pm\) 2) \({}^{\circ}\)C & Uniform & 0.68 \({}^{\circ}\)C \\ Transfer path distance & (0.733 \(\pm\) 0.05) m & Normal & 0.42 \({}^{\circ}\)C \\ Emissivity & 0.998 \(\pm\) 0.00116 & Uniform & 0.29 \({}^{\circ}\)C \\ Atmospheric pressure & (1013.25 \(\pm\) 10) hPa & Uniform & 0.063 \({}^{\circ}\)C \\ Reflected temperature & (23 \(\pm\) 2) \({}^{\circ}\)C & Uniform & 2.8 \(\times\) 10\({}^{-8}\)\({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}