# A Traceable Spectral Radiation Model of Radiation Thermometry
## 5 Discussion
### Uncertainty of Radiation Thermometry Due to Uncertainty of Spectral Emissivity  
Each surface can be classified as an idealized grey body with corresponding spectral homogeneity uncertainty. To assure traceability of measurements, input uncertainties must be evaluated and included in the total measurement uncertainty. A demonstration of the evaluation of uncertainty due to spectral emissivity is shown in Figure 18.  
In general, the measurement uncertainty of any radiation thermometer is lowest near the apparent temperature of reflection and increases approximately linearly with the difference from the environment temperature. The linearity was explored in Figure 19, where the measurement uncertainty is expressed in relation to the temperature difference between the measured object and the 25 \({}^{\circ}\)C environment. The results in Figure 18 indicate that different sensors with different spectral sensitivities respond differently to measurement uncertainty, presumably due to different emission/reflection ratios in different spectral sensitivity ranges and at different object temperatures. As can be seen from the simulation results, the measurement uncertainty increases with decreasing emissivity of the surface (at constant input uncertainty of the emissivity). As the emissivity uncertainty interval approaches an emissivity value of 0, the total measurement uncertainty will seemingly increase to infinity. This is also logical, since non-emissive surfaces cannot be measured due to the lack of emission. Another error was found to occur frequently when the compensation algorithms overestimate the influence of influence parameters. In this case, the compensated signal may be calculated to a negative incident radiance of the environment. Overcompensation is very problematic when low temperatures (below 0 \({}^{\circ}\)C) are measured at higher environmental temperatures. Due to the steepness of the inverse sensor characteristic (Figure 11) at low temperatures, a small uncertainty in the inverse model translates to a high temperature measurement uncertainty. This is evident in Figure 19 for TRT II and FLIR detectors in 8-14 \(\upmu\)m range. **Author Contributions:** Conceptualization, V.M. and I.P. ; methodology, V.M. and I.P. ; software, V.M. ; validation, V.M. ; formal analysis, V.M. and I.P. ; investigation, V.M. ; resources, V.M. and I.P. ; data curation, V.M. ; writing--original draft preparation, V.M. ; writing--review and editing, I.P. ; visualization, V.M. ; supervision, I.P. ; project administration, I.P. ; funding acquisition, I.P. All authors have read and agreed to the published version of the manuscript. **Funding:** The authors acknowledge the financial support from the Slovenian Research Agency (research core funding No. P2-0225). The research was also supported partially by the Ministry of Economic Development and Technology, Metrology Institute of the Republic of Slovenia, in scope of contract 6401-18/2008/70 for the national standard laboratory for the field of thermodynamic temperature and humidity. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** All data, presented in this study, are publicly available from cited sources. Plot scripts in MATLAB environment are available upon request. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**  
**Terminology**  
* a non-contact method of temperature measurement. Specific to this group of measurement methods is indirect temperature measurement using thermal radiation.