## 3 Materials and Method  
### Long Wavelength Range Analysis: Experimental Results  
The first attempt on the use of the dual-color technique was performed with a long wavelength (LW) range camera (FLIR A655 sc), equipped with two SPECTROGON filters applied through an external wheel in front of the camera [6]. On the left side of Figure 1, the object signal (OS; OS1 and OS2 represent the object signal that is the radiation captured by the IR sensor in \(W/m^{2}sr\)) experimental trends as a temperature function is shown. Note that the OS corresponds to the \(G_{bb,i}\) in Equation (2), and the first notation (i.e., object signal, OS) is used to be coherent with the denomination of the parameter used by FLIR ResearchIR Max software that has been adopted in the performed measurements. The calibration phase was performed with the MIKRON black body [8] M305) up to 625 \({}^{\circ}\)C. On the right side of Figure 1, the SR (OS2/OS1) trend as temperature function has been also reported. Figure 1: (**Left**)—the experimental object signal (OS); OS1 = BP-10400-737, OS2 = BP-10500-775, respectively, with the center at 10.454 \(\upmu\)m and 10.464 \(\upmu\)m; trends versus temperature. (**Right**)—the experimental SR = OS2/OS1 curve [6]. With this configuration and this camera, on the right side of Figure 1, the object signals ratio is not adequate to obtain a single temperature value. In this case, the environmental temperature (\(T_{env}\) = 20 \({}^{\circ}\)C) was negligible compared to that of the black body, and filters were located next to the camera in order to avoid reflection coming from the external environment. However, the signal ratio is affected significantly by reflection phenomena. Mathcad simulation tool has been used to obtain the reflection mean value coming from the environment. A comparison between the experimental and the theoretical data is shown in Figure 2.  
The reflection amount evaluated through Mathcad simulation has been subtracted from the single OS for each of two filters, which in this way, makes it possible for the two signals ratio to be free from the reflection. Moreover, despite the subtracted reflection contribution, an SR experimental ratio variation is still observed (Figure 3). The discrepancies between the experimental and the Mathcad results are related to the OS variations due to the black body stability and camera sensitivity,  
\[\Delta SR=\sqrt{\left(\frac{\partial SR}{\partial\text{OS2}}*\Delta\text{OS2 }\right)^{2}+\left(\frac{\partial SR}{\partial\text{OS1}}*\Delta\text{OS1} \right)^{2}} \tag{5}\]  
\[\Delta SR=\sqrt{\left(\frac{1}{OS1}*\Delta\text{OS2}\right)^{2}+\left(-\frac{ OS2}{OS1^{2}}*\Delta\text{OS1}\right)^{2}} \tag{6}\]  
with this filter characteristic, it can be assumed that OS1 \(\approx\) OS2 \(\approx\) OS and \(\Delta\)OS2 \(\approx\)\(\Delta\)OS1 \(\approx\)\(\Delta\)OS because the central wavelength are close,  
\[\Delta SR\cong\frac{\Delta\text{OS}}{OS}\sqrt{2} \tag{7}\]  
and  
\[SR-\Delta SR\leq SR\leq SR+\Delta SR. \tag{8}\]  
in the temperature range between 100-650 \({}^{\circ}\)C and OS oscillation of \(\pm\)0.5 counts on the last digit of a signal of 250 W/m\({}^{2}\)Sr (T = 400 \({}^{\circ}\)C) was observed. Hypothesizing a temperature invariant ratio of the \(\Delta\)OS/OS with temperature, the uncertainty of the signal ratio \(\Delta\)SR can be obtained and the dispersion curve can consequently be represented (Figure 3). Figure 2: Mathcad simulation and OS1 experimental comparison, see text. For a better understanding of the shift between the curves see [6]. A way to reduce the dispersion related to the OS uncertainty can be achieved through the increase of the sensitivity (e.g., slope) related to the SR curve expressed as a temperature function. The two filters' central wavelengths, in this case, have been spaced out of one order of magnitude (up to 0.1 \(\upmu\)m). Two filters centered at 10.400 \(\upmu\)m and 10.500 \(\upmu\)m were considered and in Figure 4 the ratio trend is reported.