## 3 Materials and Method
### Near-Medium Infrared Wavelength Analysis: Theoretical Results  
Finally, in order to increase the sensitivity of the ratio between the signals captured at two close wavelengths, a camera with a working range starting from the near wavelength (NW) spectral range (1.5-5 um) was chosen. It consists of a FLIR ORION SC 7600 multispectral camera operating in MW and filled out with an internal filter wheel that can rotate fast enough in such a way to consider the object thermal state unchanged, thus, meeting the requirements needed to apply the dual-color technique [7]. The validated numerical model has been used to determine a proper couple of filters in order to make the thermocamera operational in the DC technique experimental applications. In order to achieve this, a virtual camera has been built using Equations (1-4) implemented in Mathcad code. In Figure 7, on the left side, different trends of SR with temperature for different couples of filters are reported. A Gaussian form was used to replicate the filter response curves that match with typical response curves of real narrow bandpass filters available on the market. The purple curve presents a greater slope than the others. Hence, filters that work at 2.1 um and 2.2 um have been chosen as the best combination for the SR sensitivity. Note that Figure 7 refers to filters centered at 2.0 um and 2.1 um, while the final choice consists of filters centered at 2.1 um and 2.2 um. In order to use these kinds of filters at high temperatures, it is necessary to couple them with an attenuator. A market survey showed that it was not easy to get attenuators below 2 um. We found most attenuators work starting from 2 um. An attenuator working from 2 um does not match with the left part of the filter response function centered at 2 um, hence in order to keep the benefits of the spectral region and the same distance between the two filters (0.1 um), we shifted the two filters ahead of 0.1 um, considering two filters centered at 2.1-2.2 um. They also keep the same features in terms of signal ratio sensitivity of the couple centered at 2-2.1 um. The more the SR varies with temperature, the more it can be associated with a single temperature value. In fact, when two wavelengths are close to each other, the SR trend becomes flat with temperature and the association to a single temperature value becomes more difficult due to oscillation of the calibration curve connected to the sensitivity. On the contrary, when the filters' central wavelengths are too far, the grey body hypothesis fails and the ratio principle cannot be used. In addition, FLIR Orion 7600 has an internal rotatable wheel (up to 100 Hz) synchronized to the acquisition system, allowing it to work in non-stationary conditions. The calibration curve obtained for the filter couple, on the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test** & **\(\mathbf{\lambda}\) (μm)** & **SR** & \(\mathbf{\epsilon}\) & \(\mathbf{\epsilon}\) & **Tij** (\({}^{\circ}\)**C**) & **T\({}_{\text{C}}\) (\({}^{\circ}\)**C**) & **\%** = 1 (**Tij** - **T\({}_{\text{C}}\))/**T\({}_{\text{C}}\)** l \\ \hline
1 & 3.80–3.97 & 0.6704 & \(\varepsilon_{3.97}\) = 0.3094 & \(\varepsilon_{3.80}\) = 0.3069 & 429 & 409 \(\pm\) 8 & \(\approx\)4.9 \\
2 & 3.80–3.90 & 1.0958 & \(\varepsilon_{3.90}\) = 0.2070 & \(\varepsilon_{3.80}\) = 0.2047 & 341 & 414 \(\pm\) 8 & \(\approx\)17.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental test results column is referred, respectively, to the test number, central wavelengths of the filter couples, signal ratio values, emissivity for different filters, dual-color measurements (Tij), thermocouple measurements, and relative temperature accuracy of dual-color (Tc) with respect to the thermocouple measurements [5,6]. Figure 6: On the (**left**), the 3.80–3.90 μm filters transmissivity curves are shown and, on the (**right**), the 3.80–3.97 μm filters transmissivity curves are shown [5,6].