## 3 Materials and Method
### Medium Wavelength Range Analysis: Experimental Results  
In the MW range (2.5-5.1 \(\upmu\)m), Mathcad simulations have been carried out first, for the FLIR SC5500 research (with an internal drum and a variable integration time) Stirling cooled camera, to implement the technique in such a way to choose directly both the best couple of filters and the best usable \(SR\) sensitivity [5; 6]. Briefly, the \(SR\) uncertainty propagation of the camera output gives \(\Delta SR=0.1\%\) and if an accuracy \(\tau=2\%\) is needed  
Figure 4: On the (**left**) side, the simulated SR trend is shown for 10.454 \(\upmu\)m and 10.464 \(\upmu\)m filters and for 10.400 \(\upmu\)m e 10.500 \(\upmu\)m. On the (**right**) side, the dispersion is shown for the last couple of filters [6]. Figure 3: Experimental SR, depleted from the reflection contribution, where a huge variability due to the black body stability and camera sensitivity is shown. The Mathcad simulation with uncertainties is shown [6]. on the temperature value (\(\Delta T<\tau\)\(T\)), it has to be satisfied for each couple of filters and \(T\) value [6] the following:  
\[\frac{\partial SR(T)}{\partial T}\geq\frac{0.001}{\tau T} \tag{9}\]  
Therefore, the goodness of the couples of filters chosen (3.80-3.90 \(\upmu\)m, 3.80-3.97 \(\upmu\)m) has been evaluated through experimental verifications. In particular, the temperature of an aluminum plate, heated through a heating slab, was measured with a thermal camera through the DC technique and with K-type thermocouples [5; 6]. The heating plate [9] was set at \(T=500\)\({}^{\circ}\)C (where the effects of reflected radiance could be neglected). In order to verify the DC methodology, a square plate with a length of 10 cm and a thickness of 0.5 cm, composed of rough aluminum alloy was used as the surface seen from the camera, as shown in Figure 5.  
Four thermocouples of K-chromel type (Ni-Cr) (+)/alumel (Ni-Al) (\(-\)), able to perform the measurement in a temperature range of 200-1260 \({}^{\circ}\)C were used to validate the experimental results as well as to calculate the target emissivity. A DC pyrometer [8] was used as a temperature regulation system with a temperature accuracy of 0.75% for the thermocouples [10]. The accuracy of the average value obtained by the four thermocouples, as shown in Table 1, is \(\pm\)2% considering both the accuracy due to the K-type used and the oscillations (in terms of standard deviation) of the different measurements indicated. Data acquisition is detailed in [11]. In order to acquire the DC temperature, a FLIR SC5500 was used, on a 20 \(\times\) 20 pixels square matrix centered on the central pixel of the thermal camera and calculating the average digital level (DL), i.e., the signal output that is proportional to the radiation impinging the IR sensor. The camera is provided with an internal wheel having the capability to host up to four filters, but three filters have been used in this case (3.80 \(\upmu\)m, 3.90 \(\upmu\)m, 3.97\(\upmu\)m), in such a way to analyse two couples of filters 3.80-3.90 \(\upmu\)m and 3.80-3.97 \(\upmu\)m. The switch between them can happen in few tenths of a second. So, the '\(-\)' is used to separate and to specify the two filters of the couple considered for the dual color measurements. The filter transmittance is shown in Figure 6.  
The results, obtained through the dual-color technique, are reported in the following Table 1.  
At the same wavelength (3.80 \(\upmu\)m), a difference in emissivity value has been obtained in the two experiments and the most likely cause is the oxidation of the plate after the first experiment. For the first test (with \(\Delta\lambda\) equal to 0.17 \(\upmu\)m), a 5% percentage accuracy was obtained. For the second experiment (with \(\Delta\lambda\) equal to 0.10 \(\upmu\)m), an 18% percentage accuracy was obtained.