## 4 Discussion  
To verify our findings, we used data obtained by several SPAS-02 and SPAS-05 emission spectrometers while determining the elemental composition of low- and medium-alloyed steels. Figure 3 shows the calibrations to determine the carbon content in low- and medium-alloyed steels by standard samples UGO4--UG9a, UGOe-UG9e, UGOk-UG9k, RG25a-RG31a for a SPAS-02 spectrometer (serial numbers \(N\)22, 25, 26) and a SPAS-05 spectrometer (serial number \(N\)18). The analytical carbon line CI 193.09 nm was used in this case. There are two types of calibration lines described: accounting for plasma background by the conventional algorithm (see above) and by adjusting using the suggested algorithm. The calibration curves were reduced to the same intensity range because the transmission coefficients of different devices may significantly vary. The corresponding coefficients were determined provided that the intensities of all devices were reduced to the same range of values \(I-I_{\rm F}\) in the area of low carbon concentrations. It can be seen that in the area of relative carbon content lower than 0.15-0.3% (according to the particular device), the calibration-curve slope (2) begins to rise, which results in the several-fold increase of the RMS deviation of the determined concentration. Simultaneously, the curves that were adjusted for the accurate background accounting in the area of low concentration have the form of straight lines with the slope of one. This is known to be optimal for emission-spectral-analysis calibration [22, 23]. Figure 4 shows the dependences of slope calibrations \(D_{0}(I)\), both unadjusted and adjusted for the accurate accounting of the plasma background \(D_{\rm F}(I)\) of the data in Figure 3 (SPAS-02 spectrometers, serial numbers \(N\)22, 26). Functions \(D_{0}(I)\), \(D_{\rm F}(I)\) are determined by the following equations:  
\[(I)=\frac{I}{F(I)}\frac{dF(I)}{dI};D_{\rm F}(I)=\frac{I-I_{\rm F}}{F_{A}(I-I_ {\rm F})}\frac{dF_{A}(I-I_{\rm F})}{dI}. \tag{29}\]  
Figure 3: Calibration curves to determine carbon concentration in low- and medium-alloyed steels on SPAS-02 and SPAS-05 emission spectrometers. The curves are reduced to the same relative intensity range by multiplying by the coefficients \(k\); 1–4 are calibration curves \(F_{A}(I-I_{\rm F})\), plotted by the developed algorithm with accurate accounting for plasma background, and 5–8 are plotted by the conventional algorithm for SPAS-05, serial number \(N\)18, \(k=0.38\); SPAS-02, serial number \(N\)22, \(k=1.07\); SPAS-02, serial number \(N\)25, \(k=1.37\); SPAS-02, serial number \(N\)26, \(k=1\), respectively. It can be seen that in the area of low relative intensities, the value \(D_{0}(I)\) is more than an order higher than the optimal value equal to 1. If \(I\) is further decreased, it becomes subzero, which lacks any physical meaning. That is why it is not shown in Figure 4 beyond this value area of \(I\). On the contrary, the slope \(D_{F}(I)\) of the adjusted calibration curve in the whole area of \(I>I_{F}\) is close to 1, which ensures a minimum RMS deviation while measuring concentrations. It should be noted that introducing coefficients \(k\) before the relative intensity will reduce all the calibrations that were plotted with an accurate accounting of the plasma background to close curves related by a linear transformation (see Figure 5), despite the fact that:  
* Various technologies for both spectrograph and generator (SPAS-02 and SPAS-05) manufacturing are utilized. * Spectrometers have significantly different focus near the CI 193 nm line (the line width differs by up to twice);
* Various sets of standard samples (UG0a-UG9a, UG0e-UG9e, and UG0k-UG9k) are used. This, in turn, creates opportunities for the primary calibration of spectrometers for specific types of alloys by a recalibration algorithm with linear-intensity transformation (see above), rather than by sets of dozens of standard samples.