## 3 Results  
CCD recording systems are usually used in spectrographs based on the Paschen-Runge configuration [22; 23]. Linear CCDs having the smallest possible horizontal pixel size and the highest possible height are typically used in emission spectrometers. The latter is designed to increase the spectrometer recording system sensitivity. For example, a Toshiba TCD1304 DG CCD with a pixel size of \(8\times 200\)\(\upmu\)m is very popular. Therefore, \"SPAS\"-05 emission spectrometers produced by Active Co., Ltd., Saint Petersburg, Russian, which use TCD1304 DG CCD, have a spectrum resolution of up to \(0.05\) nm. The analytical line width of the intensity \((0.5\div 0.7)I_{max}\) in the pixel corresponding to the spectral line center is about 6 to 7 pixels at the base, when the spectrum is spark-excited in argon atmosphere. The linewidth is determined both by the conditions in the plasma (Doppler and Lorentz broadening) and by the instrumental function of the spectrometer. At a normal width of the entrance slit, the contribution of these factors is comparable. It should be noted that, in CCD emission devices that have the Paschen-Runge configuration, in addition to the natural width of the spectral line (Doppler line profile, which is associated with a high temperature, and Lorentzian shape, which is associated with the finite lifetime of the excited level), there is one more reason for line-broadening: it is due to the fact that linear CCDs that are used have a flat shape, whereas the focal surface has a non-zero curvature. Because of this, at any position of the CCD relative to this surface, a maximum of two points of the receiver are in focus. The rest are inevitably out of focus. Apparently, the closer the value \(\overline{I}_{nm}\) is to \(I_{max}\), the greater the difference will be between \(\overline{I}_{nm}\) and \(\overline{I}_{n}\). Due to this fact, the effect considered will be significant for the pixels that form the spectral line center. Earlier in the paper we designated the number of pixels constituting the intensity \(\overline{I}_{nm}\), by \(K<L\). We number them from left to right. Then, for the actual intensity of the spectral line:  
\[\overline{I}_{0r}=\sum_{n=1}^{K}\overline{I}_{n}=\frac{1}{M}\sum_{n=1}^{K}\sum _{k=1}^{M}I_{nk} \tag{6}\]  
we obtain the correlation:  
\[\overline{I}_{0r}=\sum_{n=1}^{K}\overline{I}_{nm}b_{n}\big{(}\overline{I}_{ nm},\Sigma_{nm}\big{)}, \tag{7}\]  
where \(b_{n}\big{(}\overline{I}_{nm},\Sigma_{nm}\big{)}\) is found from Equation (5). Thus, the algorithm for applying the results obtained when used to measure spectral line intensities is as follows. Cyclic signal accumulation occurs during the recording process simultaneously in each pixel of the CCD for a period of time, called a frame. The analog signal is then read out and sent to the ADC, where it is converted into digital format. Furthermore, there is an accumulation during the subsequent frames. As stated previously, to improve the measurement statistics (to reduce the root-mean-square value--RMS), the number of frames \(M\) usually exceeds 100 depending on the measurement technique. It should be noted that when working with relative intensities, when it is also necessary to calculate the intensity of the reference line (i.e., the properly selected base line), it is sufficient to perform adjustment according to the designed procedure only for the analytical line of the impurity or alloying element. The reference line intensity weakly depends on their concentration and, in advance, is chosen to be not too large (as a rule, not more than \((0.5\div 0.7)I_{max}\)); otherwise, the adjustment is also needed for the reference line. The aforementioned mathematical model is applied according to the following algorithm. The signal accumulated in each pixel constituting the analytical line intensity during each frame is saved. Thus, we have a dimensional dataset \(M\cdot K\) for one analytical line.