## 4 Discussion
For the measured intensity in pixel \(n\) we have:  
\[\overline{I}_{nm}(n)=I_{0}exp\left\{-\left[\frac{n-\frac{(L-1)}{2}}{\Delta} \right]^{2}\right\}\text{; }\Delta=\frac{(L-1)}{2\sqrt{3\cdot ln(10)}}\text{,} \tag{9}\]  
Figure 9: A view of the corresponding window of the software used in the SPAS-02 emission spectrometer ([[http://activespectr.com/en/products/emission-spectrometers/optical-emission-spectrometer-oes-spas-02-metal-analysis](http://activespectr.com/en/products/emission-spectrometers/optical-emission-spectrometer-oes-spas-02-metal-analysis)]([http://activespectr.com/en/products/emission-spectrometers/optical-emission-spectrometer-oes-spas-02-metal-analysis](http://activespectr.com/en/products/emission-spectrometers/optical-emission-spectrometer-oes-spas-02-metal-analysis)) (accessed on 27 February 2022)) in the area of the analytical line **Ni** 351.505 nm; the red line shows the standard sample of low-alloy steel 1104 with a **Ni** content of 0.094%; the green line shows the standard sample of low-alloy steel 1101 with a **Ni** content of 3.34%. When determining the intensity of the line, the signals from the pixels located inside the yellow shading are summed. and for the line measured intensity we obtain:  
\[\overline{I}_{0M}=I_{0}\sum_{n=\frac{L-K}{2}+1}^{\frac{L+K}{2}}exp\left\{-\left[ \frac{n-\frac{(L-1)}{2}}{\Delta}\right]^{2}\right\}. \tag{10}\]  
Consequently, for the actual intensity of the spectral line we obtain:  
\[\overline{I}_{0r}=I_{0}\sum_{n=\frac{L-K}{2}+1}^{\frac{L+K}{2}}exp\left\{- \left[\frac{n-\frac{(L-K)}{2}}{\Delta}\right]^{2}\right\}b_{nm};\ b_{nm}=b_{nm} \left(exp\left\{-\left[\frac{n-\frac{(L-1)}{2}}{\Delta}\right]^{2}\right\}, \Sigma_{nm}\right). \tag{11}\]  
For simplicity, we assume that the relative dispersions \(\Sigma_{nm}\) are unrelated to the frame number and equal to value \(\Sigma_{0m}\). Figure 10 shows Formulas (9)-(11) for calculating the dependency of value \(b_{0}=\frac{\overline{I}_{0r}}{I_{0M}}\) for \(L=7\) and \(K=3\) (typical values for modern emission spectrometers designed to analyze metals and alloys) on parameter \(\alpha_{4m}\) (i.e., parameter \(\alpha_{nm}\) calculated for the central pixel, which, if \(L=7\), is number 4) at different relative dispersions \(\Sigma_{0m}\). Comparing these data with the data in Figure 5 shows that, all other things being equal, the inequation is satisfied:  
The same can be said of the value \(b_{0}\) calculations, shown in Figure 11 (depending on \(\Sigma_{0m}\) at different values of \(\alpha_{4m}\)). The reason for this, as previously discussed, is that, when moving away from the center of the line, the effect considered decreases due to a decrease in the intensity in the corresponding pixels. Figure 12 shows the results of a numerical experiment on the application of the proposed algorithm. The frame-by-frame accumulation of the CCD signal was simulated using a random number generator with a probability density defined by Formula (3). The line contours were recorded by the recording system on CCD rulers and reconstructed using the above algorithm for our model problem when \(L=5;\Sigma_{0m}=0.4;b_{3m}=0.95\) and \(L=9;\Sigma_{0m}=0.4;b_{5m}=0.95\). As indicated, the measured and the reconstructed contours have different half-widths if the width at the base is the same. The reasons for this are discussed above. For the central pixel, the effect considered is at its maximum, so the half-width decreases. In this case, the effect for the edge pixels is almost equal to null, which provides the same width at the base of the recorded and the actual contours.