## 2 Materials and Methods  
**Key formulas**. Let us consider an algorithm for measuring the line intensity using a CCD in emission spectrometers. Intensity is measured repeatedly (each measurement will be called a \"frame\"), and in each frame during a certain time (frame duration), the signal is integrated. Due to the random nature of emission of radiation by atoms, with its sufficiently high intensity, the values of the charge accumulated by the pixels for some frames are higher than the upper limit of the CCD. As a result, their measured intensity, which is equal to the upper limit of the CCD, becomes lower than the actual one. However, the intensities of the remaining frames (which are below the upper limit of the CCD) are measured accurately, to a certain extent, and distributed according to a certain statistical law. The task is to use the array of measured frame intensities and the fact that all real intensities of each frame obey one statistical law to restore the real average intensity of the analytical line and its variance, which are calculated for all registered frames. Our aim is to restore the real intensity of the spectral line as an average of a certain number of frames using frames whose intensity as a statistically variable parameter did not exceed the threshold after which the blooming effect manifests itself. In this sense, the proposed intensity adjustment method is mathematical rather than instrumental. It is well known that the substance analysis for the content of a certain element is carried out in emission spectrometers with the so-called calibration curves--the dependences of intensities \(I\) (absolute or relative, depending on the analytical technique) on an impurity level \(C\) in a sample:  
\[I=I(C). \tag{1}\]  
The dependence of the relative intensity of the analytical line **A1** I 394.4 nm (reference line--**Fe I 389.57 nm) on the concentration \(C\) of aluminum in steels that is shown in Figure 2 has the following form:  
\[\frac{I_{Al}}{I_{Fe}}=-0.019C^{3}+0.443C^{2}+0.049C-6.79\times 10^{-4}+\frac{0. 001}{1+C^{5}}. \tag{2}\]  
A benchtop spark emission spectrometer with the following characteristics was used in the research to analyze alloys:  
* type of discharge--low-voltage spark in an argon atmosphere;
* spectral resolution--no more than 0.05 nm;
* optical configuration--Paschen-Runge;
* spectral range--170-450 nm;
* recording system--8 CCD TCD1304 DG. The effect considered above leads to the fact that, in the area of high concentrations, derivative \(\frac{dI}{dC}\), decreases (or it can be said that the derivative \(\frac{dC}{dI}\) increases), which negatively affects the quality of the measurements (see Figure 2) due to an increase in both random and systematic errors. Thus, studying the adjustment possibility of the analytical line intensity when measured by CCD recording systems at the upper limit of the analytical signal seems to be highly relevant. To avoid uncertainty, we consider linear CCDs. Let the analytical line image in the focal plane of a linear CCD spectrograph take \(L\) pixels. We first consider some arbitrary pixel number \(n\). Taking into account the set task, first, we are interested in the pixels at the maximum of the analytical line. As is well known, the algorithm of CCD signal accumulation in an individual pixel can be described as follows: the signal is accumulated for some time, called the accumulation time, after which it is read out, digitized, and summed with the previous signals. After completing a certain number of cycles, called the frame count, the stack is divided by the number of frames. This is the measured signal in the given pixel.