## 3 Results
### Key formulas. Calibration-curve recalibration accounting for background precise value.
In this case, the correlation between the intensity from the optical-system radiation entrance to the device's recording system, as well as the parameters of radiation conversion into an electric signal by this recording system may vary. Otherwise, the shape of the calibration curves may differ significantly and recalibration using this algorithm will be impossible. Then, knowing that for an arbitrary sample (standard or unknown-composition sample) due to the function definition of \(F_{A}(x)\), the following is fulfilled:  
\[F_{A}(I-I_{F})=F_{A}[F_{I}(I^{\prime})-F_{I}(I^{\prime}{}_{F})]\]  
We get:  
\[I-I_{F}=F_{I}(I^{\prime})-F_{I}(I^{\prime}{}_{F}). \tag{15}\]  
We divide all the independent parameters that determine the measured analytical-line intensity into three groups (see Figure 2):* The parameters that determine the spectral-transmission coefficient of the spectrometer (let their number be \(s\)). * The parameters that determine the analytical-line intensity before it enters the slit-light entrance system (their number is \(g\)). * The parameters that determine the conversion coefficient of incoming CCD radiation intensity as a digitized signal that is processed by the spectrometer software (their number is \(m\)). We shall indicate them as (a) \((x_{1},\ldots,x_{s})=\overset{\rightarrow}{X}\), (b) \((y_{1},\ldots,y_{g})=\overset{\rightarrow}{Y}\) and (c) \((z_{1},\ldots,z_{m})=\overset{\rightarrow}{Z}\). We also assume that the analytical-line intensity is \(I_{0}(\overset{\rightarrow}{Y})\) before it enters the spectrometer's slit-light entrance system, and that it is \(I_{I}(\overset{\rightarrow}{X},\overset{\rightarrow}{Y})\) in the CCD plane before conversion by the recording system. Thus, \(I\) is the intensity \(I_{l}\) converted by the recording system with the conversion coefficient \(K_{C}(\overset{\rightarrow}{X},\overset{\rightarrow}{Y},\overset{ \rightarrow}{Z})\), which generally also dependents on the incoming CCD radiation intensity. The radiation in turn depends on the parameters \(\overset{\rightarrow}{X}\), \(\overset{\rightarrow}{Y}\). Thus, the relation between the values \(I_{0}\), \(I_{l}\), \(I\) is as follows:  
\[\frac{I_{l}}{I_{0}}=K[\overset{\rightarrow}{X},I_{0}(\overset{\rightarrow }{Y})];I=K_{C}(\overset{\rightarrow}{Z},I_{l})I_{l}=K_{C}(\overset{ \rightarrow}{X},\overset{\rightarrow}{Y},\overset{\rightarrow}{Z})I_{l} \tag{16}\]  
where \(K[\overset{\rightarrow}{X},I_{0}(\overset{\rightarrow}{Y})]\) is the spectrometer-transmission coefficient. Now we consider the most general case and assume that the transmission coefficient depends not only on the parameter \(\overset{\rightarrow}{X}\), but also on the intensity \(I_{0}\), whereas the conversion coefficient depends on \(I_{l}(\overset{\rightarrow}{X},\overset{\rightarrow}{Y})\). Now we identify Equation (13) based on the most general correlations. As a rule, while using modern emission spectrometers, a dark signal of the recording system is automatically accounted for. Nevertheless, we assume that due to, for instance, a change in the dark signal (and noise) of the CCD recording-system receivers during continuous operation of the spectrometer, there is some additional signal \(I_{n}(\overset{\rightarrow}{X})\), that contributes to the measured intensity. Under these assumptions, the correlation between the analytical-line intensity,  
Figure 2: Spectrometer units, of which the characteristics are determined by the parameters \(\overset{\rightarrow}{X},\overset{\rightarrow}{Y},\overset{\rightarrow}{Z}\); (a) spectrum-excitation source and sample-atomization system (1), radiation source (2); (b) sample-substance-radiation-spectrum-capturing system, including the spectrometer slit-light entrance system (3), entrance slit (4), spectrum-capturing and focusing system on the focal surface (5); (c) recording system including CCD radiation receiver and CCD signal converter (6).