## 3 Results
### Key formulas. Calibration-curve recalibration accounting for background precise value.
But the conversion coefficient \(K_{\rm C}(\stackrel{{\rightarrow}}{{Z^{\prime}}})\) is still the function of only the parameters \(\stackrel{{\rightarrow}}{{Z^{\prime}}}\). We expand function \(\widetilde{K}(\stackrel{{\rightarrow}}{{X}},\stackrel{{ \rightarrow}}{{Y}})\) in a Taylor series expansion in powers of \((\stackrel{{\rightarrow}}{{X}}-\stackrel{{\rightarrow}}{{X^{ \prime}}}),(Y-\stackrel{{\rightarrow}}{{Y^{\prime}}})\). In this case, when we expand in powers of \((\stackrel{{\rightarrow}}{{X}}-\stackrel{{ \rightarrow}}{{X^{\prime}}}),(\stackrel{{\rightarrow}}{{Z}}- \stackrel{{\rightarrow}}{{Z^{\prime}}})\) we allow the arbitrary number of terms \(L\), but in powers of \((\stackrel{{\rightarrow}}{{Y}}-\stackrel{{ \rightarrow}}{{Y^{\prime}}})\) we only allow two terms. Then, performing similarly, we obtain the relationship between the intensities \(I\), \(I^{\prime}\) as follows:  
\[I=a_{L1}+b_{L1}I^{\prime}+d_{L1}I^{\prime 2}, \tag{26}\]  
where the parameters \(a_{L0}\), \(b_{L0}\) (as well as \(a_{L},b_{L}\)) are determined by the derivatives of the functions \(\stackrel{{\rightarrow}}{{K}}(\stackrel{{ \rightarrow}}{{X^{\prime}}},\stackrel{{\rightarrow}}{{Y^{ \prime}}}),A(\stackrel{{\rightarrow}}{{Y^{\prime}}}),\ I_{pl}( \stackrel{{\rightarrow}}{{Y^{\prime}}})\) of the order up to and including \(L\) (we do not provide the formulas because they are cumbersome). For the parameter \(d_{L0}\), the following is true:  
\[d_{L0}=\frac{1}{A(\stackrel{{\rightarrow}}{{Y^{\prime}}})}\frac{ dA(\stackrel{{\rightarrow}}{{Y^{\prime}}})}{d\stackrel{{ \rightarrow}}{{Y^{\prime}}}}(\stackrel{{\rightarrow}}{{Y}}- \stackrel{{\rightarrow}}{{Y^{\prime}}})\sum_{l=0}^{L}\frac{1}{ \bar{\eta}!}\frac{\partial^{i}\vec{K}(\stackrel{{\rightarrow}}{{Y^ {\prime}}},\stackrel{{\rightarrow}}{{Y^{\prime}}})}{\partial \stackrel{{\rightarrow}}{{X^{\prime}}}}(\stackrel{{ \rightarrow}}{{X}}-\stackrel{{\rightarrow}}{{X^{\prime}}})\,. \tag{27}\]  
Similarly, if we expand \(\stackrel{{\rightarrow}}{{K}}(\stackrel{{ \rightarrow}}{{X}},\stackrel{{\rightarrow}}{{Y}})\) into a double Taylor series up to the terms that are proportional to \((\stackrel{{\rightarrow}}{{X}}-\stackrel{{ \rightarrow}}{{X^{\prime}}})\stackrel{{ L}}{{( \rightarrow}}-\stackrel{{\rightarrow}}{{Y^{\prime}}})\stackrel{{ M}}{{( \rightarrow}}-\stackrel{{\rightarrow}}{{Y^{\prime}}})\), and the function \(A(\stackrel{{\rightarrow}}{{Y^{\prime}}})\) up to the terms that are proportional to \((\stackrel{{\rightarrow}}{{Y}}-\stackrel{{ \rightarrow}}{{Y^{\prime}}})\), then we obtain the relation between the values \(I,I^{\prime}\) in the form of the polynomial dependence of the order of \(M+1\) by a variable \(I^{\prime}\), and the particular case in which \(M=1\) is Equation (26). It is clear that in the case when the conversion coefficient \(K_{C}(\stackrel{{\rightarrow}}{{Z}},I_{l})\) depends on the incoming CCD radiation intensity \(I_{l}\), similarly, depending on the number of terms of this value in the Taylor expansion with accuracy up to the number of linear terms in powers of \((\stackrel{{\rightarrow}}{{Y}}-\stackrel{{ \rightarrow}}{{Y^{\prime}}})\) and \((\stackrel{{\rightarrow}}{{Z}}-\stackrel{{ \rightarrow}}{{Z^{\prime}}})\), there is a case when the correlation (26) is valid. Thus, based on the analysis performed, we may conclude that the form of analytical-signal dependence on the spectrometer parameters \((y_{1},\ldots,y_{S})=\stackrel{{\rightarrow}}{{Y}}\) (responsible for radiation-intensity formation before it enters the spectrometer's slit-light entrance system) does not affect the linear character of the relationship between the intensities \(I,I^{\prime}\) if the spectrometer-transmission coefficient does not depend on these parameters, and the conversion coefficient is independent of the incoming CCD radiation intensity. On the contrary, the dependence of this coefficient on \(I_{0}\) and/or the conversion coefficient on \(I_{l}\) leads to the deviation of function \(I(I^{\prime})\) from the linear one.