## 2 Materials and Methods
Let the frame count be \(M\gg 1\), and the distribution density of by-frame intensity probabilities (i.e., not the measured but the actual intensity) that goes into pixel \(n\), obeys a Gaussian distribution:  
\[P_{n}(I_{nk})=A_{n}exp\Bigg{[}-\frac{\big{(}I_{nk}-\overline{I}_{n}\big{)}^{2}}{2 \sigma_{n}{}^{2}}\Bigg{]} \tag{3}\]  
where \(I_{nk}\) is the intensity value during the \(k\) frame in pixel \(n\); \(\sigma_{n}\) is the standard deviation of the average value for the frame-by-frame distribution of \(P_{n}(I_{k})\) in pixel \(n\); \(\overline{I}_{n}=\frac{1}{M}\sum\limits_{k=1}^{M}I_{nk}\) is the average intensity value for \(M\) frames in pixel \(n\); \(A_{n}\) is the normalization constant. \(I_{nk}\) varies within the limits:  
\[I_{nk}\in[I_{nN},\infty);I_{nN}\ll\overline{I}_{n}, \tag{4}\]  
where \(I_{nN}\) is some sufficiently small value of the order of plasma background radiation intensity at a wavelength, corresponding to the location of pixel \(n\). We assume that this CCD maximum allowable intensity does not depend on a pixel number and is equal to \(I_{max}\). We also assume that the measurement results in some average intensity \(\overline{I}_{nm}\). The qualitative considerations clarify that if \(\overline{I}_{n}\) is significantly less than \(I_{max}\), the values \(\overline{I}_{n},\overline{I}_{nm}\) will be close. When \(\overline{I}_{n}\) approaches the value of \(I_{max}\), the frames in which the pixel is exposed to radiation of an intensity exceeding \(I_{max}\) will have \(I_{max}\) as a measurement result. Thus, \(\overline{I}_{nm}<\overline{I}_{n}\). This circumstance must be taken into account when taking measurements. In this regard, it is necessary to find the correlation between the values \(\overline{I}_{nm},\sigma_{n}\), and \(\overline{I}_{n}\). Following Appendix A, we obtain the correlation of the actual intensity and the relative dispersion \(\overline{I}_{n},\sigma_{n}\), with the measured values \(\overline{I}_{nm},\sigma_{nm}\) (see the definitions of values \(b_{nm}\), \(\Sigma_{n},\alpha_{nm},\Sigma_{nm}\) in Appendix A):  
\[b_{nm}\bigg{[}1+erf\bigg{(}-\frac{\alpha_{nm}-b_{nm}}{\sqrt{2} \Sigma_{n}b_{nm}}\bigg{)}\bigg{]}-\frac{\Sigma_{n}\alpha_{nm}}{\sqrt{2}\pi} exp\Bigg{[}-\bigg{(}\frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}} \bigg{)}^{2}\Bigg{]}+\alpha_{nm}\bigg{[}1-erf\bigg{(}-\frac{\alpha_{nm}-b_{nm} }{\sqrt{2}\Sigma_{n}b_{nm}}\bigg{)}\bigg{]}=1, \tag{5}\] \[\frac{\Sigma_{nm}{}^{2}}{b_{nm}{}^{2}}=\Sigma_{n}{}^{2}\Big{[}1- \frac{1}{\sqrt{\pi}}\Gamma\Big{(}\frac{3}{2},\frac{\alpha_{nm}-b_{nm}}{\sqrt{2 }\Sigma_{n}b_{nm}}\Big{)}\Big{]}-\sqrt{\frac{2}{\pi}}\Sigma_{n}(b_{nm}-1)exp \bigg{[}-\big{(}\frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\big{)}^{2 }\bigg{]}\] \[+\frac{(b_{nm}-1)^{2}}{2}\Big{[}1+erf\Big{(}-\frac{\alpha_{nm}-b_{ nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\Big{)}\Big{]}-\frac{1}{2}\Big{[}1-erf\Big{(}- \frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\Big{)}\Big{]}\]  
when \(\alpha_{nm}\geq b_{nm}\);  
\[\frac{\Sigma_{nm}{}^{2}}{b_{nm}{}^{2}}=\frac{\Sigma_{n}{}^{2}}{ \sqrt{\pi}}\Gamma\Big{(}\frac{3}{2},\frac{b_{nm}-\alpha_{nm}}{\sqrt{2}\Sigma_ {n}b_{nm}}\Big{)}-\sqrt{\frac{2}{\pi}}\Sigma_{n}(b_{nm}-1)exp\bigg{[}-\big{(} \frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\big{)}^{2}\bigg{]}\] \[+\frac{(b_{nm}-1)^{2}}{2}\Big{[}1+erf\Big{(}-\frac{\alpha_{nm}-b_{ nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\Big{)}\Big{]}-\frac{1}{2}\Big{[}1-erf\Big{(}- \frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\Big{)}\Big{]}\]  
if \(\alpha_{nm}<b_{nm}\), where \(\Gamma(a,x)=\int_{x}^{\infty}t^{a-1}exp(-t)dt\) is the gamma function; \(\Sigma_{n}=\frac{\sigma_{n}}{\overline{I}_{n}}\) is the relative dispersion of the actual intensity; \(b_{nm}=\frac{\overline{I}_{n}}{\overline{I}_{nm}};b_{nm}\geq 1\); \(\alpha_{nm}=\frac{I_{max}}{\overline{I}_{nm}}>1\). Thus, Equation (5) represent the desired system of equations in order to obtain the actual intensity and density dispersion of its distribution probability.