## Appendix A  
We calculate value \(T_{nm}\), using the probability density (Equation (3)). It should be noted that, strictly speaking, value \(I_{nk}\) takes discrete values when \(k=1,2,\ldots,M\). In practice, when taking measurements by emission spectrometers, a number of frames \(M\) of the order of several hundreds is used. In this case, the relative dispersion value \(\Sigma_{n}=\frac{\sigma_{n}}{I_{n}}\) does not usually exceed 30-40% (and, as a rule, is significantly lower). Therefore, we can proceed to the limit \(M\rightarrow\infty\) and then use a continuous value \(I_{n}\) rather than a discrete one \(I_{nk}\). Firstly, we calculate the normalization constant \(A_{n}\). From Correlation (3) we have:  
\[A_{n}\cdot\sqrt{2}\sigma_{n}\int\limits_{\frac{(I_{nk}-I_{n})}{\sqrt{2}\sigma_ {n}}}^{\infty}exp\left(-x^{2}\right)dx=1.\]  
Considering that \(I_{nN}\ll\overline{I}_{n}\) (in practice \(\frac{I_{nm}}{I_{nN}}\sim 10^{3}\)) and  
\[\frac{\overline{I}_{n}}{\sqrt{2}\sigma_{n}}\sim\frac{I_{max}}{\sqrt{2}\sigma_ {n}}>2, \tag{1}\]we obtain:  
\[A_{n}=\frac{1}{\sqrt{2\pi}\sigma_{n}}+O\Bigg{\{}exp\left[-\left(\frac{\overline{I}_ {n}}{\sqrt{2}\sigma_{n}}\right)^{2}\right]\Bigg{\}}, \tag{10}\]  
where \(\lim\limits_{x\to 0}\frac{\mathcal{O}(x)}{x}=const<\infty;const\
eq 0\). If there is an intensity limit, the probability density distribution of the measured values \(I_{nmk}\) varies. Indeed, if the actual intensity is \(I_{nk}\leq I_{max}\), the distribution \(I_{nmk}\) satisfies the correlation (3), and \(I_{nmk}=I_{nk}\), but if \(I_{nk}>I_{max}\), then \(I_{nmk}=I_{max}.\) Thus, the probability density of the measured intensity value \(P_{nm}(I_{nmk})\) is:  
\[P_{nm}(I_{nmk})=P_{n}(I_{nmk})\theta(I_{max}-I_{nmk})+A_{nm}\delta(I_{nmk}-I_{ max}), \tag{11}\]  
where \(\theta(x)=0\) if \(x<0\), \(\theta(x)=1\) when \(x>0\); \(\delta(x)\)--delta-Dirac function. According to the definition, if there is a maximum intensity \(I_{max}\), the measured average \(\overline{I}_{nm}\) is equal to:  
\[\overline{I}_{nm}=\int\limits_{I_{nN}}^{I_{max}}xP_{nm}(x)dx. \tag{12}\]  
If we take \(\int_{I_{nN}}^{I_{max}}P_{nm}(x)dx=1\), for the constant \(A_{nm}\) we obtain:  
\[A_{nm}=1-\int\limits_{I_{nN}}^{I_{max}}P_{n}(x)dx. \tag{13}\]  
If we take (11)-(13) and neglect the second summand in Formula (10), with the same accuracy as in (10), we have:  
\[\overline{I}_{nm}=\frac{\overline{I}_{n}}{2}\left[1+erf\left(-\frac{I_{max}- \overline{I}_{n}}{\sqrt{2}\sigma_{n}}\right)\right]-\frac{\sigma_{n}}{ \overline{I}_{n}\sqrt{2}\pi}exp\left[-\left(\frac{I_{max}-\overline{I}_{n}}{ \sqrt{2}\sigma_{n}}\right)^{2}\right]+\frac{I_{max}}{2}\left[1-erf\left(- \frac{I_{max}-\overline{I}_{n}}{\sqrt{2}\sigma_{n}}\right)\right]. \tag{14}\]  
Then we finally obtain the equation linking the measured and actual intensities:  
\[b_{nm}\left[1+erf\left(-\frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}} \right)\right]-\frac{\Sigma_{n}\alpha_{nm}}{\sqrt{2}\pi}exp\left[-\left(\frac {\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\right)^{2}\right]+\alpha_{nm} \left[1-erf\left(-\frac{\alpha_{nm}-b_{nm}}{\sqrt{2}\Sigma_{n}b_{nm}}\right) \right]=1, \tag{15}\]  
where \(\Sigma_{n}=\frac{\sigma_{n}}{\overline{I}_{n}}\) is the relative dispersion of the actual intensity; \(erf(x)=\frac{2}{\sqrt{\pi}}\int_{0}^{x}exp\left(-x^{2}\right)dx\); \(b_{nm}=\frac{\overline{I}_{n}}{I_{nm}};b_{nm}\geq 1\); \(\alpha_{nm}=\frac{I_{max}}{I_{nm}}>1\). It necessary to note that the dispersions of the measured and actual intensities \(\sigma_{nm},\sigma_{n}\), respectively, may vary significantly. This becomes clear from the following considerations. When intensity \(\overline{I}_{nm}\) approaches value \(I_{max}\), the selected intensities \(I_{nk}\) for the frames (having some index \(k\)) may exceed \(I_{max}\). For these frames, the measured values \(I_{nmk}\) will be equal to \(I_{max}\), i.e., their distribution does not satisfy Correlation (3) when the dispersion is \(\sigma_{n}\).