# In Situ Measurement of Alkali Metals in an MSW Incinerator Using a Spontaneous Emission Spectrum
## 3 Measurement Principle  
The spectra of the spontaneous emissions of flames with a certain wavelength range can be obtained by an emission spectrometer. Generally, the raw output of the spectrometer will be in  
Figure 1: Schematic diagram of the experimental setup. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & **Moisture** & **Ash** & **Volatile** & **Fixed Carbon** & **Total Sulfur** & **Hydrogen** & **Calorific Value** \\ \hline
1 & 3.62 & 55.62 & 29.64 & 11.12 & 0.32 & 2.50 & 6.40 MJ/kg \\
2 & 3.59 & 54.63 & 29.72 & 12.06 & 0.41 & 2.60 & 6.63 MJ/kg \\
3 & 3.68 & 55.46 & 28.82 & 12.04 & 0.38 & 2.46 & 6.66 MJ/kg \\ \hline \end{tabular}
\end{table} 
Table 1: Proximate and ultimate analysis of the MSW (air dried basis, %). photon counts \(S(\lambda)\) of the radiation as a function of the wavelength \(\lambda\); these counts represent the relative spectral profile of the flame. To quantitatively analyze the spectra of the flame's spontaneous emission, it is necessary to calibrate the profile of the spectral radiation intensities \(I(\lambda)\) along the wavelength. As described in [14; 15; 17], a blackbody furnace was used to obtain the calibration coefficients \(k(\lambda)=I_{b}(\lambda)/S_{b}(\lambda)\). Figure 2 shows the profiles of \(k(\lambda)\) within the wavelength range from 500 nm to 900 nm at four temperatures: 1273, 1373, 1473, and 1573 K. It can be seen that profiles of the calibration coefficients at different blackbody temperatures were consistent with each other; thus, it can be concluded that the calibration coefficients remained independent of temperature. The flame's spectral radiation intensities can be obtained by \(I(\lambda)=S(\lambda)\cdot k(\lambda)\). Three cases of relative spectral profiles and their corresponding spectral radiation intensities of the MSW flame are shown in Figure 3. As shown in Figure 3b, the flame's spectral radiation intensities \(I_{e}\) were equal to the sum of the continuous spectral radiation intensities \(I_{c}\) produced by particulates in the flame plus the discontinuous spectral intensities \(I_{d}\), such as the intensities of the emission lines of the alkali metals:  
\[I_{e}=I_{c}+I_{d} \tag{1}\]  
where every term is wavelength dependent. Figure 3: Three typical of MSW flame spectra. (**a**) Relative spectral profiles \(S(\lambda)\); and (**b**) corresponding spectral radiation intensities \(I(\lambda)\). Figure 2: Calibration coefficients for the spectrometer at different blackbody temperatures. Some algorithms have been proposed to automatically separate the continuous and discontinuous spectral information from the measured flame emission spectra [18]. In this paper, continuous spectral radiation intensities in a wavelength range from 500 nm to 900 nm were extracted from the measured spectral radiation intensities of the MSW flame, and they were then fitted by a fourth-order polynomial. Figure 4 shows a comparison of the original continuous spectral radiation intensities (dotted line) extracted from Figure 3b and the corresponding fitting curves (solid line). In order to evaluate the fitting performance, the goodness-of-fit coefficient (GFC) [18] quality metrics between the fitting \({l_{c}}^{\prime}\) and the original \({l_{c}}\) spectral radiation intensities in the absence of discontinuous emission lines were calculated as:  
\[GFC=\frac{\left|\sum_{j}{{{I_{c}}\left({{\lambda_{j}}}\right){{I_{c}}^{\prime} \left({{\lambda_{j}}}\right)}}}\right|}{\sum_{j}\left[{{{\left[{{I_{c}}\left({{ \lambda_{j}}}\right)}\right]}^{2}}}\right]^{1/2}}\sum_{j}\left[{{{\left[{{I_{c} }^{\prime}\left({{\lambda_{j}}}\right)}\right]}^{2}}}\right]^{1/2}} \tag{2}\]  
Generally, an accurate fitting yields a GFC higher than 0.99. The results of the GFC for the three cases in Figure 4 were 0.9933, 0.9973, and 0.9988, respectively. Figure 4: Comparison of the original continuous spectral radiation intensities (dotted line) separated from Figure 3b and the corresponding fitting curves (solid line).