## 4 Experiment Process and Analysis  
The TDLAS-based tomography system is shown in Figure 7a. Figure 7b shows a photograph of the optical test section and the configuration of the probe beams: 8 horizontally and 8 vertically, and with a spacing of 4 cm between neighboring probe beams. To be specific, the diode laser controller and function generator provide stable temperature and precise current controlling signals for a DFB laser. Thus, two vapor transitions \(v_{1}=7165.84\) cm\({}^{-1}\) and \(v_{2}=7164.91\) cm\({}^{-1}\) can be covered by the saw tooth scanning current. The output laser is split into 16 channels with a 1 \(\times\) 16 fiber coupler. Each separated output beam is firstly collimated by a collimator and then guided through the interest region. Finally, the laser beam comprising absorption information is sampled by two arrays that contain 16 equally spaced photodiodes. Each signal is transferred into the Personal Computer to reconstruct the 2D distributions of temperature and H\({}_{2}\)O mole fraction by the on-line manner modified ART. The sampling data of the photodetector output and the data processing are performed using a LabVIEW 2014 (National Instruments, Austin, TX, USA) program. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Wavenumber/cm\({}^{-1}\)** & **Line Strength** & **Lower State Energy/cm\({}^{-1}\)** & **Line Separation/cm\({}^{-1}\)** \\ \hline \(v_{1}\) & 7164.91 & 0.00385 & 1394 & \\ \hline \(v_{2}\) & 7165.82 & 0.14409 & 212 & 1.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The selected absorption transition spectral parameters. Figure 6: (a) The mean relative errors of temperature on the different number of beams. The \(e_{T}\_1\) flame, \(e_{T}\_2\) flames, \(e_{T}\_3\) flames, and \(e_{T}\_4\) flames are the temperature mean relative errors within one, two, three, and four flames. (b) The mean relative errors of H\({}_{2}\)O concentration on the different number of beams. The \(e_{C}\_1\) flame, \(e_{C}\_2\) flames, \(e_{C}\_3\) flames, and \(e_{C}\_4\) flames are the H\({}_{2}\)O concentration mean relative errors within one, two, three, and four flames. In order to online get the integrated absorbance \(A_{v}\), the output wavelength is measured by a wavelength meter 621B-IR (Bristol Instruments, Victor, NY, USA). The output wave number is inversely proportional to the laser drive current, and the variation is 0.032 cm\({}^{-1}\)/mA obtained by linear fitting. The relationship between the output wavenumber and the laser drive current at different temperatures is shown in Figure 8. In our tomography experiments, the laser temperature is set to 31 \({}^{\circ}\)C and the drive current from 63 mA to 118 mA aims to scan over the two vapor absorptions from 7164.64 cm\({}^{-1}\) to 7166.40 cm\({}^{-1}\). The wavenumber tuning speed of the DFB laser is 10 Hz, and the average of 10 measurements has been done to remove the white noise. A 16-channel synchronous A/D (Analog to Digital) acquisition card is used in this condition, so that the time to record 16 sets of photodetector signal is 1 s including all beam positions. In principle, a more accurate analysis of the integrated absorbance areas at atmospheric pressures can be achieved by fitting the experimental spectra with a Voigt functions, for instance, the standard Humlicek algorithm [30]. It is worth noting that the homogeneous temperature distribution is assumed along the paths of each beam. However, in these experiments, there is no observed improvement in the accuracy of the Voigt fitting, and it will be computationally more intensive than Lorentzian functions. Therefore, the Lorentzian line-shape function is used to fit all the absorption spectrums. Figure 9 shows the final direct absorption signals in flame (red solid line) and in room air (black dot line) for two transitions at \(v_{1}\) = 7164.91 cm\({}^{-1}\) and \(v_{2}\) = 7165.82 cm\({}^{-1}\), respectively. The two integrated absorbance for each channel can be calculated by fitting and the modified ART.