## 4 Experimental Setup and Condition  
### Preliminary Experimental Setup  
The experimental process in this study can be divided into two steps. The first step was to confirm the accuracy of the measured temperature using two partially overlapped H\({}_{2}\)O absorption signals. Here, the temperature set in the electric furnace by the T/C gauge was compared to the temperature measured by TDLAS. The temperatures (1073.15, 1173.15, 1273.15, 1373.15, 1473.15, and 1573.15 K) including the predicted flame temperature range, were set in the electric furnace. Figure 3 shows a schematic diagram of an overall preliminary experiment for measuring the temperature set in an electric furnace.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{\lambda(\mu m)}\) & \(\mathbf{\
u_{r}}\) (cm\({}^{-1}\)) &
\begin{tabular}{c} _S(T) at 1073.15 K,_ \\ **(cm/molecule)** \\ \end{tabular} & \(E^{\prime\prime}\),**(cm\({}^{-1}\))** & \(\mathbf{\Delta E^{\prime\prime}\),**(cm\({}^{-1}\))** \\ \hline
1.34923 & 7411.589 & 1.188 \(\times 10^{-22}\) & 3655.4833 & 3052.709 & 0.2126 \\
1.34927 & 7411.376 & 2.227 \(\times 10^{-22}\) & 602.7735 & 3052.709 & 0.2126 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Two selected H\({}_{2}\)O absorption lines for measuring the temperature and concentration from the HITRAN database.  
Figure 2: (**a**) Calculated temperature sensitivity of the linestrength ratio at the temperature range 550–1800 K, and (**b**) calculated linestrength ratios for the two selected absorption lines at 300–1800 K.  
As shown in the schematic diagram in Figure 3, the inside of the electric furnace was composed of ceramic board insulation to maintain a steady state (for internal temperature), and a quartz tube (170 cm) was inserted in the center of the electric furnace. In addition, calcium fluoride (CaF\({}_{2}\)) wedged windows were installed at both ends of the electric furnace because the reflected light generated between the light source and the window causes signal distortion (etalon noise). The temperature was set as the measured value from the R-type T/C installed in the insulation at the center of the electric furnace. Next, in the case of a laser system, the laser was largely divided into a transmitter and a receiver. For the transmitter part, the laser of the irradiated light source was a distributed feedback laser (butterfly 14 pin, NTT), which contained wavelengths of 1.34923 and 1.34927 \(\upmu\)m within a single scan range. A laser controller (ILX Lightwave, LDC-3908) was used to apply a constant current and temperature to the laser to emit the light source of the selected H\({}_{2}\)O absorption wavelength. Here, the current and temperature of the laser controller were determined using a wavemeter (HighFinesse laser and electronic system, WS-6) to accurately confirm the selected wavelength region. In addition, a waveform with a constant period and amplitude was applied to the laser controller using a function generator (Tektronix, AFG320) for wavelength tuning and signal analysis of the absorption signal. The receiver part was composed of a photodetector (Thorlabs, PDA20 CS-EC) to detect light sources and a data acquisition (DAQ) system for data acquisition. Then, the light source transmitted through the inside of the electric furnace was focused on the photodetector on the receiver. Here, photodetector 2 was used to receive the initial intensity also, light source was detected at the photodetector 2 through the solid etalon with a free spectral range (FSR, 2.00 GHz) to convert the time domain of the light absorption signal into the wavelength domain. Additionally, photodetector 1 was used to analyze the transmitted intensity, including the H\({}_{2}\)O absorption signal. The signals acquired by the DAQ system (500 kS/s) were analyzed using MATLAB.