## 4 Experiment Process and Analysis
In the case of computing efficiency, it takes less than 1 s to reconstruct the images of temperature and H\({}_{2}\)O mole fraction. Therefore, the reconstructed 2D distributions of temperature and H\({}_{2}\)O mole fraction can be updated and displayed only every 1 s. If we need to analyze the change of combustion more quickly, we need to increase the scanning frequency (hundred or thousand times) to meet the requirements. Figure 7: The experimental system. (**a**) The scheme of the tunable diode laser absorption tomography (TDLAT) system with 8 \(\times\) 8 grids, (**b**) the photograph of the optical test section: left and upper are 16 collimators, right and under are 16 detectors. In the experiment, a premixed flame is generated by a circular flat flame burner (Holthuis & Associates, Sebastopol, CA, USA). Figure 10 shows the schematic of the burner. The gas fuel and air were mixed in a buffering zone and then passed through the honeycomb grids before flew in to the flame region. In order to build a flat flame, the burner was equipped with a mesh screen. The volumetric flow-rates of the gas fuel and air were accurately controlled by two float-type flowmeters (Shuanghuan, Changzhou, China). The diameter of burner is 12 cm, and the side length of the square measurement region is 32 cm. The height of the laser beams 8 \(\times\) 8 grids is adjusted 2 cm above the burner surface, as shown in Figure 11. That is to say, the 2D distributions of temperature and H\({}_{2}\)O mole fraction on the cross section of the flame at H = 2 cm are reconstructed per second in this experiment. In the combustion process, the air flow rate is set to 20 L/min and three different combustion states are operated by setting the gas fuel (CH\({}_{4}\)) flow rates to 1.0 L/min, 1.6 L/min, and 2.1 L/min, which resulted in the fuel-air equivalence ratio (\(\phi\)) approximate to 0.5, 0.75, and 1, respectively. When the flame is stabilized, the 2D distributions of temperature \(T^{cal}\) and H\({}_{2}\)O mole fraction \(C^{cal}\) are obtained. In order to smooth the reconstructed image, the cubic spline interpolating function is applied to the final image data process [31]. In the core of the flame, the value of \(T^{cal}\) and \(C^{cal}\) are larger than beside value in case of a higher equivalent ratio. As shown in Figure 12a, their temperature peaks are 955 K, 992 K, and 1127 K under three different kinds of equivalence ratios, respectively. Based on the analysis, the combustion temperature reaches the highest when the equivalence ratio of the premixed flow is exactly stoichiometric. At the same time, the core flame temperatures have been recorded by a B-type thermocouple, and the measurement results are 905 K, 970 K, and 1066 K, respectively. Therefore, the temperature relative errors between the peaks value of \(T^{cal}\) and the B-type thermocouple (Huakong, Beijing, China) are less than 5.6%. The same effect is observed in the case of the H\({}_{2}\)O mole fraction distribution \(C^{cal}\) as in the case of \(T^{cal}\), as seen in Figure 12b. The core flame theoretical value of H\({}_{2}\)O mole fraction \(C^{cal}\) is also consistent with the experimental results. Figure 8: The relationship of the output wave number and the laser drive current at different operation temperatures. Figure 9: The obtained direct absorption signals in room air (black dot line) and in the flame (red solid line) for two transitions at \(v_{1}\) = 7164.91 cm\({}^{-1}\) and \(v_{2}\) = 7165.82 cm\({}^{-1}\), respectively. -mode fraction is 0.190 when calculated with chemical equilibrium method for a fuel-air equivalence ratio of 1. The H\({}_{2}\)O mole fraction \(C^{cal}\) of the other two combustion states, whose equivalent ratio are 0.75 and 0.5, are 0.146 and 0.099 from theoretical estimates. The experimental measurements are 0.174, 0.135, and 0.092 in the core flame of three combustion states. Therefore, the relative errors between theoretical value and reconstruction \(C^{cal}\) are less than 8.6%.