## 3 Simulated Results and Error Analysis  
### Reconstructed Distribution Setup for Dynamic Temperature Field Simulation  
In hydrocarbon flames, water vapor, the main product of the combustion process, absorbs strongly in the near-infrared region. Therefore, water vapor was chosen as the target absorbing species in both simulations and experiments. Two absorption spectra, centered at \(v_{1}\) = 7185.6 cm\({}^{-1}\) and \(v_{2}\) = 7444.36 cm\({}^{-1}\), were used in this work because of their moderate line intensities and good temperature sensitivity. The specific parameters of the two chosen spectral lines can be combined with the HITRAN database [30]. The absorbances of the two spectral lines at different temperatures are given in Figure 2a,b, and the line intensities and intensity ratio of the two spectral lines are depicted in Figure 2c.  
Figure 1: Flowchart of MIARO algorithm.  
Figure 2: Absorbance and line intensity ratio of selected spectral lines: (**a**) 7185.60 cm\({}^{-1}\) and (**b**) 7444.36 cm\({}^{-1}\). (**c**) The line intensities and line intensity ratios of the two spectral lines.  
According to some classical combustion field parameter data, in an adducted combustion chamber, the temperature T is in the range of 600-1600 K, and the concentration \(X\) is between 0.02 and 0.05 mol/mol. In order to verify the validity of the proposed method, two regions with non-uniform temperature and H\({}_{2}\)O concentration distributions were chosen to simulate the complex combustion field distributions. Figure 3 shows the axisymmetric and non-axisymmetric distributions used for simulations. The axisymmetric distributions for both water vapor and temperature are Gaussian. The non-uniform regions were created using one symmetric and three overlaid asymmetric Gaussian distributions. The scanning area for reconstruction was 200 mm \(\times\) 200 mm, with a grid division of \(120\times 120\) and a grid size of 1.67 mm \(\times\) 1.67 mm. The specific field distributions are expressed using Equations (11) and (12):  
\[T=600+\sum_{k=1}^{K}1600\cdot\eta^{k}\cdot\exp\left[-\frac{\left(x-x_{c}^{k} \right)^{2}+\left(y-y_{c}^{k}\right)^{2}}{\sigma^{2}}\right] \tag{11}\]  
\[X=0.02+\sum_{k=1}^{K}0.05\cdot\eta^{k}\cdot\exp\left[-\frac{\left(x-x_{c}^{k} \right)^{2}+\left(y-y_{c}^{k}\right)^{2}}{\sigma^{2}}\right] \tag{12}\]  
where \(x\) and \(y\) denote the horizontal and vertical coordinates of the reconstructed region, respectively. \((x_{c}^{k},y_{c}^{k})\) is the center of the \(k\)-th Gaussian peak, \(\eta\) is the Gaussian distribution peak parameter, and \(\sigma\) is the standard deviation. The detailed distribution parameters used for the simulations are provided in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline  & \(\eta\) & \((x_{k}^{c},y_{k}^{c})\) **(cm)** & \(\sigma\) **(cm)** \\ \hline Axisymmetric simulation distribution & 0.4 & \((10,10)\) & 4 \\  & 0.4 & \((6,14)\) & \\ Non-axisymmetric simulation distribution & 0.35 & \((14,14)\) & 4 \\  & 0.2 & \((9,6)\) & \\ \hline \end{tabular}
\end{table}
Table 2: Axisymmetric and non-axisymmetric distribution settings.  
Figure 3: Simulated non-uniformly distributed regions of (**a**) axisymmetric temperature distribution, (**b**) axisymmetric H\({}_{2}\)O concentration distribution, (**c**) non-axisymmetric temperature distribution and (**d**) non-axisymmetric H\({}_{2}\)O concentration distribution.  
Often, in complex combustion flame parameter tests, the acquired signals are inevitably affected by mechanical vibrations and thermal radiation in the flame. Photodetectors are also subjected to calibration errors. In order to evaluate the performance of the system in noisy environments, 2%, 4%, 6% and 8% uniform noise levels were added to the LOS measurements \(A\) to study and analyze the stability of the MIARO algorithm in complex combustion field reconstruction applications [31; 32].