## 3 Simulated Results and Error Analysis
### Discussion and Analysis of Reconstruction Simulation Results
#### 3.3.1 Axisymmetric Simulation Distribution  
Using the above-mentioned four algorithms, simulations were conducted to reconstruct axisymmetrically distributed temperature and vapor concentration fields. Figure 4 shows the reconstruction results. It can be seen that there are no notable differences between ART, Landweber and MAART. In fact, the Landweber algorithm presents the largest error at the edge. In contrast, the reconstruction error and the fluctuation at the edge achieved using the MIARO algorithm are significantly reduced, which clearly demonstrates the superiority of MIARO. Figure 4: Temperature and concentration field reconstruction results and errors for axisymmetric distribution with different algorithms (**a**,**b**) ART iterative algorithm, (**c**,**d**) Landweber iterative algorithm, (**e**,**f**) MAART iterative algorithm, (**g**,**h**) MIARO iterative algorithm. Further analyses were conducted on the reconstruction results at the symmetric peak centers over various cross-sections. The reconstruction results over a typical cross-section are presented in Figure 5. It can be found that the reconstruction errors at the peak with the MIARO algorithm for both temperature and concentration are much smaller. The maximum error of temperature with MIARO is within 5%, and that of concentration is below 4%. The fluctuations at the edges of the cross-section are much milder, which further demonstrates the advantages of MIARO. To evaluate the performance of the reconstruction algorithm in noisy environments, uniform noise signals of 2%, 4%, 6% and 8% were added to the LOS measurement A database for simulations. Figures 6 and 7 show the temperature and concentration reconstruction results with the different levels of added noise. As can be seen in Figure 6, the characteristic peaks can be clearly identified in the temperature reconstruction results with 4% noise for all algorithms. The contour lines in the figure reveal that with the MIARO algorithm, the high-temperature region is better presented, while for the other tested algorithms, the reconstructed fields become flattened around this region to some extent. At the 8% noise level, the reconstruction results with MIARO still show obvious characteristic peaks, and the edge fluctuation is smaller. From the concentration reconstruction results, similar conclusions can be drawn. The fluctuations in the reconstructed distribution are more severe with increased noise levels, especially at the edge of the targeted region. Using the ART, Landweber and MAART algorithms, artifacts at the edges under the influence of noise are much more significant. The MIARO algorithm can still be used to achieve better reconstruction results even with a lower signal-to-noise ratio, showing its robustness. In order to achieve the quantitative validation of the MIARO algorithm, two criteria, ARE and ARMSE, were used to compare the aforementioned four algorithms with added noise at different intensities. The results are shown in Figures 8 and 9, where 100 repeated measurements were taken for each algorithm at a given noise level. In Figures 8 and 9, it can be seen that with 2%, 4%, 6% and 8% random noise levels for all four algorithms, both the average error and standard deviation rise with the increase in noise. The overall trend of ARE is the same as that of ARMSE, although the ARMSE values are generally higher than ARE. However, the error proportional factor between ARE and ARMSE using different reconstruction algorithms in some cases is slightly different, which reflects the inconsistency when two criteria are used. Yet, the reconstruction errors are lower in general when the MIARO algorithm is used.