Tomographic absorption spectroscopy (TAS) typically employs multiple projections to reconstruct the spatial distribution of temperature and species concentration, making it a promising method for combustion diagnostics. However, the geometric arrangement of the laser beams significantly affects its accuracy, especially under limited beam conditions. In this work, we propose a beam arrangement optimization method to maximize the utilization efficiency of limited beams, thereby improving reconstruction accuracy in a simpler and more intuitive manner. We designed a cost function that combines the beam number matrix (BNM) and the total weight matrix (TWM). This approach ensures that the maximum number of rays passes through each grid while also maximizing the optical path length in the regions covered by the beam distribution. The optimization is performed using a simulated annealing algorithm to obtain the optimal beam arrangement. For a TAS sensor comprising 12 laser beams, numerical simulations demonstrate that the BNM-TWM optimized beam arrangement achieves lower reconstruction errors across various synthetic temperature fields when compared to traditional orthogonal beam arrangements and those optimized for orthogonality (OD). This improvement is particularly significant when the performance of the orthogonal and OD-optimized arrangements is suboptimal. Finally, we demonstrate the application of the BNM-TWM optimized beam arrangement for reconstructing temperature distributions of asymmetric butane flames, where parallel beam distributions were ineffective. The results effectively pinpoint the location of the flame, showing a temperature difference of less than 3% compared to thermocouple measurements for the center of the flame. These findings indicate that the developed beam arrangement optimization method has the potential to enhance the accuracy of TAS reconstruction under limited beam conditions and could be extended to other tomographic imaging systems.
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