Physics-guided stepwise tomography framework for high-precision reconstruction of temperature and concentration

This paper presents a physics-guided stepwise tomography framework that decouples the ill-posed tomography of temperature and concentration into three measurement- and prior-guided stages. By sequentially embedding two-line thermometry, projection matrix, and structural similarity, the framework first reconstructs a preliminary temperature field via a physics-data collaborative network, then employs it as a structural prior to guide iterative concentration inversion, and finally restores spatial details through a joint superresolution network, achieving high-fidelity reconstruction under a sparse optical layout with 40 optical paths and 2 absorption lines. Comprehensive validation in three cases supports improved robustness in the tested cases. In Case A, an in-distribution LES test dataset achieved dataset-averaged temperature/concentration mean relative errors ( $$E_T/E_X$$ ) of 1.35%/2.51% and temperature/concentration structural similarity indices ( $$SSIM_T/SSIM_X$$ ) of 0.991/0.989. In Case B, an out-of-distribution LES flame with modified inlet conditions showed section-dependent performance, with representative noise-free longitudinal sections giving $$E_T=4.54\%-7.67\%$$ , $$E_X=5.55\%-14.11\%$$ , $$SSIM_T=0.742-0.974$$ , and $$SSIM_X=0.763-0.965$$ . In Case C, an experimentally derived axisymmetric flame case constructed from Sandia Flame D measurements further showed that the main jet, reaction-zone, and diffusion-region structures can still be captured; representative cross-sections achieved $$E_T<5\%$$ , $$E_X<8\%$$ , $$SSIM_T>0.98$$ , and $$SSIM_X>0.96$$ . This strategy provides a promising route toward real-time combustion diagnostics in geometrically complex environments with restricted optical access.