AUTHOR=Jin Ying , Situ Guohai TITLE=A Survey for 3D Flame Chemiluminescence Tomography: Theory, Algorithms, and Applications JOURNAL=Frontiers in Photonics VOLUME=Volume 3 - 2022 YEAR=2022 URL=https://www.frontiersin.org/journals/photonics/articles/10.3389/fphot.2022.845971 DOI=10.3389/fphot.2022.845971 ISSN=2673-6853 ABSTRACT=The combustion diagnostic plays essential role in energy engineering, transportation, and aerospace industries, which has great potential in combustion efficiency improvement and polluting emission control. The three-dimensional (3D) visualization of the combustion field and the measurement of key physical parameters such as temperature, species concentration and velocity during the combustion process are important topics in the field of combustion diagnostic. Benefiting by the noncontact and nonintrusive advantages of the optical detection method as well as the advantages of the 3D full-field measurement of the measured field by computational tomography, flame chemiluminescence tomography (FCT) has ability to realize nonintrusive and instantaneous 3D quantitative measurement and 3D full-field visualization of key physical parameters in combustion process, which has crucial research significance in combustion diagnostic. In this paper, we review the progress of FCT technique. Firstly, we provide an extensive review of practical applications of FCT in state-of-the-art combustion diagnostic and research. Then the basic concepts and mathematical theory of FCT are elaborated. Finally, we introduce the conventional reconstruction algorithms, and proceeding to more popular artificial intelligence-based algorithms.