The reconstruction of a three-dimensional flame structure mainly includes multi-view measurement and unidirectional optical path measurement methods. As for the former, the number of cameras needs to be increased for the spatial resolution improvement of test results. However, it is not suitable for reconstructing a three-dimensional flame field in a burner due to the constraint of limited test space, which refers to the light occlusion by the burner wall. On the contrary, the latter is immune to testable space limitations and has remarkable advantages in diagnosing a three-dimensional flame structure by means of tomography based on light field imaging. Traditional light field imaging is achieved with the aid of a liquid zoom lens or a micro-lens array, which can reconstruct the three-dimensional field by refocusing different objects from one projection. The focused surface of the liquid lens can be changed easily by adjusting the voltage, which is helpful to get refocused images. But the temporal resolution of this operation is so insufficient that it is not applicable to highly dynamic flames. The position and direction information of a three-dimensional flame field can also be reconstructed by acquiring refocused images with a micro-lens array. However, the existing light field imaging method based on a micro-lens array processes images by data calculation, which leads to the compatible problem of temporal and spatial resolution. Therefore, it is not applicable to a highly dynamic flame environment with temporal-spatial heterogeneity. It is necessary to establish a three-dimensional reconstruction method with high temporal and spatial resolution for dynamic flame.

In this paper, the multi-camera common-optical-path imaging method is proposed to characterize the temporal and spatial resolution characteristics of flame by tomography. In the optical imaging path structure, cascaded optical splitters are used to allocate light energy to different detection channels, and cameras are placed at each detection channel for light collection. By a synchronous controller, cameras are driven to focus on different sections of the transient flame at the same time. On the basis of Fourier optics theory, the defocused mapping relationship between a spatial object and an image of the optical tomography system is established by convolution, and the spontaneous emission characteristics at different sections of flame are numerically analyzed by the deconvolution algorithm. When light radiation passes from the interior to the surface of flame, light attenuation properties corresponding to the divided flame sections are different. The attenuated light intensity needs to be further compensated for each section. Here, the attenuation is calculated by comparing the recorded image of a light spot passing through flame with that when only a light spot is present. According to the distance between each focused section and the flame edge along the main optical axis of the imaging system, different energy compensation on tomographic images is carried out to obtain the real radiation characteristics of each section.

The results show that the focused images of different flame sections can be captured by different cameras simultaneously and independently (Fig. 9), which improves the temporal resolution greatly and realizes the high spatial resolution test of dynamic flame at the same time. The performance of the tomographic imaging system is verified by reconstructing the three-dimensional combustion flame of carbon oxides and propane-butane mixed combustion flame. The spatial evolution characteristics of flame are analyzed by observing different sections of flame at the same time (Fig. 12 and Fig. 15), and the temporal evolution characteristics of flame can be analyzed by comparing the changes of gray values at different time in the same position (Fig. 13 and Fig. 16). The reconstructed flame structure is unevenly distributed in space, and the section near the flame center is brighter than that at the edge. The flame varies quickly in a short time, which is consistent with the temporal and spatial resolution characteristics of flame. In addition, combustion is also related to the contact area between flame and air as well as the spatial distribution of fuel. For the combustion of carbon oxides, the flame is brighter where the fuel gathers (Fig. 11), and the propane-butane mixed combustion flame is brighter where the air contact area is larger (Fig. 14). This difference is because fuels used in these two experiments are solid and gas, respectively. The flame brightness distribution of solid fuel combustion depends on the spatial distribution of the fuel, while that of gas fuel combustion is related to the contact area with air.

This paper proposes a method of multi-camera common-optical-path flame tomography using cascaded optical splitters based on unidirectional optical path projection. It is verified that the proposed method can reconstruct a three-dimensional flame structure effectively by the tomography of the combustion flame of carbon oxides and propane-butane mixed combustion flame. Compared with the light field tomography method based on a micro-lens array, the method in this paper has improved compatibility between time and space detection, which can be used to diagnose the temporal and spatial evolution characteristics of dynamic combustion flame structure. The proposed system can be potentially applied to a more highly dynamic and unevenly distributed combustion field environment by improving camera configuration.