Exact reconstruction condition for angle-limited computed tomography of chemiluminescence

Computed tomography of chemiluminescence (CTC) is an effective technique for three-dimensional (3D) combustion diagnostics. It reconstructs the 3D concentrations of intermediate species or 3D images of flame topology by multiple chemiluminescence projections captured from different perspectives. In the previous studies of CTC systems, it was assumed that projections from arbitrary perspectives are available. However, for some practical applications, the range of view angles and the number of projections might be restricted due to the optical access limitation, greatly affecting the reconstruction quality. In this paper, the exact reconstruction condition for angle-limited computed tomography of chemiluminescence was studied based on Mojette transform theories, and it was demonstrated by numerical simulations and experiments. The studies indicate that the object tested within limited angles can be well reconstructed when the number of grids, the number of projections, and the sampling rate of projections satisfy the exact reconstruction condition. By increasing the sampling rate of projections, high-quality tomographic reconstruction can be achieved by a few projections in a small angle range. Although this technique is discussed under combustion diagnostics, it can also be used and adapted for other tomography methods.