Exact reconstruction condition for angle-limited computed tomography of chemiluminescence

Camera spatial arrangement influence on reconstruction accuracy of chemiluminescence tomography

Computed tomography of chemiluminescence (CTC) has been demonstrated to be a powerful tool for three-dimensional (3D) combustion visualization and measurement, in which the number of cameras and their spatial arrangement significantly impact the tomographic reconstruction quality. In this work, the relationship of the camera spatial arrangement and tomographic reconstruction accuracy is theoretically established based on two-dimensional (2D) and 3D Mojette transforms and their accurate reconstruction conditions. Numerical simulations and experiments were conducted to demonstrate the theories. The results suggest that the exact reconstruction conditions of the Mojette transforms can be used to determine the minimum number of cameras required for tomography reconstruction, and its achieved reliability can be used as an indicator to predict the reconstruction quality. Besides, the 2D coplanar semicircular configuration exhibits a better performance than that of the 3D non-coplanar arrangement. When the 3D non-coplanar arrangement is adopted, the cameras should be widely distributed in the hemispherical space. The related research provides a theoretical basis for the establishment of the CTC system and other tomography modalities.

Computed tomography in resolving flame topology with internal optical blockage involved

This work reports the modification and optimization of a computed tomography (CT) algorithm to become capable of resolving an optical field with internal optical blockage (IOB) present. The IOB-practically, the opaque mechanical parts installed inside the measurement domain-prevents a portion of emitted light from transmitting to optical sensors. Such blockage disrupts the line-of-sight intensity integration on recorded projections and eventually leads to incorrect reconstructions. In the modified algorithm developed in this work, the positions of the obstacle are measured a priori, and then the discretized optical fields (i.e., voxels) are classified as those that participate in the CT process (named effective voxels) and those that are expelled, based on the relative positions of the imaging sensors, IOB, and light signal distribution. Finally, the effective voxels can be iteratively reconstructed by combining their projections on sensors that provide direct observation. Moreover, the impact of IOB on reconstruction accuracy is discussed under different sensor arrangements to provide hands-on guidance on sensor orientation selection in practical CT problems. The modified algorithm and sensor arrangement strategy are both numerically and experimentally validated by simulated phantoms and a two-branch premixed laminar flame in this work.

Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime

For the inverse problem in physical models, one measures the solution and infers the model parameters using information from the collected data. Oftentimes, these data are inadequate and render the inverse problem ill-posed. We study the ill-posedness in the context of optical imaging, which is a medical imaging technique that uses light to probe (bio-)tissue structure. Depending on the intensity of the light, the forward problem can be described by different types of equations. High-energy light scatters very little, and one uses the radiative transfer equation (RTE) as the model; low-energy light scatters frequently, so the diffusion equation (DE) suffices to be a good approximation. A multiscale approximation links the hyperbolic-type RTE with the parabolic-type DE. The inverse problems for the two equations have a multiscale passage as well, so one expects that as the energy of the photons diminishes, the inverse problem changes from well- to ill-posed. We study this stability deterioration using the Bayesian inference. In particular, we use the Kullback–Leibler divergence between the prior distribution and the posterior distribution based on the RTE to prove that the information gain from the measurement vanishes as the energy of the photons decreases, so that the inverse problem is ill-posed in the diffusive regime. In the linearized setting, we also show that the mean square error of the posterior distribution increases as we approach the diffusive regime.