Development of a beam optimization method for absorption-based tomography

Absorption tomography is an imaging technique that has been used simultaneously to image multiple scalar parameters, such as temperature and species concentration for combustion diagnostics. Practical combustors, such as internal combustion engines and gas turbine engines, only allow limited optical access, and typically a few (ca. 20-40) beams are available to probe the domain of interest. With such limited spatial sampling, it is non-trivial to optimize beam arrangement for a faithful reconstruction. Previous efforts on beam optimization rely on either heuristic/empirical methods lacking rigorous mathematical derivation or were derived by assuming certain prior information in the tomographic inversion. This paper aims to develop an approach that is expected to be especially useful when prior information is not easily available or intended to be included in the inversion processes. We demonstrate that the orthogonality between rows of the weight matrix directly correlates with reconstruction fidelity and can be used as an effective predictor for beam optimization. A systematic comparison between our method and the existing ones in the literature suggests the validity of our method. We expect this method to be valuable for not only the absorption tomography but also other tomographic modalities.