In the last few decades. optical diagnostics tools have become the most commonly used techniques for measuring concentration distribution of gas species The facts that they have high spatial and temporal resolution, do not perturb the flow, and can work in harsh environments (such as combustion), make them superior to traditional physical probe tools. From among these optical diagnostics techniques laser absorption tomography is one of the most promising ones .

As discussed in the paper by Twynstra and Daun, laser absorption tomography reconstructs the flow field distribution using laser line-of-sight attenuation measurements. These measurements are taken using several coplanar lasers having wavelengths corresponding to an absorption line of the target species.

The authors pointed out as their inspiration experimental and numerical results showing that a good beam arrangement is required for better reconstruction results; the high cost and complexity of the required tools make their efficient use necessary. They proposed an algorithm based on the properties of the resolution matrix in order to optimize beam arrangements.

The fact that the number of beams used to solve the concentration profile matrix is much smaller than the desired number of spatially resolved data points demands a limited-data tomography-like approach.
The chosen approach consists therefore in modelling the true concentration profile as a sum of a least square solution and a non-trivial vector belonging to the null space.

The paper discusses how the arrangement of the laser/detector pairs affects the reconstruction accuracy by showing a Gaussian phantom and its reconstruction. The reconstruction error is defined as a sum of regularized and perturbation errors. The authors show that the perturbation error is negligible and that the arrangement of laser beams with minimized regularized error improves significantly the reconstruction accuracy. The regularized error is defined as a function of the augmented kernel matrix. The reconstruction error is estimated by a function called a candidate fitness function. A genetic algorithm is used to minimize the fitness function in order to optimize the beam arrangement. According to the paper, the optimized beam arrangements based on this method shows superior reconstruction accuracy to other arrangements presented in previous literature. The paper shows that beam misalignment has an insignificant effect on the reconstruction accuracy for the optimized array of beams. The correlation between the number of beams and reconstruction accuracy is also discussed.

The authors mention as a future task the inclusion of restrictions deriving from the geometry of particular problems by expressing them as constraints on the minimization problem. It will also be interesting to see how arranging beams using the proposed optimization algorithm outperforms the other arrangements in practice.

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