Results and Discussions According to the results, the uniformity coefficient of the sensitivity matrix is directly related to the reconstruction performance. When the uniformity coefficient is low, the reconstruction error is small. When the uniformity coefficient is large, the reconstruction error is large. Hence, the uniformity coefficient is considered as a predictor of the reconstruction performance (Fig. 3). In the iteration process of GA, it can be found that the uniformity coefficient decreases continuously with the process of iteration. At the beginning, the coefficient declines significantly. While between the 200th and 808th generations, the uniformity coefficient decreases slowly from 0.296 to 0.288 (Fig. 5). The uniformity coefficient reaches minimum of 0.288 at the 808th iteration. The optimized configuration has much low uniformity coefficient than the random configuration (0.437) and regular configuration (0.305). Reconstruction results with five specific distributions indicate the superiority of the optimized configuration over the other two configurations (Fig. 8). For the first three distributions with circular phantoms, the errors of the random configuration are 15.54%, 22.36% and 16.09%, which are the largest among the three configurations. The regular configuration has errors of 14.66%, 20.80% and 16.68%. The optimized one has the lowest errors, which are 11.57%, 18.39% and 13.07%. For the fourth distribution with a 'cross' phantom, the reconstruction errors of the three configurations are 19.59%, 22.83% 18.60%, respectively. For the fifth distribution, the errors have been increased intensively due to the complex phantom, which are 33.74%, 27.68% and 25.15%. For all the five distributions, the optimized configuration has much lower error than the random and regular ones. In the research work, we also introduce local error to evaluate the reconstruction performance. The local error of the random configuration fluctuates obviously among the whole region, and the maximum local error is up to 84%. The local error of the regular configuration is neglectable outside the boundary of the phantom to be reconstructed. However, within this range, its local error maintains high level with maximum of 81%. The local error of the optimized configuration is nearly zero outside the range, and inside the range, the maximum of the local error is only 50% (Fig. 9).

Optical tomography aims to reconstruct the cross-sectional distribution from numerous projections along various orientations. Due to its 'hard-field', high spatial and temporal resolution, this technique has been widely used in multi-phase flow monitoring, temperature and species concentration measurement and functional tissue imaging. Optical tomography adopts light emitters to emit laser beams, which are attenuated by the medium. The outgoing light is then detected by photosensitive receivers. Reconstruction algorithms are used to reconstruct the absorption distribution of the medium. Intrusively, increasing light beams and receivers will improve the reconstruction performance. However, this approach is not appropriate when the light access or installation space is limited. Meanwhile, the reported tomography sensors usually have regular arrangement, which forms a non-uniform sensitivity matrix and the region of interest (ROI) is detected unevenly. In this work, we propose an optimization method based on uniformity coefficient and genetic algorithm (GA). We hope our method can provide an optimized sensor configuration that has a uniform sensitivity matrix and improved reconstruction performance.

Sensitivity matrix relates the practical distribution to the numerous projections, which is important for image reconstruction. It is well recognized that uniform sensitivity matrix promises improved reconstruction performance. While the reconstructed images have large error when the matrix has low uniformity. In this work, uniformity coefficient is introduced to represent the uniformity of the matrix. Meanwhile, we assume that the uniformity coefficient is directly related to the quality of image reconstruction, namely, lower uniformity coefficient leads to improved reconstruction performance, and larger value leads to deteriorated performance. The optimization procedure mainly includes the following steps. Firstly, reconstruction with 60 configurations and 10 distributions are implemented to verify the effectiveness of the uniformity coefficient as a predictor. The number of the light emitters and receivers are both 25. Secondly, we adopt GA to optimize the arrangement of the emitters and receivers. The fitness function is set as the uniformity coefficient. Finally, we analyze the optimized configuration and compare its reconstruction performance with the random and regular configurations.

This paper presents an optimization method for optical tomography sensor configuration based on GA. The following conclusions can be concluded. Firstly, simulation experiments of randomly generated configurations and distributions verify that the uniformity coefficient is an effective predictor for reconstruction performance. Configuration with low uniformity coefficient has uniform sensitivity matrix and beam arrangement, and improved reconstruction performance. On the contrary, configuration with large uniformity coefficient has uneven beam arrangement, and its reconstruction performance is deteriorated. Secondly, GA is used to implement the optimization, and we take the uniformity coefficient as the fitness function. The optimized configuration provided by GA has a uniformity coefficient of 0.288. Different distributions have been considered and the reconstruction results indicate the superiority of the optimized configuration over the random and regular configurations. The optimization method has been proven to be effective. Thirdly, reconstruction results display that the practical distribution has significant influence on the performance of the configurations. Since the uniformity coefficient is only related to the configuration, the optimization results are independent to the practical distribution and this optimization method can be used in the applications where the priori information of the distributions is difficult to obtain.