Three-dimensional optical tomography techniques were developed to reconstruct three-dimensional objects using a set of two-dimensional projection images. Five basis functions, such as cubic B-spline, o-Moms, keys, and cosine functions and Gaussian basis functions, were used to calculate the weighting coefficients for a projection matrix. Two different forms of a multiplicative algebraic reconstruction technique were also used to solve inverse problems. The reconstruction algorithm was examined by using several phantoms, which included droplet behaviors and random distributions of particles in a volume. The three-dimensional volume comprised of particles was reconstructed from four projection angles, which were positioned at an offset angle of 45° between each other. Then, three-dimensional velocity fields were obtained from the reconstructed particle volume by three-dimensional cross correlation. The velocity field of the synthetic vortex flow was reconstructed to analyze the three-dimensional tomography algorithm.
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