Principles of computerized tomographic imaging
Principles of computerized tomographic imaging
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In recent publications we have presented method for the computed tomography reconstruction from the X-ray refraction contrast. It was shown that the method has many advantages over conventional absorption contrast-based tomography. However, those papers were mainly dedicated to the experimental realization of the technique and the results of the reconstruction while the details of the mathematical algorithm were left out of consideration. Although the mathematical formalism used for the algorithm is very similar to the well developed Filtered Back Projection method, it has important peculiarities which do not allow the adoption of the currently present algorithms. Thus, the material of this paper concentrates on the originally developed mathematical algorithm of the CT-reconstruction from the refraction contrast (i.e. the information on the x-ray refraction after penetration through the object). It also includes the gradient-to-field transformation method applicable in the context of the algorithm.