Mathematical Details of the Refraction-based Computed Tomography

A. Maksimenko, T. Yuasa, and M. Ando (Japan)


computed tomography, refraction contrast, X-ray, recon struction algorithm


In recent publications we have presented method for the computed tomography reconstruction from the X-ray re fraction contrast. It was shown that the method has many advantages over conventional absorption contrast-based to mography. However, those papers were mainly dedicated to the experimental realization of the technique and the re sults of the reconstruction while the details of the math ematical algorithm were left out of consideration. Al though the mathematical formalism used for the algorithm is very similar to the well developed Filtered Back Projec tion method, it has important peculiarities which do not al low the adoption of the currently present algorithms. Thus, the material of this paper concentrates on the originally de veloped 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 appli cable in the context of the algorithm.

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