An accurate projection model for diffraction image formation and inversion using a polychromatic cone beam

• Published in: Journal of applied crystallography Vol. 48; no. 2; pp. 334 - 343
• Main Authors: van Aarle, Wim, Ludwig, Wolfgang, King, Andrew, Penumadu, Dayakar
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01-04-2015; Blackwell Publishing Ltd
• Subjects: Beams (radiation); Crystallography; Diffraction; diffraction contrast tomography; Engineering Sciences; Illumination; Inversions; laboratory sources; Materials; Projection; Projection model; Reconstruction; Three dimensional; Tomography; X-ray diffraction; Cone-beam projection; Iterative tomographic reconstruction; Laboratory source; Three-dimensional shape; Tomography; Three dimensional computer graphics; Forward-and-backward; Diffraction image formation; Projection models; X ray diffraction; Diffraction contrast; Computerized tomography
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576715000928

Recently, the concept of X‐ray diffraction contrast tomography (DCT) has been extended to the case of more widely available laboratory source CT systems. Using well known concepts from geometrical ray optics, an exact formulation is derived for the forward and backward projection geometry encountered under polychromatic cone beam illumination, and it is shown how this projection model can be efficiently implemented in practice. The new projection model is subsequently used for iterative tomographic reconstruction of the three‐dimensional shape of a grain from a set of experimentally observed cone beam projections and shows a clear improvement compared to the simplified projection model used previously.