Lionheart, William R.B. and Korsunsky, Alexander M.
(2021)
*Diffraction tomography inversion and the transverse ray transform.*
Proceedings of 16th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine.
(In Press)

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## Abstract

We show that a reciprocal space squared intensity map of a material can be recovered, for each characteristic length scale, from diffraction tomography data by a simple slice-by-slice reconstruction method. Moreover if the reciprocal space map can be represented by a finite sum of spherical harmonic components for each length scale then the coefficients of that expansion can be recovered from inverting the transverse ray transform (TRT), where the data are polynomial coefficients of the azimuthal diffraction pattern for each length scale.

Item Type: | Article |
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Uncontrolled Keywords: | diffraction tomography, SAXS, WAX, x-ray, transverse ray transform |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equations PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 60 CONDENSED MATTER - STRUCTURAL, MECHANICAL AND THERMAL PROPERTIES > 61 Structure of solids and liquids; crystallography PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 80 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY > 81 Materials science PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 80 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY > 87 Biological and medical physics |

Divisions: | Manchester Institute for the Mathematical Sciences |

Depositing User: | Prof WRB Lionheart |

Date Deposited: | 14 Jul 2021 07:32 |

Last Modified: | 14 Jul 2021 07:32 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2828 |

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