Formation of images from projections: Radon and Abel transforms*
- 1 September 1974
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America
- Vol. 64 (9) , 1215-1218
- https://doi.org/10.1364/josa.64.001215
Abstract
The problem of determining the structure of an object from knowledge of its projections along straight lines arises in a variety of optical contexts. The general solution to this problem is given by the inverse Radon transform of the projections. A superposition principle is developed to show the relation between this general inversion and the more familiar inverse Abel transform that is associated with radially symmetric objects.Keywords
This publication has 9 references indexed in Scilit:
- Reconstruction of Three-Dimensional Refractive Index Fields from Multidirectional Interferometric DataApplied Optics, 1973
- Reconstruction of densities from their projections, with applications in radiological physicsPhysics in Medicine & Biology, 1973
- The reconstruction of three-dimensional structure from projections and its application to electron microscopy II. Direct methodsProceedings of the Royal Society of London. B. Biological Sciences, 1972
- Calculation of three-dimensional refractive-index field using phase integralsOptics Communications, 1972
- The interpretation of X-ray shadowgraphsPhysics Letters A, 1970
- The interpretation of optical projectionsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1970
- Quantitative Interpretation of Three-Dimensional Weakly Refractive Phase Objects Using Holographic InterferometryJournal of the Optical Society of America, 1969
- Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spacesInformation and Control, 1962
- Strip Integration in Radio AstronomyAustralian Journal of Physics, 1956