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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 27, Iss. 19 — Oct. 1, 1988
  • pp: 3962–3964

Reconstruction of discontinuous density profiles of cylindrically symmetric objects from single x-ray projections

Moshe Deutsch, Amos Notea, and Dvora Pal  »View Author Affiliations


Applied Optics, Vol. 27, Issue 19, pp. 3962-3964 (1988)
http://dx.doi.org/10.1364/AO.27.003962


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No abstract available.

History
Original Manuscript: March 4, 1988
Published: October 1, 1988

Citation
Moshe Deutsch, Amos Notea, and Dvora Pal, "Reconstruction of discontinuous density profiles of cylindrically symmetric objects from single x-ray projections," Appl. Opt. 27, 3962-3964 (1988)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-19-3962


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References

  1. E. T. Whitaker, G. N. Watson, A Course of Modern Analysis (Macmillan, New York, 1948).
  2. I. J. D. Craig, “The Inversion of Abel’s Integral Equation in Astrophysical Problems,” Astron. Astrophys. 79, 121 (1979).
  3. R. Gordon, R. Bender, G. Herman, “Algebraic Reconstruction Techniques for Three Dimensional Electron Microscopy and X-Ray Photography,” J. Theor. Biol. 29, 471 (1970); A. J. Jakeman, R. S. Anderssen, “Abel Type Integral Equations in Stereology. I: General Discussion,” J. Microsc. Oxford 105, 121 (1975). [CrossRef] [PubMed]
  4. M. Deutsch, I. Beniaminy, “Derivative-Free Inversion of Abel’s Integral Equation,” Appl. Phys. Lett. 41, 27 (1982). [CrossRef]
  5. A. Kuthy, “An Interferometer and Abel Inversion Procedure for the Measurement of the Electron Density Profile in a Cold Gas Blanket Experiment,” Nucl. Instrum. Methods 180, 7 (1981); A. M. Cormack, “Representation of a Function by its Line Integrals with Some Radiological Applications,” J. Appl. Phys. 34, 2722 (1963); G. H. Minerbo, E. M. Levy, “Inversion of Abel’s Integral Equation by Means of Orthogonal Polynomials,” SIAM J. Numer. Anal. 6, 598 (1969); E. W. Hanson, Phaih-Lanlaw, “Recursive Methods for Computing the Abel Transform and its Inverse,” J. Opt. Soc. Am. A 2, 510 (1985); R. S. Anderssen, “Stable Procedures for the Inversion of Abel’s Equation,” J. Inst. Math. Appl. 17, 329 (1976); C. J. Cremers, R. C. Birke-back, “Application of the Abel Integral Equation to Spectrographs Data,” Appl. Opt. 5, 1057 (1966). [CrossRef] [PubMed]
  6. M. Deutsch, “Abel Inversion with a Simple Analytic Representation for Experimental Data,” Appl. Phys. Lett. 42, 237 (1983). [CrossRef]
  7. M. Deutsch, I. Beniaminy, “Inversion of Abel’s Integral Equation for Experimental Data,” J. Appl. Phys. 54, 137 (1983). [CrossRef]
  8. A. Notea, “Resolving Power of Dynamic Radiation Gauges,” Nucl. Tech. 63, 121 (1983); A. Notea, “Evaluating Radiographic Systems Using the Resolving Power Function,” NDT Int. 16, 263 (1983); Y. Bushlin, D. Ingman, A. Notea, “Moments Analysis Method for the Determination of Dimensions from Radiographs,” Nucl. Tech. 74, 218 (1986). [CrossRef]
  9. A. Notea, D. Pal, M. Deutsch, “Density Distribution in Cylindrically Symmetric Objects from a Single Radiographic Image,” in Proceedings, Fourth European Conference on Non-Destructive Testing, London, Sept.1987 (in print).
  10. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1978).
  11. T. H. Newton, D. G. Potts, “Radiology of the Skull and Brain,” in Technical Aspects of Computed Tomography, Vol. 5 (Mosby, London, 1981).

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