[abel reconstruction of piecewise constant radial density profiles from x-ray radiographs

Moshe Deutsch, Amos Notea, Dvora Pal

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We present a method for reconstructing the radial density profile of a cylindrically symmetric object from a single x-ray projection, when the profile consists of a number of different constant sections. A forward Abel transform based algorithm is employed whereby the profile is recovered recursively, onion peelinglike, starting from the outside diameter of the object and moving in. Distortions originating in the Gibbs phenomenon, unavoidable in most available Abel inversion methods, are completely eliminated. The method is simple enough to be carried out on a handheld calculator or a spreadsheet program on a personal computer, and no elaborate computer fits or application programming are required. The method is demonstrated by inverting a simulated three-section noisy set of data and is shown to yield results of a quality equal to that of a recent powerful Abel inversion method, based on full nonlinear least-squares computer fits.

Original languageEnglish
Pages (from-to)3183-3186
Number of pages4
JournalApplied Optics
Issue number15
StatePublished - Aug 1989


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