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Title: Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation

Abstract

The determination of the spectral distribution of an x-ray beam from attenuation measurements in a narrow beam has aroused great interest since it was first proposed by Silberstein in 1932. Since then, it has become clear that this is an ill-conditioned problem. Then, due to the intrinsic difficulties of the problem, care has been taken to improve the mathematical and numerical inversion techniques. Alternative ways to circumvent the explicit inversion by using the attenuation curve itself to calculate directly generalized moments of the solution have also been found. In this work, the explicit reconstruction of the spectral distribution is carried out by an expectation-maximization method that satisfies the a priori condition of positiveness of the solution and allows us to impose the boundness of its support easily, conditions which are known to be fulfilled by physically acceptable solutions. The simulations made and the experimental validation of the proposed method allow us to prove its scope and limitations.

Authors:
 [1]
  1. ICTP Visiting Scholar at FaMAF, Laboratorio de Espectroscopia de Radiaciones, Universidad Nacional de Cordoba, Ciudad Universitaria (5010) Cordoba (Argentina)
Publication Date:
OSTI Identifier:
20951113
Resource Type:
Journal Article
Resource Relation:
Journal Name: Medical Physics; Journal Volume: 34; Journal Issue: 3; Other Information: DOI: 10.1118/1.2436971; (c) 2007 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ATTENUATION; BEAMS; DISTRIBUTION; VALIDATION; X RADIATION; X-RAY SPECTRA

Citation Formats

Delgado, Victor. Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation. United States: N. p., 2007. Web. doi:10.1118/1.2436971.
Delgado, Victor. Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation. United States. doi:10.1118/1.2436971.
Delgado, Victor. Thu . "Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation". United States. doi:10.1118/1.2436971.
@article{osti_20951113,
title = {Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation},
author = {Delgado, Victor},
abstractNote = {The determination of the spectral distribution of an x-ray beam from attenuation measurements in a narrow beam has aroused great interest since it was first proposed by Silberstein in 1932. Since then, it has become clear that this is an ill-conditioned problem. Then, due to the intrinsic difficulties of the problem, care has been taken to improve the mathematical and numerical inversion techniques. Alternative ways to circumvent the explicit inversion by using the attenuation curve itself to calculate directly generalized moments of the solution have also been found. In this work, the explicit reconstruction of the spectral distribution is carried out by an expectation-maximization method that satisfies the a priori condition of positiveness of the solution and allows us to impose the boundness of its support easily, conditions which are known to be fulfilled by physically acceptable solutions. The simulations made and the experimental validation of the proposed method allow us to prove its scope and limitations.},
doi = {10.1118/1.2436971},
journal = {Medical Physics},
number = 3,
volume = 34,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • The determination of the spectral distribution of an x-ray beam from attenuation measurements in a narrow beam is an ill-conditioned problem that has aroused great interest since it was first proposed by Silberstein in 1932. In this work, the explicit reconstruction of the spectral distribution directly from the attenuation curve, without differentiating it, is carried out by a maximum likelihood method that allows one to impose a priori physical features of an x-ray spectral distribution, such as the positiveness of the solution, the boundness of its support, and the position and shape of the spikes and edges associated with themore » characteristic radiation. The numerical simulations made and the experimental validation of the proposed method have shown that it is possible to reconstruct x-ray spectra that, having a realistic shape, accurately fit the attenuation curve and predict the energy fluence. Nevertheless, the reconstruction of spectra including the K x rays of W is less accurate than the reconstruction of spectra including L x rays of W or K x rays of Mo, even when a priori information about the position and shape of the spikes and edges associated with the characteristic radiation is used.« less
  • An analytical method to compute x-ray spectra from attenuation data utilizing the Laplace transformation has been extended to include characteristic radiation. It is based on an a priori technique of determining the ratio of characteristic radiation exposure to the total radiation exposure in diagnostic spectra. The technique is shown to produce characteristic intensities in good agreement with experimentally determined values.
  • A mixed-valence uranium phosphate, U(UO[sub 2])(PO[sub 4])[sub 2], has been synthesized through dry and wet chemical processes. The crystal structure has been solved ab initio from conventional monochromatic X-ray powder diffraction. The unit cell is triclinic (space group P1, Z = 2) with the cell dimensions a = 8.8212(4) [angstrom], b - 9.2173(5) [angstrom], c = 4772(3) [angstrom], [alpha] = 102.622(4)[degrees], [beta] = 97.748(4)[degrees], [gamma] = 102.459(5)[degrees], and V = 416.55(3) [angstrom][sup 3]. Initial positional parameters for two independent uranium atoms were obtained by solution of the Patterson map resulting from 509 integrated intensities. Phosphorus and oxygen atoms were localizedmore » by Fourier methods. The final indicators from the Rietveld refinement was R[sub F] = 0.039 and R[sub wp] = 0.144. The overall quality of the structure was improved from the refinement of atomic coordinates from neutron diffraction data (R[sub F] = 0.029, R[sub wp] = 0.057). 42 refs., 7 figs., 5 tabs.« less
  • The thickness of the zone from which truly secondary electrons are emitted (the escape depth) and the yield of the electrons for NaCl, KCl, and KBr, were determined. The determination is based on an analysis of the energy spectrum of x-ray photoemission. (auth)