Narrow‐beam attenuation curve as a functional description of a low‐energy x‐ray beam

Delgado, V.; Ortiz, P.

doi:10.1002/xrs.1300200617

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…6 A new methodology which uses the measured attenuation curves as a functional description of the x-ray beam and overcomes the instability of reconstruction by avoiding the explicit calculation of the spectral distribution has been proposed. 7 The narrow beam attenuation curve is shown to be of itself a functional description of the x-ray beam. This functional description of the x-ray beam by means of its narrow beam attenuation curve in aluminum has been used for the determination of radiometric and dosimetric quantities.…”

Section: Introductionmentioning

confidence: 98%

Comparison between measured and predicted attenuation curves of x-ray beams

Delgado

1999

Med. Phys.

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Measurements of the attenuation curves of low energy x-ray beams are used in this work as a functional description of such beams. Measurements of the transmission curves through aluminum made with a low volume ionization chamber have been used to predict transmission curves through copper. The results are compared with the data of attenuation in copper measured with the above-mentioned ionization chamber, and also with calculations of attenuation in copper made from reference x-ray spectra and tabulated values of the mass attenuation coefficients of copper.

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Section: Introductionmentioning

confidence: 98%

Comparison between measured and predicted attenuation curves of x-ray beams

Delgado

1999

Med. Phys.

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“…In this way, the author has proposed and exploited a method that considers the attenuation curve in itself as a functional description of the x-ray beam. [31][32][33][34][35] This method is well suited to the calculation, in a stable way, of radiometric and dosimetric quantities, and, in general, of generalized moments of the spectral distribution, along the lines presented in Zahrt's book. 30 The aim of the present work is to check the feasibility of an inversion method for the Laplace transform, with the a priori conditions that the solution has to be positive and that its support has to be bounded to a fixed energy range.…”

Section: Introductionmentioning

confidence: 99%

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

Delgado

2007

Medical Physics

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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.

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The number of Kα photons produced on a set of thin targets as a functional description of the fluorescence exciting x‐ray beam

Martinez

Hidalgo

1993

X-Ray Spectrometry

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This work suggests a theoretical approach for the description of a primary x‐ray beam by means of the K fluorescence which it excites on a set of thin targets made of pure elements. Physical quantities, defined as weighted integrals over hv of the photon spectral distribution, are obtained directly as weighted integrals of the Kα yields over the variable Ez (the ionization energy of the K shell of the element with atomic number Z), without needing any explicit reconstruction of the spectral distribution. The set of Kα yields produced by an x‐ray beam as a function of Ez is a functional description of the exciting beam. Theoretically, such a description is suited to x‐ray fluorescence analysis.

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Narrow‐beam attenuation curve as a functional description of a low‐energy x‐ray beam

Cited by 6 publications

References 13 publications

Comparison between measured and predicted attenuation curves of x-ray beams

Comparison between measured and predicted attenuation curves of x-ray beams

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

The number of Kα photons produced on a set of thin targets as a functional description of the fluorescence exciting x‐ray beam

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