A New Method for Numerical Abel-Inversion

Pretzier, G.

doi:10.1515/zna-1991-0715

Cited by 124 publications

(65 citation statements)

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“…In an approach very different from those shown above, the unknown radial distribution f(r) is expanded in a series similar to a Fourier series [11]:…”

Section: Fourier Methodsmentioning

confidence: 99%

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Comparison of Different Methods of Abel Inversion Using Computer Simulated and Experimental Side-On Data

Pretzier

Jäger

Neger

et al. 1992

Zeitschrift Für Naturforschung A

113

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A recently devised new method for numerical Abel inversion is compared with four other commonly used methods. One of them, the convolution method, is employed in computer tomography for reconstructing asymmetrical objects. It is investigated whether this method can be adapted for the case of radial symmetry.As a first approach the comparison is performed by computer simulation. Special attention is given to the propagation of errors according to their origin. The result is a recipe for minimizing errors and for choosing the optimal method for reconstruction.The second step is a comparison of experimentally obtained radial profiles with functions resulting from Abel inversion of measured side-on data. Thus it is shown that the concept developed by computer simulation can be applied in practice.

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“…In an approach very different from those shown above, the unknown radial distribution f(r) is expanded in a series similar to a Fourier series [11]:…”

Section: Fourier Methodsmentioning

confidence: 99%

“…Very many numerical methods have been developed and used for performing these calculations e.g. [2][3][4][5][6][7][8][9][10][11]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Different Methods of Abel Inversion Using Computer Simulated and Experimental Side-On Data

Pretzier

Jäger

Neger

et al. 1992

Zeitschrift Für Naturforschung A

113

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show abstract

“…First, restricting analysis to events near the peak of the time-of-flight distribution is used to suppress large q z -values. Second, the fact that the scattering has rotational symmetry around the y-axis allows the use of an inverse Abel transform [29,30] to reconstruct the full 3D-scattering cross section from the x-y projection, based on the axial symmetry of the scattering. Both sets of results are compared to the predictions from simulations.…”

Section: Discussionmentioning

confidence: 99%

Novel method for state selective determination of electron-impact-excitation cross sections from 0° to 180°

et al. 2014

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We use an improved target recoil momentum spectroscopy setup to determine differential cross sections for excited metastable state production in atoms and molecules by electron impact and show its capabilities for an atomic helium target. A crossed beam setup with a supersonic helium jet and a pulsed electron beam at energies close to the excitation threshold of 19.82 eV was used. Measuring the recoil momentum vector of the target instead of the momentum of the scattered electron removes common restrictions to the accessible scattering angles while the microchannel plate detector ensures a high counting efficiency. Using a photoemission electron source we reach an energy resolution of about 200 meV at 1 μA peak current. Results are compared with simulations using theoretical convergent-close-coupling (CCC), R-matrix with pseudo-states (RMPS) and B-spline R-matrix (BSR) calculations and show good agreement.

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“…A mirror-tower rotated the (live-sized) image of the discharge by 90 , so that radial side-on measurements could be performed along the entrance slit of a monochromator. The data were Abel inverted with the inversion algorithm described in [6] to yield spatially resolved emission coefficients for argon line and continuum emission. The radial resolution was defined by the pixel-size of the CCD detector used ð% 30 mmÞ.…”

Section: Introductionmentioning

confidence: 99%

The role of ArIII in quantitative spectroscopy on hot argon plasmas

Kühn

Könemann

Kock

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

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We perform quantitative optical emission spectroscopy on the hot core of the cathode region of a free-burning arc in argon under atmospheric pressure. As the peak temperatures in the centre of the discharge exceed 22 000 K we are able to observe three spectra of argon (Ar I, Ar II and Ar III) and the continuum emission. We report on some inconsistencies concerning the evaluation of Ar III radiation in both line and continuum emission. These are caused by erroneous data in the literature and common misconceptions about the influence of Ar III on the plasma emission. We discuss the impact of this fact on published data. r

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A New Method for Numerical Abel-Inversion

Cited by 124 publications

References 0 publications

Comparison of Different Methods of Abel Inversion Using Computer Simulated and Experimental Side-On Data

Comparison of Different Methods of Abel Inversion Using Computer Simulated and Experimental Side-On Data

Novel method for state selective determination of electron-impact-excitation cross sections from 0° to 180°

The role of ArIII in quantitative spectroscopy on hot argon plasmas

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