Monte-Carlo error analysis in x-ray spectral deconvolution

Shirk, D.G.; Hoffman, N. M.

doi:10.1063/1.1138180

Cited by 16 publications

(9 citation statements)

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“…The signals for a particular time and their corresponding uncertainties were input into the code SHAZAM (Shirk and Hoffman, 1985). New currents are calculated for the adjusted spectrum and the process continues.…”

Section: Discussionmentioning

confidence: 99%

An experimental measurement of metal multilayer x-ray reflectivity degradation due to intense x-ray flux

Hockaday¹

1987

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Section: Discussionmentioning

confidence: 99%

An experimental measurement of metal multilayer x-ray reflectivity degradation due to intense x-ray flux

Hockaday¹

1987

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“…An alternative method (e.g., [61]) that is numerically more intensive, involves calculating a family of profiles that would be consistent with the measured data. The ability to find several profiles that work is a consequence of the underdetermined nature of the problem.…”

Section: 3-forward Optimization Methods For Inferring the Spatial mentioning

confidence: 99%

“…The technique of Monte Carlo error analysis is described by Shirk and Hoffman [61] for x-ray spectral deconvolution applications, although it is flexible enough for inverting any scalar quantity. The method for performing the inversion was described in the previous section (2.3.2), where a family of possible profiles are calculated.…”

Section: Techniques Used To Study Error Propagation Imentioning

confidence: 99%

Far-infrared polarimetry/interferometry for poloidal magnetic field measurement on ZT-40M

Erickson¹,

Forman²,

Jahoda³

1986

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The measurement of internal magnetic field profiles may be a very important step in the understanding of magnetic confinement physics issues. The measurement of plasma-induced Faraday rotation is one of the more promising internal magnetic field diagnostics, This thesis describes the development of a heterodyne polarimeter/interferometer for internal poloidal magnetic field measurement on ZT-40M. Heterodyne techniques were employed because of the insensitivity to spurious signal amplitude changes that cause errors in other methods. I am grateful to the ZT-40M program management for the contribution of machine access (as poor as it was) and funding, and for their patience during the diagnostic development. I would also like to thank the ZT-40M team for their interest, and for supplying some of the data that is presented in this thesis. I appreciate the friendship and support of the people I have come to know at Los Alamos. Finally, I would like to thank my wife, Laura, for typing the text of this thesis, and Dr. Cris W. Barnes for his help in the preparation of this document. Ill 4.11 Baseline with Four-Signal Technique 112 4.12 Heterodyne Polarimeter on ZT-40M 116 4.13 ZT-40M Interferometer 4.14 Simultaneous Configuration 119 4.15 Revised Simultaneous Configuration 122 4.16 Two-Chord Simultaneous Configuration 123 4.17 Preamplifier Circuit for GaAs Photoconductor 124 4.18 Method for Calculating Carrier-Signal Phase 128 5.1 Polarimetric Measurements Indicating Sensitivity Problems 134 5.2 Theoretical Beam Profiles for Geometry of ZT-40M 139 5.3 Setup for Beam Propagation Measurements 140 5.4 Measured Intensity Profiles for Geometry of ZT-40M 141 5.5 Crossed Polarizer Test Setup 142 5.6 Polarization Azimuth Rotation for Bare Metal, Quartz, and Threaded Tubulations 144 5.7 Reflectivities and Phase Difference for s and p Polarizations for Grazing Angles of Incidence 146 5.8 Polarization Rotation vs. Incident Azimuth 5.9 Quartz Inserts after Removal from ZT-40M 5.10 Profile of Metallic Deposition on Quartz 5.11 Polarimetric Phase for ZT-40M Discharges with Bare Tubulations, Bypassing Torus, and with Threaded Inserts 6.1 Interferometric Measurement with Two-Signal Technique 6.2 Example of Interferometric Measurement in Simultaneous Configuration 6.3 Central-and Edge-chord-averajred Densities 6.4 Examples of Density Sawtooth Oscillations 6.5 Density of Ramped (70 kA to 170 kA) Discharge Compared to Standard 170 kA Discharge 165 6.6 Carrier Signal Measured by the Polarimeter 166 6.7 Toroidal Current and Faraday Rotation for a Design-Mode Discharge 168 7 List of Tables 1.1 Relative Merits of Measurement Techniques 4.1 Laser Gases 6.1 Calculated Faraday Rotation Levels for Various Profiles

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“…[11], while the confidence band of the reconstruction has been computed with the Monte Carlo procedure proposed in ref. [18]. Since each of the methods presented suffers from the generation of artifacts in the reconstructed distribution, cumulative statistics has been studied as well.…”

Section: Analysis Techniquesmentioning

confidence: 99%

Comparison of unfolding methods for the inference of runaway electron energy distribution from γ-ray spectroscopic measurements

et al. 2021

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Unfolding techniques are employed to reconstruct the 1D energy distribution of runaway electrons from Bremsstrahlung hard X-ray spectrum emitted during plasma disruptions in tokamaks. Here we compare four inversion methods: truncated singular value decomposition, which is a linear algebra technique, maximum likelihood expectation maximization, which is an iterative method, and Tikhonov regularization applied to χ 2 and Poisson statistics, which are two minimization approaches. The reconstruction fidelity and the capability of estimating cumulative statistics, such as the mean and maximum energy, have been assessed on both synthetic and experimental spectra. The effect of measurements limitations, such as the low energy cut and few number of counts, on the final reconstruction has also been studied. We find that the iterative method performs best as it better describes the statistics of the experimental data and is more robust to noise in the recorded spectrum.

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Monte-Carlo error analysis in x-ray spectral deconvolution

Abstract: The deconvolution of spectral lnformatiGn from sparse x-ray data is z widely encountered problem in data analysis. An often-neglected aspect of this problem 1s Lhe propagation of random error in the deconvolutlon process. We have developed a Monte Carlo

Cited by 16 publications

References 1 publication

An experimental measurement of metal multilayer x-ray reflectivity degradation due to intense x-ray flux

An experimental measurement of metal multilayer x-ray reflectivity degradation due to intense x-ray flux

Far-infrared polarimetry/interferometry for poloidal magnetic field measurement on ZT-40M

Comparison of unfolding methods for the inference of runaway electron energy distribution from γ-ray spectroscopic measurements

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