Computer-aided tomography and physical experiment

Pikalov, V. V.; Preobrazhenskii, N. G.

doi:10.1070/pu1983v026n11abeh004538

Cited by 9 publications

(4 citation statements)

References 6 publications

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“…Our data are streaked and only 1D in space, in direction perpendicular to the target surface. So, it is not possible to perform the Abel inversion [13] procedure, which is usually associated with the analysis of interferometric data [4].…”

Section: Resultsmentioning

confidence: 99%

Hydrodynamics of laser-produced plasma corona measured by optical interferometry

Aliverdiev¹,

Batani²,

Dezulian³

et al. 2008

Plasma Phys. Control. Fusion

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We present the results of an experimental investigation of the temporal evolution of plasmas produced by high power laser irradiation of various types of target materials. We obtained 'high-quality' interferometric data on the evolution of the plasma electronic profile, which can be directly compared with analytical models and numerical simulations. For aluminium and plastic targets, the agreement with 1D simulations performed with the hydrocode MULTI is excellent, at least for large times (t 400 ps). In this case, simulations also show that the effect of radiation transport is negligible. The situation is quite different for gold targets for which, in order to get a fair enough agreement, we must take radiation transport into account.

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Section: Resultsmentioning

confidence: 99%

Hydrodynamics of laser-produced plasma corona measured by optical interferometry

Aliverdiev¹,

Batani²,

Dezulian³

et al. 2008

Plasma Phys. Control. Fusion

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“…Here we also demonstrate behavior of solution k mα (r) derived with Tikhonov regularization using (27), (29), (30) and (9). Regularization parameter α is chosen using discrepancy principle (28) where δ = 0.037, as a result α = 10 −0.09 = 0.813. Fig.…”

Section: Infrared Tomography Examplementioning

confidence: 86%

Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomography

Sizikov

Sidorov

2016

Applied Numerical Mathematics

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We propose the generalized quadrature methods for numerical solution of singular integral equation of Abel type. We overcome the singularity using the analytic computation of the singular integral. The problem of solution of singular integral equation is reduced to nonsingular system of linear algebraic equations without shift meshes techniques employment. We also propose generalized quadrature method for solution of Abel equation using the singular integral. Relaxed errors bounds are derived. In order to improve the accuracy we use Tikhonov regularization method. We demonstrate the efficiency of proposed techniques on infrared tomography problem. Numerical experiments show that it make sense to apply regularization in case of highly noisy (about 10%) sources only. That is due to the fact that singular integral equations enjoy selfregularization property.

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“…The subscript in the formula for the operator R-of Radon inversion is used because Radon inversion is an unstable procedure, and thus regularization must be used [3].…”

Section: Rmentioning

confidence: 99%