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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2012 Volume 52, Number 3, Pages 372–378 (Mi zvmmf9665)

This article is cited in 8 papers

Problem of two-beam tomography

D. S. Anikonova, V. G. Nazarovb

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090 Russia
b bInstitute of Applied Mathematics, Far East Branch, Russian Academy of Sciences, ul. Radio 7, Vladivostok, 690041 Russia

Abstract: An idea was developed suggested in a number of studies dealing with the search for inhomogeneous inclusions inside an unknown medium given the radiation measured in a plane outside the desired body. Specifically, the medium was proposed to be probed in two directions (at two angles) in contrast to previous works, where a single direction was used. Accordingly, the probing results became more informative: the determination of the object’s shadow on the measurement area (antenna) was supplemented with the possibility of localizing the desired body in space. A tomographic location algorithm was proposed that can underlie a new orientation method in arbitrary absorbing and scattering media. As before, the case was considered where direct visualization (photograph) fails to produce a distinguishable structure of the medium. The problem was solved by analyzing signals passing through the medium. A number of numerical experiments were performed by applying computer simulation. The numerical results were illustrated by plots and tomograms.

Key words: tomography, radiation, location, radiation transfer equation.

UDC: 519.624.2

Received: 22.04.2011
Revised: 18.08.2011


 English version:
Computational Mathematics and Mathematical Physics, 2012, 52:3, 315–320

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