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.
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References
D. S. Anikonov, V. G. Nazarov, and I. V. Prokhorov, “Algorithm of Finding a Body Projection within an Absorbing and Scattering Medium,” Inverse Ill-Posed Probl. 18, 885–893 (2011).
D. S. Anikonov, V. G. Nazarov, and I. V. Prokhorov, “The Problem of Single-Beam Probing of an Unknown Medium,” J. Appl. Ind. Math. 5, 500–505 (2011).
V. S. Vladimirov, “Mathematical Problems in One-Speed Theory of Particle Transport,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 61, 3–158 (1961).
T. A. Germogenova, Local Properties of Solutions to the Transport Equation (Nauka, Moscow, 1976) [in Russian].
D. S. Anikonov, A. E. Kovtanyuk, and I. V. Prokhorov, Transport Equations and Tomography (Logos, Moscow, 2000; VSP, Utrecht, 2002).
J. H. Hubbell and S. M. Seltzer, “Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients 1 KeV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest,” NISTIR-5632 (Natl. Inst. of Stand. and Technol., Gaithersburg, 1995).
B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modern Geometry-Methods and Applications (Nauka, Moscow, 1979; Springer-Verlag, Berlin, 1985).
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Original Russian Text © D.S. Anikonov, V.G. Nazarov, 2012, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2012, Vol. 52, No. 3, pp. 372–378.
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Anikonov, D.S., Nazarov, V.G. Problem of two-beam tomography. Comput. Math. and Math. Phys. 52, 315–320 (2012). https://doi.org/10.1134/S0965542512030037
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DOI: https://doi.org/10.1134/S0965542512030037