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E-raamat: Poorly Visible Media in X-Ray Tomography [De Gruyter e-raamatud]

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The tomography problem considered in this monograph consists of finding an essential part of information about the internal structure of an unknown medium. More particularly, the contact boundaries between various materials in the medium are sought. This investigation is implemented by studying an appropriate mathematical model, which is represented as a transport equation (linear Boltzmann's equation) together with certain boundary conditions. Both theoretical and numerical methods have been used and the results consist of proved theorems, computer testing of the corresponding algorithms, together with a number of tables.

Introduction 1(4)
Main notations 5(2)
Chapter
1. The theoretical aspects of invisibility in X-ray tomography
7(80)
1.1. The direct problem to the monoenergetic transport equation
7(12)
1.2. Setting the tomography problems and preliminary remarks
19(5)
1.3. The preliminary statements
24(19)
1.4. Modification of the indicator of heterogeneity and its properties
43(15)
1.5. Invisible and poorly visible media in X-ray tomography
58(16)
1.6. Examples of invisible media in X-ray tomography
74(3)
1.7. Consideration of the case with energy dependence
77(10)
Chapter
2. The tables of poorly visible pairs of substances in soft X-ray tomography
87(204)
2.1. The tables of poorly visible pairs at the points of their coefficients continuity
87(163)
2.2. The tables of poorly visible pairs at the points of their absorption edges
250(34)
2.3. Extension of the approach onto arbitrary substances
284(7)
Bibliography 291