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The embedding method and differential run equations for the inverse scattering problem in a layered medium
Author(s) -
Klyatskin V. I.,
Koshel K. V.,
Shevtsov B. M.
Publication year - 1995
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/94rs03170
Subject(s) - inverse scattering problem , inverse problem , inverse scattering transform , scattering , mathematical analysis , embedding , exponential function , mathematics , inverse , physics , optics , computer science , geometry , artificial intelligence
The one‐dimensional transient problem of a wave incidence on a layer of inhomogeneous medium is considered. It is shown that a measurement of the internal fields allows one to reconstruct the permittivity profile in certain parts of the slab. Combining the embedding and differential run equations, we obtain the closed equations for the internal fields and construct the solution procedure for the inverse scattering problem. The generalization of the analytical solution of the inverse problem, for the case in which the time dependence of scattering field is exponential, is presented.