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Regularized inner products of distorted plane waves and near‐forward inverse scattering
Author(s) -
Kurylev Yaroslav V.
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150604
Subject(s) - radon transform , wkb approximation , mathematics , inverse , mathematical analysis , plane wave , inverse scattering problem , product (mathematics) , plane (geometry) , scattering , field (mathematics) , inverse problem , geometry , physics , optics , quantum mechanics , pure mathematics
Regularized inner products, r ( s , e 1 , e 2 ,) of the distorted plane waves fór the plasma wave equation u u − Δ u + qu = 0 are introduced for potentials with compact support. The regularized inner product may be represented in terms of the far‐field pattern. The use of the WKB approximation shows that the behaviour of r as e 2 → − e 1 is closely related to the Radon transform of q . This observation indicates the possibility of finding the Radon transform of q in terms of r ( s , e 1 , e 2 ) and then of recovering q by means of the inverse Radon transform.