Regularized inner products of distorted plane waves and nearforward inverse scattering
Abstract
Regularized inner products, r(s,e sub 1, e sub 2) of the distorted plane waves for the plasma wave equation are introduced for potentials with compact support. The regularized inner product may be represented in terms of the farfield pattern. The use of the WKB approximation shows that the behavior 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 sub 1, e sub 2) and then of recovering q by means of the inverse Radon transform.
 Publication:

Mathematical Methods in the Applied Sciences
 Pub Date:
 August 1992
 DOI:
 10.1002/mma.1670150604
 Bibcode:
 1992MMAS...15..411K
 Keywords:

 Inverse Scattering;
 Plane Waves;
 Plasma Waves;
 Schroedinger Equation;
 WentzelKramerBrillouin Method;
 Backscattering;
 Far Fields;
 Forward Scattering;
 Fourier Transformation;
 Operators (Mathematics);
 Wave Equations;
 Plasma Physics