Open AccessINVERSE PROBLEMS FOR THREE-DIMENSIONAL LOCALIZATION OF AN INHOMOGENEITY IN A STRATIFIED SCATTERING MEDIUM BY USING A WEIGHTED FOURIER TRANSFORM
Author(s) -
Zhang Hang,
Sailing He,
Pan Chen,
Wenbei Shi
Publication year - 2001
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.50.1481
Subject(s) - fourier transform , singularity , ball (mathematics) , scattering , mathematical analysis , inverse , diffusion equation , physics , optics , geometry , mathematics , economy , economics , service (business)
Characterization of the structure of spatial inhomogeneities embedded in a highly scattering medium is required in many fields. In this paper, a model of a stratified medium embedded with an inhomogeneous ball is considered. With an assumption that the ball is small enough, a perturbation solution to diffusion equation is obtained with some boundary treatments. According to the characteristics of this solution in the two-dimensional Fourier space, a new weighted Fourier transform is used to process the surface data. After this process, a singularity appears at the center of the ball. Combining with the symmetry of the surface data, the information of three-dimensional position of the ball is determined.