INVERSE PROBLEMS FOR THREE-DIMENSIONAL LOCALIZATION OF AN INHOMOGENEITY IN A STRATIFIED SCATTERING MEDIUM BY USING A WEIGHTED FOURIER TRANSFORM | Zendy

ZHANG HANG | Zendy; Sailing He | Zendy; CHEN PAN | Zendy; Sun We | Zendy

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INVERSE 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,

CHEN PAN,

Sun We

Publication year - 2001

Publication title -

acta physica sinica

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.

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