2012
DOI: 10.1080/00036811.2011.619981
|View full text |Cite
|
Sign up to set email alerts
|

On a two-dimensional inverse scattering problem for a dielectric

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2

Citation Types

0
38
0

Year Published

2013
2013
2023
2023

Publication Types

Select...
6
3

Relationship

0
9

Authors

Journals

citations
Cited by 28 publications
(38 citation statements)
references
References 41 publications
0
38
0
Order By: Relevance
“…In practice, equation (2) is posed on a subset Γ obs of the far-field sphere S 2 . By straightforward modifications of the algorithm described in Section 5, one could simultaneously invert for Γ and the dielectric constants [1,Section 3.2]. In this situation Hähner [21] showed a uniqueness result assuming knowledge of the far-field patterns for all incoming plane waves.…”
Section: E4mentioning
confidence: 99%
See 1 more Smart Citation
“…In practice, equation (2) is posed on a subset Γ obs of the far-field sphere S 2 . By straightforward modifications of the algorithm described in Section 5, one could simultaneously invert for Γ and the dielectric constants [1,Section 3.2]. In this situation Hähner [21] showed a uniqueness result assuming knowledge of the far-field patterns for all incoming plane waves.…”
Section: E4mentioning
confidence: 99%
“…, m, where d j , p j ∈ S 2 and d j · p j = 0. We denote by F j the boundary to far-field operator that maps a parametrisation of the boundary Γ onto the far-field pattern E ∞ j of the scattered field E s j of the solution (E j ) 1 N , E s j to the problem (1a)-(1e) for the incident wave E inc j . For simplicity we do not distinguish between the boundary Γ and its parametrisation in this introduction.…”
Section: E4mentioning
confidence: 99%
“…This type of problem occurs in various applications such as radar, remote sensing, geophysics, medical imaging, and nondestructive testing. Let D 0 denote an impenetrable obstacle which is embedded in a bounded, penetrable obstacle D with C 2 -boundary ∂D, that is, D 0 ⊂ D. Assume that D 1 ∂u s ∂r − iku s = 0r = |x|, (1.5) where ν is the unit outward normal to the interface ∂D and boundary ∂D 0 , λ is a (complex) constant with Re(λ) > 0. Here, the total field u = u s + u i in D 2 is given as the sum of the unknown scattered wave u s which is required to satisfy the Sommerfeld radiation condition (1.5) and the incident plane wave u i = e ikx·d , where d interface ∂D.…”
Section: Introductionmentioning
confidence: 99%
“…For more detailed overview of the factorization method, we refer to the monograph [15] and the references therein, where many related inverse problems for different kinds of partial differential equations are studied by using this method. For the inverse medium scattering problems, there are also lots of different reconstruction algorithms; see, e.g., [14] for the music-algorithm method, [21] for the singular sources method, [1,10,30] for the iteration method and [4,5,12,20] for the linear sampling method.…”
Section: Introductionmentioning
confidence: 99%