2019
DOI: 10.1088/1361-6420/ab1c66
|View full text |Cite
|
Sign up to set email alerts
|

Reconstruction of a local perturbation in inhomogeneous periodic layers from partial near field measurements

Abstract: We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in R d , d = 2, 3, using near field measurements of the scattered wave on an open set of the boundary above the medium, or, the measurements of the full wave in some area. The appearance of the perturbation prevents the reduction of the problem to one periodic cell, such that classical methods are not applicable and the problem becomes more challenging. We first show the equivalence of the dir… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2

Citation Types

1
25
0

Year Published

2019
2019
2023
2023

Publication Types

Select...
4
1

Relationship

3
2

Authors

Journals

citations
Cited by 5 publications
(26 citation statements)
references
References 33 publications
1
25
0
Order By: Relevance
“…In particular, the right hand side is analytical w.r.t. β and it follows by [16,Theorem 8], that the solution J R u s is analytical in β ∈ R \ {−k, k}. Therefore, the Fourier transform of the traces F u s Γ ±R are analytical in ξ ∈ R \ {−k, k} and vanishes everywhere in R, and in particular, the traces u s Γ ±R equal to zero on Γ ±R .…”
Section: 3mentioning
confidence: 97%
See 4 more Smart Citations
“…In particular, the right hand side is analytical w.r.t. β and it follows by [16,Theorem 8], that the solution J R u s is analytical in β ∈ R \ {−k, k}. Therefore, the Fourier transform of the traces F u s Γ ±R are analytical in ξ ∈ R \ {−k, k} and vanishes everywhere in R, and in particular, the traces u s Γ ±R equal to zero on Γ ±R .…”
Section: 3mentioning
confidence: 97%
“…The smooth and periodic function β+α) is the truncated Fourier series expansion of the 1-periodic delta distribution, since the j-th Fourier coefficient is given by δ −β,j = e −i2πjβ , the sum converges to δ −β with respect to H −s per (I) for some s > 1 /2 (see [22,Chapter 5]). Since the Bloch transformed right hand side is analytical in β, we know by [16,Theorem 8] that the scattered field is continuous in β ∈ I and the evaluation at point α is allowed, such the the evaluation of the distribution is well-defined. Hence, we conclude that…”
Section: 3mentioning
confidence: 99%
See 3 more Smart Citations