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February  2020, 14(1): 133-152. doi: 10.3934/ipi.2019067

## Factorization method for imaging a local perturbation in inhomogeneous periodic layers from far field measurements

 1 CMAP, École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France 2 Center for Industrial Mathematics, University of Bremen, Bibliothekstraẞe 5, 28359 Bremen, Germany

* Corresponding author: Alexander Konschin

Received  April 2019 Revised  August 2019 Published  November 2019

Fund Project: A. Konschin was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number 281474342/GRK2224/1.

We analyze the Factorization method to reconstruct the geometry of a local defect in a periodic absorbing layer using almost only incident plane waves at a fixed frequency. A crucial part of our analysis relies on the consideration of the range of a carefully designed far field operator, which characterizes the geometry of the defect. We further provide some validating numerical results in a two dimensional setting.

Citation: Houssem Haddar, Alexander Konschin. Factorization method for imaging a local perturbation in inhomogeneous periodic layers from far field measurements. Inverse Problems & Imaging, 2020, 14 (1) : 133-152. doi: 10.3934/ipi.2019067
##### References:

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##### References:
Example for the refractive index $n = n_p + q$
Three periods of the parameters and results for Example $1$
Three periods of main parameters for the numerical experiments
Results for Example $2$ with $k^2 = 0.4$, $q = q_1$, $\nu = 10^{-3}$ and $\nu = 10^{-6}$
Results for Example $3$ with $k^2 = 1.8$, $\nu = 1$ and $\nu = 10^{-3}$
Results for Example $4$ with $k^2 = 0.09$, $\nu = 10^{-3}$ and with $k^2 = 3$, $\nu = 1$
Results for FM and LSM with $k^2 = 3$ and $1\%$ relative noise
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