A Complete Factorization Method for Scattering by Periodic Surfaces

Arens, Tilo; Grinberg, N I

doi:10.1007/s00607-004-0092-0

Cited by 45 publications

(64 citation statements)

References 17 publications

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“…Our analysis extends approaches in [4,20,22] to Maxwell's equations in a biperiodic setting. We adapt the special plane incident fields introduced in [4] for the periodic scalar case to the vectorial problem, which allows us to suitably factorize the near field operator.…”

Section: Introductionmentioning

confidence: 73%

“…Due to the linearity of the problem, a linear combination of several incident fields will lead to a corresponding linear combination of the resulting scattered fields. We obtain such linear combination using sequences (a j ) 4 and define the corresponding operator by…”

Section: Problem Settingmentioning

confidence: 99%

“…Recently this method has been extended to periodic inverse scattering problems. In [4,5] the authors studied the Factorization method for the imaging problem of impenetrable periodic structures with Dirichlet and impedance boundary 1 conditions. The paper [23] considered imaging of penetrable periodic interfaces between two dielectrics in two dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…We adapt the special plane incident fields introduced in [4] for the periodic scalar case to the vectorial problem, which allows us to suitably factorize the near field operator. Further, a modified version of the method studied in [22] treats the case that the imaginary part of the middle operator in the factorization is just semidefinite.…”

Section: Introductionmentioning

confidence: 99%

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Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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This paper is concerned with the inverse scattering problem of electromagnetic waves from penetrable biperiodic structures in three dimensions. We study the Factorization method as a tool for reconstructing the periodic media from measured data consisting of scattered electromagnetic waves for incident plane electromagnetic waves. We propose a rigorous analysis for the method. A simple criterion is provided to reconstruct the biperiodic structures. We also provide three-dimensional numerical experiments to indicate the performance of the method.

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Section: Introductionmentioning

confidence: 73%

Section: Problem Settingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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“…The recent development in the qualitative method has led to the establishment of the Factorization Method (FM) by Kirsch [14]. Since being established, the FM has attracted much research consideration and has already been successfully applied to different inverse scattering problems [15], [16], [17]. Recently, the application of the FM in ultrasonic testing to achieve super resolution imaging (i.e.…”

Section: Introductionmentioning

confidence: 99%

The Application of the Factorization Method to the Subsurface Imaging of Surface-Breaking Cracks

Zhang

Huthwaite

Lowe

2018

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Abstract-A common location for cracks to appear is at the surface of a component; at the near surface, many nondestructive evaluation (NDE) techniques are available to inspect for these, but at the far surface this is much more challenging. Ultrasonic imaging is proposed to enable far surface defect detection, location and characterisation. One specific challenge here is the presence of a strong reflection from the backwall, which can often mask the relatively small response from a defect. In this paper, the Factorization Method (FM) is explored for the application of subsurface imaging of the surface-breaking cracks. In this application, the component has two parallel surfaces, the crack is initiated from the far side and the phased array is attached on the near side. Ideally, the pure scattered field from a defect is needed for the correct estimation of the scatterer through the FM algorithm. However, the presence of the backwall will introduce a strong specular reflection into the measured data which should be removed before applying the FM algorithm. A novel subtraction method was developed to remove the backwall reflection. The performance of the FM algorithm and this subtraction method were tested with the simulated and experimental data. The experimental results showed a good consistency with the simulated results. It is shown that the FM algorithm can generate high quality images to provide a good detection of the crack and an accurate sizing of the crack length. The subtraction method was able to provide a good backwall reflection removal in the case of small cracks (1-3 wavelengths).

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The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure

Zhang

2010

Math. Meth. Appl. Sci.

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In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the structure is assumed to be homogeneous and lossless with a positive dielectric coefficient. Below the structure is a perfect conductor partially coated with a dielectric. A periodic version of the linear sampling method is developed to reconstruct the doubly periodic structure using the near field data. In this case, the far field equation defined on the unit ball of R 3 is replaced by the near field equation which is a linear integral equation of the first kind defined on a plane above the periodic surface.

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A Complete Factorization Method for Scattering by Periodic Surfaces

Cited by 45 publications

References 17 publications

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

The Application of the Factorization Method to the Subsurface Imaging of Surface-Breaking Cracks

The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure

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