研究目的
To determine the support of local perturbations in an infinite penetrable periodic layer without using the Green’s function of the periodic layer nor reconstructing the periodic background inhomogeneities.
研究成果
The paper provides a rigorous method to recover the support of local perturbations in periodic layers without the need for explicit knowledge of the periodic background or its Green’s function. The analysis of a new interior transmission problem is central to justifying the inversion method, and numerical examples confirm the theoretical behavior of the differential indicator function.
研究不足
The technical and application constraints include the need for the refractive index n and the wave number k > 0 to be such that the new interior transmission problem has a unique solution. Additionally, the method requires that the defect does not intersect the inhomogeneous components of the background for certain cases.
1：Experimental Design and Method Selection:
The methodology involves a differential linear sampling method for reconstructing the support of anomalies without explicitly knowing or reconstructing the background. The imaging method is based on the generalized linear sampling method, adapted to the case of locally perturbed periodic layers.
2：Sample Selection and Data Sources:
The samples or datasets used in the experiment are the measured scattered fields outside the layer due to appropriate incident fields.
3：List of Experimental Equipment and Materials:
The required instruments include a setup for generating and measuring scattered fields from periodic layers with local perturbations.
4：Experimental Procedures and Operational Workflow:
The process involves using incident plane waves to interrogate the periodic layer, measuring the scattered field, and applying the differential linear sampling method to reconstruct the support of the perturbations.
5：Data Analysis Methods:
The approach for analyzing experimental data includes statistical techniques and software tools for processing the measured scattered fields and applying the inversion algorithm.
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