On orthogonality sampling method for Maxwell's equations and its applications to experimental data.

Area of Science:

• Electromagnetism
• Applied Mathematics
• Inverse Problems

Background:

• The inverse scattering problem for Maxwell's equations is crucial for characterizing materials.
• Bianisotropic scatterers require advanced methods for unique determination.
• Existing methods may face challenges with complex experimental data.

Purpose of the Study:

• To demonstrate the unique determination of bianisotropic scatterers from multi-static far-field data.
• To adapt and apply the orthogonality sampling method (OSM) for numerical reconstruction.
• To validate the method using unprocessed 3D experimental and synthetic scattering data.

Main Methods:

• Factorization analysis of the far-field operator for unique determination.
• Modified orthogonality sampling method (OSM) for scatterer reconstruction.
• Inversion of unprocessed 3D experimental data from the Fresnel Institute.

Main Results:

• Unique determination of bianisotropic scatterers is proven through factorization analysis.
• The modified OSM effectively reconstructs scatterer properties.
• Successful application to real-world experimental data and synthetic datasets.

Conclusions:

• The proposed method provides a robust solution for inverse scattering problems involving bianisotropic materials.
• The adapted OSM is effective for reconstructing scatterers from complex, unprocessed data.
• This work contributes to the frontiers of applied inverse problems in science and engineering.