Profile reconstruction of periodic interface

Area of Science:

• Electromagnetics and wave physics
• Computational physics
• Inverse problems

Background:

• Reconstructing complex periodic boundaries between homogeneous media is challenging.
• Existing methods may lack efficiency or accuracy for arbitrary profiles.
• Understanding boundary characteristics is crucial for wave propagation analysis.

Purpose of the Study:

• To develop and validate a robust method for reconstructing periodic boundary profiles.
• To apply Tikhonov regularization for solving the inverse problem of boundary reconstruction.
• To utilize wave diffraction analysis for accurate boundary identification.

Main Methods:

• Employing Tikhonov regularization for inverse problem solving.
• Utilizing the analytical numerical C method for direct wave diffraction problems.
• Implementing a scheme for numerical testing and accuracy verification of algorithms.

Main Results:

• Successfully reconstructed periodic boundary profiles between two homogeneous media.
• Demonstrated the effectiveness of the Tikhonov regularization approach combined with wave diffraction.
• Verified the accuracy and validity of the proposed reconstruction algorithm through numerical experiments.

Conclusions:

• The Tikhonov regularization technique, coupled with wave diffraction analysis, provides a valid and efficient method for reconstructing periodic boundaries.
• The proposed numerical testing scheme ensures reliable algorithm performance.
• This approach offers a promising solution for characterizing complex interfaces in wave physics.