A projection-based approach to diffraction tomography on curved boundaries

Area of Science:

• Physics
• Applied Mathematics
• Imaging Science

Background:

• Diffraction tomography is a powerful imaging technique.
• Reconstructing images with arbitrary source/receiver geometries presents challenges.
• Integral theorems provide a foundation for wave propagation analysis.

Purpose of the Study:

• To develop a new diffraction tomography approach for 2D image reconstruction.
• To handle arbitrarily-shaped curves of sources and receivers.
• To enable image construction using synthetic aperture methods.

Main Methods:

• Utilizing the integral theorem of Helmholtz and Kirchhoff.
• Employing appropriate Green's functions for boundary conditions.
• Projecting fields from receivers to external locations and then to virtual receivers.
• Applying a mapping technique optimized for the approach.

Main Results:

• Demonstrated a method for field projection from receivers to arbitrary external locations.
• Showcased how to determine the field of a hypothetical source along the boundary.
• Enabled data reformation suitable for synthetic aperture imaging.
• Validated the approach with synthetic data examples.

Conclusions:

• The proposed diffraction tomography approach effectively reconstructs 2D images.
• The method accommodates complex, arbitrarily-shaped source and receiver configurations.
• This work provides a foundation for advanced imaging using synthetic aperture techniques.