One-dimensional inverse scattering with a Born model in a three-layered medium

Area of Science:

• Electromagnetics
• Applied Physics
• Inverse Problems

Background:

• Inverse scattering problems are crucial for non-invasive material characterization.
• The Born approximation simplifies complex scattering scenarios but introduces model errors.
• Multifrequency scattered field data offers rich information for reconstruction.

Purpose of the Study:

• To investigate the inverse-scattering problem for a dielectric slab in a three-layered medium.
• To analyze the impact of dielectric property discontinuities on reconstruction accuracy.
• To assess the limitations of the Born approximation in such scenarios.

Main Methods:

• Formulating the problem as a linear inverse problem.
• Utilizing multifrequency scattered field data.
• Applying singular-value decomposition (SVD) for analysis and solution.
• Analyzing model error associated with the Born approximation.

Main Results:

• Singular-value decomposition (SVD) enables the investigation and solution of the linear inverse problem.
• SVD provides insights into the spatial variability of retrievable dielectric profiles.
• The discontinuity of dielectric properties between the second and third medium was identified as a significant challenge.

Conclusions:

• The Born approximation, while useful, can lead to model errors, particularly with dielectric discontinuities.
• Discontinuities in dielectric properties between media can impede the accurate retrieval of dielectric profiles.
• Careful consideration of medium interfaces is necessary for reliable inverse scattering solutions.