Resolution limits in inverse source problem for strip currents not in Fresnel zone
Summary
This study estimates achievable resolution in inverse source problems by removing far-field approximations. New formulas for magnetic and electric sources offer insights into geometrical parameter effects on resolution.
Area of Science:
- Electromagnetics and Inverse Problems
- Computational Electromagnetics
- Signal Processing
Background:
- Inverse source problems aim to reconstruct sources from observed fields.
- Existing resolution estimates are limited by far-field or Fresnel approximations.
- Reconstructing strip sources from radiated fields in 2D is a key challenge.
Purpose of the Study:
- To develop new resolution estimation formulas for inverse source problems.
- To remove geometrical limitations of far-field and Fresnel approximations.
- To analyze resolution for both magnetic and electric strip sources.
Main Methods:
- Recasting radiation operators as Fourier-type integral operators.
- Using variable transformations to simplify analysis.
- Employing a weighted adjoint inversion method for electric currents.
- Approximating singular systems for magnetic sources.
Main Results:
- Derived unified resolution formulas for magnetic and electric currents.
- Demonstrated the influence of geometrical parameters on achievable resolution.
- Showed that formulas coincide with Fresnel zone results under Fresnel approximation.
Conclusions:
- The developed resolution formulas are general and applicable beyond Fresnel approximations.
- The study provides a more accurate estimation of resolution in inverse source problems.
- Numerical examples validate the theoretical findings.
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