研究目的
To justify the solution to inverse problems by establishing one-to-one correspondence between the sought quantities and the measured noisy data sets, specifically for the determination of permittivity of dielectric bodies in a waveguide.
研究成果
The mathematical imaging technique provides a robust method for justifying the unique solvability and constructing numerical methods for the inverse problem of permittivity reconstruction in waveguides. The approach is based on verifying one-to-one correspondence between reconstructed quantities and measurement data, with potential for generalization to arbitrary dielectric inclusions in waveguides of arbitrary cross section.
研究不足
The reconstruction of real layer permittivity is an ill-posed problem due to the potential for in?nitesimal shifts from the set of measurement data to remove images of points from its range, destroying unique solvability. However, reconstruction of complex layer permittivity is well-posed under small perturbations of the measurement data.
1：Experimental Design and Method Selection:
The study employs mathematical imaging techniques to analyze the mappings that couple the sought quantities (permittivities of dielectric layers) with the forward scattering (measured) data.
2：Sample Selection and Data Sources:
The study considers a single-mode waveguide containing layered dielectric inclusions, with permittivity values to be determined from the transmission coefficient measured at several frequencies.
3：List of Experimental Equipment and Materials:
Not explicitly mentioned.
4：Experimental Procedures and Operational Workflow:
The solution involves solving a boundary value problem for Maxwell's equations describing TE-modes, applying transmission conditions on boundary surfaces, and using explicit expressions for field components and transmission coefficients.
5：Data Analysis Methods:
The study analyzes the injectivity of functions coupling permittivity and transmission coefficients, using mathematical imaging to ensure one-to-one correspondence between permittivity sets and measured data.
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