Reconstruction of permittivity profiles in cylindrical objects illuminated by higher order TE sub(mn) and TM sub(mn) modes

• Published in: IEEE transactions on microwave theory and techniques 2000-01, Vol.48 (12), p.2721-2729
• Main Authors: Akhtar, MJ, Omar, Abbas S
• Format: Article
• Language: English
• Subjects: Biomedical engineering; Data points; Dielectric constant; Differential equations; Electromagnetic wave scattering; Image reconstruction; Integral equations; Inverse problems; Mathematical analysis; Mathematical transformations; Microwaves; Permittivity; Reconstruction; Reflection coefficient; Remote sensing; Tomography; Transforms
• ISSN: 0018-9480
• DOI: 10.1109/22.899036

An improved and accurate technique for the reconstruction of radially dependent permittivity profiles in cylindrical objects illuminated by higher order TE sub(mn) and TM sub(mn) cylindrical modes is presented in this paper. The technique is based on a general kind of integral transform of the measured frequency-dependent reflection data and the recently suggested renormalization technique to obtain a unique solution of the corresponding inverse problem. Nonlinear Riccati-similar differential equations for a properly defined reflection coefficient for both TE sub(mn) and TM sub(mn) cylindrical modes have first been derived in a unified way for this purpose. These equations have then been inverted using our proposed renormalization technique to uniquely obtain the unknown permittivity profile in terms of a Hankel transform of measured reflection coefficient data. About 150-200 measurement data points over a wide frequency band (wavelength ranging from one-fifth of the inner diameter of the cylindrical object to infinity) have been used for the reconstruction. A dummy time variable has been introduced to improve the overall reconstruction process. This variable has then been transformed into the spatial one with the help of a proposed numerical algorithm. A number of reconstruction examples has been considered and a very good agreement has been found between the original and reconstructed profiles even for very high values of permittivity.