Aleksin S. Layered structures permittivity profile reconstruction by the value of reflection coefficient

Object of investigation - reconstruction of permittivity profile (PP) of stratified dielectric structures on the basis of reflection coefficient in frequency domain. Subject of investigation - electrophysics parameters of layers materials and geometrical parameters of layers of the stratified dielectric structures. Methods of investigation - mathematical apparatus of complex variable functions theory, differential and integral calculus, integral and differential equations, linear algebra, probability theory and correlation analysis. Three well-known methods of layered structure PP reconstruction on the basis of microwave probing are under consideration. The methods are discrete analog of Gel’fand-Levitan method (DAGLM) that supposes model of structure having layers with equal electrical thickness, the method of dynamic deconvolution (MDD), and the method based on Newton-Kantorovich iterative scheme (NKIS) implementation to Riccati differential equation. The equation connects reflection coefficient in frequency and spatial domains with complex permittivity distribution. The new modifications of the methods are proposed in thesis. The aims of the modifications development are PP reconstruction process acceleration (for DAGLM and NKIS), generalization of the basic methods having been developed in plane-wave probing supposition to the case of divergent-beam probing (for MDD and DAGLM), improvement of reconstruction process stability in the case of lossy layers material (for NKIS). In addition, the improved variants of two existing methods of layers interface electrical depth estimation are proposed. The parametrical spectral analysis (PSA) method based on rational-fraction interpolation in Fourier-conjugate domain is also improved. The new approach for PSA optimal order choosing is proposed. The results of work allow improving characteristics of measuring and computing complexes that perform visualization of stratified dielectric structures PP on the basis of microwave reflectometry data. Application fields - subsurface sensing of soils, non-destructive testing of industrial products and building constructions.