Восстановление толщины слоя дермы по коэффициенту отражения электромагнитной волны

Abstract

The need to determine the internal structure of an investigated medium and to determine the indicators characterizing its states and properties is often faced in carrying out various kinds of diagnostics, e.g., the one aimed at reconstructing the profile of the investigated object. The inverse electrodynamic problem consists in determining the geometrical and electrodynamic parameters of the studied dielectric medium from the characteristics of scattered electromagnetic field. The article considers the inverse problem of reconstructing the layer thickness from the coefficient characterizing the reflection of electromagnetic wave from the derma biological layer. Media having a layered structure form a special class. In this case, the profile reconstruction problem boils down to estimating the number of layers and their parameters, namely, their thicknesses and dielectric constants. The formulated inverse problem is solved using the smoothing functional minimization method, which is based on the algorithm for minimizing the generalized discrepancy between the reflection coefficient frequency dependence and its theoretical model. The reflection coefficient frequency dependence in the microwave band from 1 to 5 GHz was obtained from the results of solving the direct problem by superposing random fluctuations simulating the errors of real experimental measurements. Further development and elaboration of mathematical and numerical methods for solving the inverse problems with the use of more sophisticated models is one of important avenues in studying layered media.