Measurement of the near electromagnetic field and restoration of inhomogeneity parameters in a dielectric body

Background. The inverse problems of electromagnetic sensing, aimed at determining the internal parameters of the object from external measurements of the electromagnetic field, are incorrectly posed and computationally complex. Non-linearity and instability of solutions require the use of special regularization methods. The development of effective non-iterative methods for solving such problems, especially for three-dimensional objects, remains an urgent task for various fields such as medical imaging, geophysics and non-destructive testing. The purpose of the work is to develop and analyze a non-iterative method for solving the inverse electromagnetic scattering problem for determining the dielectric constant of a limited three-dimensional object based on near-field measurements. Materials and methods. The work is based on solving the direct problem of diffraction of a monochromatic electromagnetic wave on a limited volume diffuser using a singular integro- differential equation of an electric field. A two-step non-iterative method is proposed to solve the inverse problem. It is based on the measurement of the near field scattered by an object, and can be applied for solutions from finite-dimensional spaces of piecewise constant functions. Results. A method for solving the inverse problem of electromagnetic scattering is implemented. The results of solving the direct and inverse problems are presented. A comparison of transmission coefficients for several experiments is obtained. Conclusions. The developed non-iterative method for solving the inverse problem of electromagnetic scattering provides determination of the dielectric constant of a limited threedimensional object based on near-field measurements. The method demonstrates its effectiveness and can be applied in various fields requiring non-invasive determination of object parameters.