Measuring a Near Electromagnetic Field and Restoring the Parameters of Inhomogeneities in a Dielectric Body

Background. The inverse problems of electromagnetic sensing that are aimed at determining the internal parameters of an object from external measurements of an electromagnetic field are incorrectly formulated and computationally complex. The nonlinearity and instability of solutions require 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, including medical imaging, geophysics, and nondestructive testing. The aim of this study is to develop and analyze a non-iterative method for solving the inverse electromagnetic scattering problem for determining the permittivity of a limited three-dimensional object by measuring a near field. Materials and methods. This study is based on solving the direct problem of diffraction of a monochromatic electromagnetic wave on a limited bulk scatterer using a singular integro-differential equation of an electric field. A two-step non-iterative method is proposed to solve the inverse problem. The method is based on the measurement of the near field scattered by an object and can be used for solutions in 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 reported. The transmittance values for several experiments are compared. Conclusions. The developed non-iterative method for solving the inverse problem of electromagnetic scattering provides determination of the permittivity of a limited three-dimensional object on the basis of the near-field measurements. The method is efficient and can find application in various fields requiring noninvasive determination of parameters of objects.