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Abstract <p>This article considers the issue of vector three-dimensional direct and inverse diffraction problems involving an inhomogeneous hemispherical scatterer with a piecewise constant permittivity distribution. Starting from the fundamental Maxwell equations, we recast the electromagnetic boundary value problem into an equivalent system of integro-differential equations. Novel numerical methods are introduced for addressing both the direct diffraction problem, enabling computation of electromagnetic fields across the hemisphere, as well as a two-step method for tackling the inverse diffraction problem aimed at reconstructing the permittivity. Experimental outcomes illustrating the recovery of internal structural anomalies through this two-phase technique are discussed. These findings demonstrate that the proposed two-step approach offers substantial promise for accurately determining material composition utilizing frequencies spanning between 1–10 GHz.</p>

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Numerical Method for Solving the Microwave Tomography Problem of Reconstruction of Inhomogeneities in Hemispherical Body

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Yu. G. Smirnov,
  • M. Yu. Medvedik,
  • V. Yu. Martynova

摘要

Abstract

This article considers the issue of vector three-dimensional direct and inverse diffraction problems involving an inhomogeneous hemispherical scatterer with a piecewise constant permittivity distribution. Starting from the fundamental Maxwell equations, we recast the electromagnetic boundary value problem into an equivalent system of integro-differential equations. Novel numerical methods are introduced for addressing both the direct diffraction problem, enabling computation of electromagnetic fields across the hemisphere, as well as a two-step method for tackling the inverse diffraction problem aimed at reconstructing the permittivity. Experimental outcomes illustrating the recovery of internal structural anomalies through this two-phase technique are discussed. These findings demonstrate that the proposed two-step approach offers substantial promise for accurately determining material composition utilizing frequencies spanning between 1–10 GHz.