We present a short review of several fundamental results, which have been obtained within frameworks of one trend of the wide spread of investigations, carried out during 1970 –2010s under the leadership of doctor of science, corresponding member of the National Academy of Sciences of Belarus P. D. Kukharchik, whose scientific interests were connected with the study of physical properties of heterogeneous dielectric and metal-containing industrial materials by the methods of holography, holographotomography, digital radiography, microwave and infrared introscopy. In this review, by the example of several base problems, we describe the semi-analytical methods of rigorous theoretical simulation of electromagnetic fields, arising under electromagnetic diffraction by slots in perfectly conducting screens of arbitrary thickness in absence and in the presence of plane dielectrics in the plane and cylindrical geometries of electromagnetic propagation. It demonstrates application of the these methods to simulation of processes of moisture measuring of paper sheet using microwave cavities with slots, which are employed on enterprises of pulp and paper industry.
On an integral equation in electromagnetic diffraction theory