Methods of the diffraction theory for microwave aquametry of paper materials
Abstract
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.
References
- Pisarevskii AN, Chernyavskii AF, Afanas’ev GK, Kukharchik PD. Sistemy tekhnicheskogo zreniya (printsipial’nye osnovy, apparatnoe i matematicheskoe obespechenie) [Systems of technical vision (fundamentals, hardware and software)]. Leningrad: Mashinostroenie; 1988. 424 p. Russian.
- Uriev NB. Vysokokontsentrirovannye dispersnye sistemy [High-concentrated disperse systems]. Moscow: Khimiya; 1980. 320 p. Russian.
- Kupfer K, editor. Electromagnetic aquametry. Electromagnetic wave interaction with water and moist substances. Berlin: Springer; 2005. 530 p. DOI: 10.1007/b137700.
- Nyfors EG, Vainikainen P. Industrial microwave sensors. Norwood: Artech House; 1989. 364 p. (Artech House Microwave Library).
- Kraszewski AW, Nelson SO. Resonant cavity perturbation – some new applications of an old measuring technique. Journal of Microwave Power and Electromagnetic Energy. 1996;31(3):178-187. DOI: 10.1080/08327823.1996.11688308.
- Weinstein LA. Teoriya difraktsii i metod faktorizatsii [The theory of diffraction and the factorization method]. Moscow: Sovetskoe radio; 1966. 431 p. Russian.
- Mittra R, Lee SW. Analytical techniques in the theory of guided waves. New York: Macmillan; 1971. 311 p. Russian edition: Mittra R, Lee S. Analiticheskie metody teorii volnovodov. Plisa AI, translator. Moscow: Mir; 1974. 327 p.
- Litvinenko LN, Prosvirnin SL. Spektral’nye operatory rasseyaniya v zadachakh difraktsii voln na ploskikh ekranakh [Spectral scattering operators in the problems of plane wave diffraction by a plane screens]. Kyiv: Naukova dumka; 1984. 240 p. Russian.
- Hönl H, Maue AW, Westpfahl K. Theorie der Beugung. In: Flügge S, editor. Kristalloptik. Beugung. Berlin: Springer; 1961. S. 218–573. (Handbuch der Physik; volume 5/25/1). Russian edition: Hönl H, Maue A, Westpfahl K. Teoriya difraktsii. Vakhitov NG, Ivanov VI, Sakharova MP, translators. Moscow: Mir; 1964. 428 p.
- Zavadskii VYu. Modelirovanie volnovykh protsessov [Simulation of wave processes]. Moscow: Nauka; 1991. 248 p. Russian.
- Norrie D, Vries G. An introduction to finite element analysis. New York: Academic Press; 1978. 301 p. Russian edition: Norrie D, Vries G. Vvedenie v metod konechnykh elementov. Demidov GV, Urvantsev AL, translators. Moscow: Mir; 1981. 304 p.
- Grigor’ev AD, Yankevich VB. Rezonatory i rezonatornye zamedlyayushchie sistemy SVCh. Chislennye metody rascheta i proektirovaniya [Cavities and resonator slow-wave structures for microwaves. Numerical methods of calculation and design]. Moscow: Radio i svyaz’; 1984. 248 p. Russian.
- Born M, Wolf E. Principles of optics. Oxword: Pergamon Press; 1968. 600 p. Russian edition: Born M, Wolf E. Osnovy optiki. Breus SN, Golovashkin AI, Shubin AA, translators. Moscow: Nauka; 1973. 713 p.
- Serdyuk VM. [Diffraction of a plane electromagnetic wave by a slot in a conducting screen of arbitrary thickness]. Zhurnal tekhnicheskoi fiziki. 2005;75(8):113-120. Russian.
- Tikhonov AN, Arsenin VYa. Metody resheniya nekorrektnykh zadach [Solutions of ill-posed problems]. Moscow: Nauka; 1979. 285 p. Russian.
- Serdyuk VM. [Diffraction of a plane electromagnetic wave by a slot in a conducting screen with a transverse dielectric layer]. Zhurnal tekhnicheskoi fiziki. 2006;76(6):98–105. Russian.
- Adams MJ. An introduction to optical waveguides. New York: Wiley; 1981. 401 p. Russian edition: Adams M. Vvedenie v teoriyu opticheskikh volnovodov. Krivoshlykov SG, Chernykh VA, translators. Moscow: Mir; 1984. 512 p.
- Serdyuk VM. Exact solutions for electromagnetic wave diffraction by a slot and strip. AEU – International Journal of Electronics and Communications. 2011;65(3):182–189. DOI: 10.1016/j.aeue.2010.04.002.
- Serdyuk VM. Diffraction field behavior near the edges of a slot and strip. Progress in Electromagnetics Research M. 2011;20: 207–218. DOI: 10.2528/PIERM11062803.
- Ditkin VA, Prudnikov AP. Integral’nye preobrazovaniya i operatsionnoe ischislenie [Integral transforms and operational calculus]. Moscow: Fizmatgiz; 1961. 524 p. Russian.
- Kukharchik PD, Serdyuk VM, Titovitsky JA. Effect of continuous modification of dielectric order in paper. In: Okamura S, Sobue N, Yagihara S, Zhang Y, editors. Proceedings of the 7 th conference on electromagnetic wave interaction with water and moist substances; 2007 April 15–18; Hamamatsu, Japan. Hamamatsu: ISEMA; 2007. p. 47–54.
- Kukharchik PD, Serdyuk VM, Titovitsky JA. Diffraction of hybrid modes in a cylindrical cavity resonator by a transverse circular slot with a plane anisotropic dielectric layer. Progress in Electromagnetics Research B. 2008;3:73–94. DOI: 10.2528/PIERB07112502.
- Kuharchik PD, Titovitsky IA, Belyachits ACh, Kourilo NI. Multi-channel microwave resonator moisture-mass meter of paper web. In: Electromagnetic wave interaction with water and moist substances; 1996 June 17; San Francisco, California, USA. New York: TAB-IEEE Press; 1996. p. 135-137.
- Sazhin BI, editor. Elektricheskie svoistva polimerov [Electrical properties of polymers]. Leningrad: Khimiya; 1977. 192 p. Russian.
- Serdyuk VM. Dielectric study of bound water in grain at radio and microwave frequencies. Progress in Electromagnetics Research. 2008;84:379–406. DOI: 10.2528/PIER08081103.
Copyright (c) 2020 Journal of the Belarusian State University. Physics

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The authors who are published in this journal agree to the following:
- The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
- The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
- The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)