Fourier diffraction theorem for the tensor fields

Alexander Leonidovich Balandin

Applications of Mathematics (2023)

  • Volume: 68, Issue: 5, page 559-570
  • ISSN: 0862-7940

Abstract

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The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The method is based on the first Born approximation.

How to cite

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Balandin, Alexander Leonidovich. "Fourier diffraction theorem for the tensor fields." Applications of Mathematics 68.5 (2023): 559-570. <http://eudml.org/doc/299437>.

@article{Balandin2023,
abstract = {The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The method is based on the first Born approximation.},
author = {Balandin, Alexander Leonidovich},
journal = {Applications of Mathematics},
keywords = {diffraction tomography; tensor Green's function; Born approximation; Fourier transform; inverse scattering},
language = {eng},
number = {5},
pages = {559-570},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fourier diffraction theorem for the tensor fields},
url = {http://eudml.org/doc/299437},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Balandin, Alexander Leonidovich
TI - Fourier diffraction theorem for the tensor fields
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 5
SP - 559
EP - 570
AB - The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The method is based on the first Born approximation.
LA - eng
KW - diffraction tomography; tensor Green's function; Born approximation; Fourier transform; inverse scattering
UR - http://eudml.org/doc/299437
ER -

References

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  1. Abhishek, A., 10.1016/j.jmaa.2019.123828, J. Math. Anal. Appl. 485 (2020), Article ID 123828, 13 pages. (2020) Zbl1444.53050MR4050692DOI10.1016/j.jmaa.2019.123828
  2. Boerner, W.-M., (Eds.), H. Überall, 10.1007/978-3-642-85112-4, Springer Series on Wave Phenomena 13. Springer, New York (1994). (1994) Zbl0807.65132DOI10.1007/978-3-642-85112-4
  3. Carney, P. S., Schotland, J. C., Near-field tomography, Inside Out: Inverse Problems and Applications Cambridge University Press, Cambridge (2003), 133-166. (2003) Zbl1081.78012MR2029680
  4. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE/OUP Series on Electromagnetic Wave Theory. IEEE Press, New York (1990). (1990) Zbl0925.78002
  5. Colton, D., Kress, R., 10.1007/978-1-4614-4942-3, Applied Mathematical Sciences 93. Springer, Berlin (1992). (1992) Zbl0760.35053MR1183732DOI10.1007/978-1-4614-4942-3
  6. Devaney, A. J., 10.1109/TGRS.1984.350573, IEEE Trans. Geosci. Remote Sensing GE-22 (1984), 3-13. (1984) MR0804623DOI10.1109/TGRS.1984.350573
  7. Devaney, A. J., Mathematical Foundations of Imaging, Tomography and Wavefield Inversion, Cambridge University Press, Cambridge (2012). (2012) Zbl1259.65140MR2975719
  8. Farhat, N., Microwave holography and coherent tomography, Medical Applications of Microwave Imaging IEEE Press, New York (1986), 66-81. (1986) 
  9. Girard, C., Dereux, A., 10.1088/0034-4885/59/5/002, Rep. Progr. Phys. 59 (1996), 657-699. (1996) DOI10.1088/0034-4885/59/5/002
  10. Gullberg, G. T., Roy, D. G., Zeng, G. L., Alexander, A. L., Parker, D. L., 10.1109/23.790810, IEEE Trans. Nucl. Sci. 46 (1999), 991-1000. (1999) DOI10.1109/23.790810
  11. Hansen, T. B., Yaghjian, A. D., Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications, IEEE Press, New York (1999). (1999) Zbl1008.78501MR1767418
  12. Kak, A. C., Slaney, M., 10.1137/1.9780898719277, Classics in Applied Mathematics 33. SIAM, Philadelphia (2001). (2001) Zbl0984.92017MR1850949DOI10.1137/1.9780898719277
  13. Lionheart, W. R. B., Withers, P. J., 10.1088/0266-5611/31/4/045005, Inverse Probl. 31 (2015), Article ID 045005, 17 pages. (2015) Zbl1331.49050MR3333716DOI10.1088/0266-5611/31/4/045005
  14. Mishchenko, M. I., Travis, L. D., Lacis, A. A., Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press, Cambridge (2002). (2002) 
  15. Morse, P. M., Feshbach, H., Methods of Theoretical Physics. Vol. I, II, McGraw-Hill, New York (1953). (1953) Zbl0051.40603MR0059774
  16. Mueller, R. K., Kaveh, M., Wade, G., 10.1109/PROC.1979.11284, Proc. IEEE 67 (1979), 567-587. (1979) DOI10.1109/PROC.1979.11284
  17. Nikolova, N. K., 10.1002/047134608X.W8214, Cambridge University Press, New York (2014). (2014) DOI10.1002/047134608X.W8214
  18. Sharafutdinov, V. A., 10.1515/9783110900095, Inverse and Ill-posed Problems Series 1. VSP, Utrecht (1994). (1994) Zbl0883.53004MR1374572DOI10.1515/9783110900095
  19. Tai, C. T., Dyadic Green Functions in Electromagnetic Theory, IEEE Press, New York (1994). (1994) Zbl0913.73002MR1420621
  20. Watanabe, K., 10.1007/978-3-319-00879-0, Lecture Notes in Applied and Computational Mechanics 71. Springer, Cham (2014). (2014) Zbl1320.74003MR3100154DOI10.1007/978-3-319-00879-0
  21. Wolf, E., 10.1016/0030-4018(69)90052-2, Optics Commun. 1 (1969), 153-156. (1969) DOI10.1016/0030-4018(69)90052-2
  22. Wolf, E., 10.1016/B978-012186030-1/50007-2, Trends in Optics Research, Developments and Applications. Academic Press, New York (1996), 83-110. (1996) DOI10.1016/B978-012186030-1/50007-2
  23. Yaghjian, A. D., 10.1109/PROC.1980.11620, Proc. IEEE 68 (1980), 248-263. (1980) DOI10.1109/PROC.1980.11620
  24. Zhang, T., Kan, L., Godavarthi, C., Ruan, Y., 10.3390/app9183834, Appl. Sci. 9 (2019), 3834-3852. (2019) DOI10.3390/app9183834
  25. Zhao, D., Wang, T., 10.1016/B978-0-44-459422-8.00005-9, Progress in Optics Elsevier, Amsterdam (2012), 261-308. (2012) DOI10.1016/B978-0-44-459422-8.00005-9
  26. Zoughi, R., 10.1007/978-94-015-1303-6, Non-Destructive Evaluation Series 4. Springer, Dordrecht (2000). (2000) DOI10.1007/978-94-015-1303-6

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