PIER B | |

Progress In Electromagnetics Research B | ISSN: 1937-6472 |

Home > Vol. 62 > pp. 1-16
## AN EXACTLY-SOLVABLE QUASISTATIC ELECTRICITY INVERSE PROBLEM: RETRIEVAL OF THE COMPLEX PERMITTIVITY OF A CYLINDER TAKING ACCOUNT OF NUISANCE PARAMETER UNCERTAINTYBy A. Wirgin
Abstract:
This study concerns the 2D inverse problem of the retrieval, using external field data, of either one of the two physical parameters, constituted by the real and imaginary parts of the permittivity, of a z-independent cylindrical dielectric specimen subjected to an external, z-independent, quasistatic electric field. Six other parameters enter into the inverse problem. They are termed nuisance parameters because: 1) they are not retrieved during the inversion and 2) uncertainty as to their actual values can adversely affect the accuracy of the retrieval of the permittivity. This inverse problem is shown to have an exact, mathematically-explicit, solution, both for continuous and discrete input data, whose properties, with respect to the various nuisance parameter uncertainties, are analyzed, first in a mathematical, and subsequently in a numerical manner for noiseless data. It is found that: a) optimal inversion requires data registered at only a small number of sensors, b) the inverse solution, satisfying pre-existing physical constraints, exists and is unique. Moreover, the inverse solution is shown to be unstable with respect to three nuisance parameter uncertainties, the consequence of which is large retrieval inaccuracy for small nuisance parameter uncertainties, acting either individually or in combination.
2. Bauer, N., K. Fajans, and S. Z. Lewin, "Refractometry," 3. Bohren, C. F. and D. R. Huffman, 4. Chen, L., Z.-Y. Lei, R. Yang, X.-W. Shi, and J. Zhang, "Determining the effective electromagnetic parameters of bianisotropic metamaterials with periodic structures," 5. Chen, X., T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," 6. Chylek, P., V. Ramaswamy, A. Ashkin, and J. M. Dziedzic, "Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data," 7. Emery, A. F., "The effect of correlations and uncertain parameters on the efficiency of estimating and the precision of estimated parameters," 8. Hadamard, J. S., 9. Hasar, U. C., J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, "Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs," 10. Hasar, U. C., J. J. Barroso, M. Ertugrul, C. Sabah, and B. Cavusoglu, "Application of a useful uncertainty analysis as a metric tool for assessing the performance of electromagnetic properties retrieval methods of bianisotropic metamaterials," 11. Lefeuve-Mesgouez, G., A. Mesgouez, E. Ogam, T. Scotti, and A. Wirgin, "Retrieval of the physical properties of an anelastic solid half space from seismic data," 12. Morse, P. M. and H. Feshbach, 13. Neittaanmaki, P., M. Rudnicki, and A. Savini, 14. Pluchino, A. B., S. S. Goldberg, J. N. Dowling, and C. M. Randall, "Refractive-index measurements of single micron-sized carbon particles," 15. Sambuelli, L., "Uncertainty propagation using some common mixing rules for the modelling and interpretation of electromagnetic data," 16. Scotti, T. and A. Wirgin, "Multiparameter identification of a lossy fluid-like object from its transient acoustic response," 17. Seitz, F., 18. Smith, D. R., D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," 19. Von Hippel, A. R., 20. Vuye, G. and T. Lopez-Rios, "Precision in the ellipsometric determination of the optical constants of very thin films," 21. Yilmaz, T., R. Foster, and Y. Hao, "Detecting vital signs with wearable wireless sensors," 22. Young, K. F. and H. P. R. Frederikse, "Compilation of the static dielectric constant of inorganic solids," |

© Copyright 2010 EMW Publishing. All Rights Reserved