We have applied the phase unwrapping technique to resolve the phase ambiguity problem arising from complex expressions of scattering parameters, for reflection-only measurement configurations, since, at some instances, only one side of the sample under test is accessible for electromagnetic measurements. We considered two different measurement configurations for testing the applicability of the phase unwrapping technique as: 1) two identical samples with different lengths flushed by a short-circuit termination and 2) one sample shorted by a varying short-circuit termination. For each measurement configuration, the underlying expressions for the reflection scattering parameters are derived. For both cases, we evaluated the suitability of the phase unwrapping technique by considering a highly-dispersive medium (distilled water) as our test sample. We note that continuity of the real part of the complex wavelength is a key issue in the unwrapping technique for (one-port) reflection-only measurements.
2. Bombay, M. S. and O. M. Ramahi, "Near-field probes using double and single negative media," Phys. Rev. E, Vol. 79, 016602, 2009.
3. Hasar, U. C., "Permittivity determination of fresh cement-based materials by an open-ended waveguide probe using amplitude-only measurements," Progress In Electromagnetics Research, Vol. 97, 27-43, 2009.
4. Nicolson, A. M. and G. F. Ross, "Measurement of the intrinsic properties of materials by time-domain," IEEE Trans. Instrum. Meas., Vol. 19, No. 4, 377-382, 1970.
5. Hyde, IV, M. W. and M. J. Havrilla, "A nondestructive technique for determining complex permittivity and permeability of magnetic sheet materials using two flanged rectangular waveguides," Progress In Electromagnetics Research, Vol. 79, 367-386, 2008.
6. Hasar, U. C. and I. Y. Ozbek, "Complex permittivity determination of lossy materials at millimeter and terahertz frequencies using free-space amplitude measurements," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 14-15, 2100-2109, 2011.
7. Ho, M., "Penetration of EM fields into circular dielectric/magnetic container: Two-dimensional simulation," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 1, 111-122, 2011.
8. Moradi, G. and A. Abdipour, "Measuring the permittivity of dielectric materials using STDR approach," Progress In Electromagnetics Research, Vol. 77, 357-365, 2007.
9. Yan, L. P., K.-M. Huang, and C. J. Liu, "A noninvasive method for determining dielectric properties of layered tissues on human back," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1829-1843, 2007.
10. Boughriet, A. -H., C. Legrand, and A. Chapoton, "A noniterative stable transmission/reflection method for low-loss material complex permittivity determination," IEEE Trans. Microw. Theory Tech., Vol. 45, No. 1, 52-57, 1997.
11. Wang, Y. and M. N. Afsar, "Measurement of complex permittivity of liquids using waveguide techniques," Progress In Electromagnetics Research, Vol. 42, 131-142, 2003.
12. Stuchly, S. S. and M. Matuszewski, "A combined total reflection transmission method in application to dielectric spectroscopy," IEEE Trans. Instrum. Meas., Vol. 27, No. 3, 285-288, 1978.
13. Seal, M. D., M. W. Hyde, and M. J. Havrilla, "Nondestructive complex permittivity and permeability extraction using a two-layer dual-waveguide probe measurement geometry," Progress In Electromagnetics Research, Vol. 123, 123-142, 2012.
14. Baker-Jarvis, J., E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microw. Theory Tech., Vol. 38, No. 8, 1096-1103, 1990.
15. Ghodgaonkar, D. K., V. V. Varadan, and V. K. Varadan, "A free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas., Vol. 39, No. 2, 387-394, 1990.
16. Muqaibel, A. H. and A. Safaai-Jazi, "A new formulation for characterization of materials based on measured insertion transfer function," IEEE Trans. Microw. Theory Tech., Vol. 51, No. 8, 1946-1951, 2003.
17. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE, Vol. 62, No. 1, 33-36, 1974.
18. Ness, J., "Broad-band permittivity measurements using the semiautomatic network analyzer," IEEE Trans. Microw. Theory Tech., Vol. 33, No. 11, 1222-1226, 1985.
19. Ball, J. A. R. and B. Horsfield, "Resolving ambiguity in broadband waveguide permittivity measurements on moist materials," IEEE Trans. Instrum. Meas., Vol. 47, No. 2, 390-392, 1998.
20. Hasar, U. C. and O. E. Inan, "Elimination of the multiple-solutions ambiguity in permittivity extraction from transmission-only measurements of lossy materials," Microw. Opt. Technol. Lett., Vol. 51, No. 2, 337-341, 2009.
21. Xia, S., Z. Xu, and X. Wei, "Thickness-induced resonance-based complex permittivity measurement technique for barium strontium titanate ceramics at microwave frequency," Rev. Sci. Instrum., Vol. 80, No. 11, 114703, 2009.
22. Hasar, U. C., "Unique permittivity determination of low-loss dielectric materials from transmission measurements at microwave frequencies," Progress In Electromagnetics Research, Vol. 107, 31-46, 2010.
23. Hasar, U. C., "Unique retrieval of complex permittivity of low-loss dielectric materials from transmission-only measurements," IEEE Geosci. Remote Sens. Lett., Vol. 8, No. 3, 562-564, 2011.
24. Chen, X., T. M. Gregorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E, Vol. 70, 016608, 2004.
25. Buyukozturk, O., T-Y. Yu, and J. A. Ortega, "A methodology for determining complex permittivity of construction materials based on transmission-only coherent, wide-bandwidth free-space measurements," Cem. Concr. Compos., Vol. 28, 349-359, 2006.
26. Varadan, V. V. and R. Ro, "Unique retrieval of complex permittivity and permeability of dispersive materials from reflection and transmitted fields by enforcing causality," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 10, 2224-2230, 2007.
27. Szabo, Z., G.-H. Park, R. Hedge, and E.-P. Li, "A unique extraction of metamaterial parameters based on Kramers-Kronig relationship," IEEE Trans. Microw. Theory Tech., Vol. 58, No. 10, 2646-2653, 2010.
28. Barroso, J. J. and U. C. Hasar, "Resolving phase ambiguity in the inverse problem of transmission/reflection measurement methods," J. Infrared Milli. Terahz Waves, Vol. 32, 857-866, 2011.
29. Chavez, S., Q.-S. Xiang, and L. An, "Understanding phase maps in MRI: A new cutline phase unwrapping method," IEEE Trans. Med. Imag., Vol. 21, No. 8, 966-977, 2002.
30. Huang, Y., "Design, calibration and data interpretation of a one-port large coaxial dielectric measurement cell," Meas. Sci. Technol., Vol. 12, 111-115, 2001.
31. Hasar, U. C. and M. T. Yurtcan, "A microwave method based on amplitude-only reflection measurements for permittivity determination of low-loss materials," Measurement, Vol. 43, No. 9, 1255-1265, 2010.
32. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, West Sussex, NJ, 2012.
33. Baker-Jarvis, J., M. D. Janezic, J. H. Grosvenor, Jr., and R. G. Geyer, "Transmission/reflection and short-circuit line methods for measuring permittivity and permeability,", Tech. Note 1355, NIST, Boulder, CO, 1992.
34. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskii, "Electrodynamics of Continuous Media," 279, Pergamon, Oxford, 1984.
35. Woodly, J. and M. Mojahedi, "On the signs of the imaginary parts of the e®ective permittivity and permeability in metamaterials," J. Opt. Soc. Am. B., Vol. 27, No. 5, 1016-1021, 2010.
36. Wang, H., X. Chen, and K. Huang, "An improved approach to determine the branch index for retrieving the constitutive effective parameters of metamaterials," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 1, 85-96, 2011.
37. Hasar, U. C., "A new calibration-independent method for complex permittivity extraction of solid materials," IEEE Microw. Wireless Compon. Lett., Vol. 18, No. 12, 788-790, 2008.