This paper addresses the possibility of displacement measurement by microwave interferometry at an unknown reflection coefficient with the use of as few as two probes. The case of an arbitrary interpobe distance is considered. The measurement error as a function of the interprobe distance is analyzed with the inclusion of variations of the detector currents from their theoretical values. The analysis has shown that as the interprobe distance decreases, the maximum measurement error passes through a minimum for reflection coefficients close to unity and increases monotonically for smaller reflection coefficients. Based on the results of the analysis, the interprobe distance is suggested to be one tenth of the guided operating wavelength λg. In comparison with the conventional interprobe distance of λg/8, the suggested one offers a marked reduction in the maximum measurement error for reflection coefficients close to unity, while for smaller ones this error remains much the same (for a detector current error of 3%, the maximum measurement error in percent of the operating wavelength is 2.2% and 1.0% at λg/10 as against 4.8% and 2.7% at λg/8 for a reflection coefficient of 1 and 0.9, respectively, and 2.9% at λg/10 as against 2.4% at λg/8 for a reflection coefficient of 0.1).
2. Benlarbi-Delai, A., D. Matton, and Y. Leroy, "Short-range two-dimension positioning by microwave cellular telemetry," IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 11, 2056-2062, 1994.
doi:10.1109/22.330119
3. Kim, S. and C. Nguyen, "A displacement measurement technique using millimeter-wave interferometry," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 6, 1724-1728, 2003.
doi:10.1109/TMTT.2003.812575
4. Cunha, A. and E. Caetano, "Dynamic measurements on stay cables of stay-cable bridges using an interferometry laser system," Experimental Techniques, Vol. 23, No. 3, 38-43, 1999.
doi:10.1111/j.1747-1567.1999.tb01570.x
5. Kaito, K., M. Abe, and Y. Fujino, "Development of a non-contact scanning vibration measurement system for real-scale structures," Structure and Infrastructure Engineering, Vol. 1, No. 3, 189-205, 2005.
doi:10.1080/15732470500030661
6. Mehrabi, A. B., "In-service evaluation of cable-stayed bridges, overview of available methods, and findings," Journal of Bridge Engineering, Vol. 11, No. 6, 716-724, 2006.
doi:10.1061/(ASCE)1084-0702(2006)11:6(716)
7. Lee, J. J. and M. Shinozuka, "A vision-based system for remote sensing of bridge displacement," NDT & E International, Vol. 39, No. 5, 425-431, 2006.
doi:10.1016/j.ndteint.2005.12.003
8. Gentile, C., "Application of microwave remote sensing to dynamic testing of stay-cables," Remote Sensing, Vol. 2, No. 1, 36-51, 2010.
doi:10.3390/rs2010036
9. Kim, S. and C. Nguyen, "On the development of a multifunction millimeter-wave sensor for displacement sensing and low-velocity measurement," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 11, 2503-2512, 2004.
doi:10.1109/TMTT.2004.837153
10. Doronin, A. V., N. B. Gorev, I. F. Kodzhespirova, and E. N. Privalov, "Displacement measurement using a two-prove implementation of microwave interferometry," Progress In Electromagnetics Research C, Vol. 32, 245-258, 2012.
11. Tischer, F. J., Mikrowellen-Messtechnik, Springer-Verlag, Berlin, 1958.
doi:10.1007/978-3-642-87504-5
12. Chavez, S., Q.-S. Xiang, and L. An, "Understanding phase maps in MRI: A new cutline phase unwrapping method," IEEE Transactions on Medical Imaging, Vol. 21, No. 8, 966-977, 2002.
doi:10.1109/TMI.2002.803106
13. Hasar, U. C., J. J. Barroso, C. Sabah, and Y. Kaya, "Resolving phase ambiguity in the inverse problem of reflection-only measurement methods," Progress In Electromagnetics Research, Vol. 129, 405-420, 2012.
14. Silvia, M. T. and E. A. Robinson, Deconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas, Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York, 1979.