Three-probe microwave interferometry for measuring displacement of mechanical objects with account for antenna reflectivity




This paper addresses the problem of displacement measurement by a three-probe implementation of microwave interferometry in cases where the reflection coefficients of the object under measurement (target) and the antenna are comparable. The paper presents a three-probe displacement measurement method that accounts for the antenna reflection coefficient. In this method, the target displacement is determined from two quadrature signals using a phase unwrapping technique. The expressions for the quadrature signals include the unknown magnitude of the target reflection coefficient. To determine this quantity, an equation that relates it to the detector currents and the antenna reflection coefficient is derived. It is shown that the magnitude of the target reflection coefficient is given by the smaller positive root of this equation provided that the sum of the target and the antenna reflection coefficient magnitudes is no greater than one. Because of the smallness of the antenna reflection coefficient, this condition is almost always met in free-space measurements. To verify the proposed method, determining the displacement of a target executing a sine vibratory motion was simulated. The simulation showed that if the target and the antenna reflection coefficients are comparable, the method offers a several-fold reduction in the displacement determination error in comparison with the case where the antenna reflection coefficient is ignored even in the presence of a marked noise component in the detector currents. The proposed method may be used in the development of microwave displacement sensors.


N. Toujani, A. B. S. Alquaity, A. Farooq, “Electron density measurements in shock tube using microwave interferometry,” Rev. Sci. Instruments, vol. 90, no. 554706, 2019, doi:

E. N. Ivanov, M. E. Tobar, R. A. Woode, “Microwave interferometry: application to precision measurements and noise reduction techniques,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 45, no. 6, pp. 1526–1536, 1998, doi:

G. A. Luk’yanchuk, “Analysis of interference-type measurer of directional coupler directivity,” Radioelectron. Commun. Syst., vol. 48, no. 8, pp. 44–49, 2005, doi:

A. Cunha, E. Caetano, “Dynamic measurements on stay cables of cable-stayed bridges using an interferometry laser system,” Exp. Tech., vol. 23, no. 3, pp. 38–43, 1999, doi:

K. Kaito, M. Abe, Y. Fujino, “Development of non-contact scanning vibration measurement system for real-scale structures,” Struct. Infrastruct. Eng., vol. 1, no. 3, pp. 189–205, 2005, doi:

A. B. Mehrabi, “In-service evaluation of cable-stayed bridges, overview of available methods and findings,” J. Bridg. Eng., vol. 11, no. 6, pp. 716–724, 2006, doi:

J. J. Lee, M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT E Int., vol. 39, no. 5, pp. 425–431, 2006, doi:

O. O. Drobakhin, “Realization of a method for synthesizing the envelope of a radio-frequency pulse based on amplitude measurements made with a horn antenna,” Russ. J. Nondestruct. Test., vol. 35, no. 7, pp. 545–551, 1999.

O. V. Pylypenko, A. V. Doronin, N. B. Gorev, I. F. Kodzhespirova, “Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement,” Tech. Mech., vol. 2018, no. 1, pp. 5–12, 2018, doi:

S. Kim, C. Nguyen, “A displacement measurement technique using millimeter-wave interferometry,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1724–1728, 2003, doi:

S. Kim, C. Nguyen, “On the development of a multifunction millimeter-wave sensor for displacement sensing and low-velocity measurement,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2503–2512, 2004, doi:

M. V. Andreev, O. O. Drobakhin, D. Y. Saltykov, “Complex reflection coefficient determination via digital spectral analysis of multiprobe reflectometer output signals,” in 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2017, pp. 170–175, doi:

S. C. Cripps, “Microwave bytes - VNA tales,” IEEE Microw. Mag., vol. 8, no. 5, pp. 28–44, 2007, doi:

M. V. Andreev, O. O. Drobakhin, D. Y. Saltykov, “Techniques of measuring reflectance in free space in the microwave range,” in 2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW), 2016, pp. 1–4, doi:

A. Maslovskiy, M. Legenkiy, “Experimental measuring of bright spots on complex shape object surface with decomposition method,” in 2018 9th International Conference on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS), 2018, pp. 181–184, doi:

A. V. Doronin, N. B. Gorev, I. F. Kodzhespirova, E. N. Privalov, “Displacement measurement using a two-probe implementation of microwave interferometry,” Prog. Electromagn. Res. C, vol. 32, pp. 245–258, 2012, doi:

M. T. Silvia, E. A. Robinson, Deconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas. Amsterdam–Oxford–New York: Elsevier Scientific Publishing Company, 1979, uri:

Schematic of three-probe measurements





Research Articles