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.