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Microwave interferometers have been attractive devices for high-precision measurements of displacement-related physical quantities in a variety of scientific and engineering applications. However, due to the long operating wavelength, the displacement measurement resolution of microwave interferometers is limited to the micrometer scale. In this article, we propose and demonstrate a novel technology based on microwave interferometry for displacement measurements with potential picometer resolution. An open-ended (OE) transmission line resonator based on a homemade hollow coaxial cable is explored in proof-of-concept numerical and experimental investigations. The technique involves two stages of displacement sensitivity amplification: one is the open end-based phase sensitivity amplification, and the other is the destructive interference-based phase sensitivity amplification. We experimentally demonstrate a wavelength sensitivity amplification factor of 1800 through spectral interrogation where only the open end-based amplification is involved, and a phase sensitivity amplification factor of 1.4 million through phase interrogation where both the open end-based amplification and the destructive interference-based phase shift amplification are involved, i.e., two-stage phase shift amplified microwave interferometry (TPAMI). The numerical investigations and the experimental results match well. [ABSTRACT FROM AUTHOR]

This article presents an ultrasensitive open-ended hollow coaxial cable resonator (OE-HCCR) that was trained to detect impact events that occurred in the surrounding space through machine learning (ML) techniques. First, inspired by the well-known mass-based accelerometer, for the first time, we propose an OE-HCCR-based accelerometer with the addition of an inertial mass block as the element responsive to acceleration. The OE-HCCR is formed by a metal shorting post welded at the RF input end and the open end of the cable. The instantaneous displacements of the mass block mounted at the endface of the cable due to accelerations lead to variations of the gap distance between the mass block and the endface of the coaxial line, which can be accurately metered by the coaxial resonating structure. Impact events that occur in the surrounding space of the OE-HCCR result in vibrations transmitted to the OE-HCCR system and thereby measured by the OE-HCCR. Second, we demonstrated that employing ML algorithms to analyze the transient responses from the OE-HCCR makes unambiguous mappings between the transient responses of the OE-HCCR and the sources of vibrations possible, due to the ultrahigh sensitivity of the OE-HCCR and the spatial anisotropy of matter in the surrounding space. The preliminary results demonstrate the feasibility of using ML-assisted OE-HCCR system for locating impact events and recognizing different impactor implements that caused the impact events. [ABSTRACT FROM AUTHOR]