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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]

For the past 50 years, open-ended coaxial lines were commonly employed for the determination of electromagnetic properties of various materials. In this article, the application of an open-ended hollow coaxial cable resonator (OE-HCCR) as a 1-D inclinometer for tilt measurements with 110 nanoradian (nrad) resolution is proposed and demonstrated. The coaxial cable resonant structure is formed between a metal post welded within the coaxial cable at the RF input end and the open end of the coaxial cable. A metal mass block, suspended in proximity to the open end in parallel is used to construct a pendulum structure, serving as the element responsive to a tilt. When the device is tilted, the distance between the mass block and the open end varies due to the displacement of the suspended pendulum. The change in the gap distance modifies the phase reflection coefficient associated with the open end, causing the resonance frequency of the coaxial cable resonator to change. By tracking the resonance frequency, the coaxial line resonator is effectively used as an inclinometer. The experimental results demonstrated that the novel device has a measurement resolution of 110 nrad over a range of 0–3 milliradians (mrad). Additionally, based on the same principle, a 2-D inclinometer based on two perpendicularly aligned OE-HCCRs, useful for simultaneous tilt measurements in two orthogonal dimensions is demonstrated. The open-ended coaxial cable resonator-based inclinometer holds several advantages, including high resolution, robustness, cost effectiveness, ease of signal interrogation, and user-configurable sensitivity and dynamic range. [ABSTRACT FROM AUTHOR]