On the Sensitivity of Microwave Fabry–Perot Interferometers for Displacement Detection

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.