Ultra-sensitive Inclinometer via Critical Coupling of a Gravitational Compound Pendulum for Nanoradian Tilt Measurement

Accurate monitoring of the horizontal tilt is essential to suppress low-frequency noise in the measurement system of micro-thrust—a requirement for spacebased gravitational wave measurements. Unfortunately, the sensitivity of modern inclinometers is fundamentally limited by the noise floors of their physical and electronic components.To overcome these limitations is a new inclinometer design which consists of a gravitational compound pendulum and a displacement sensor that reach ultrahigh sensitivity. Our inclinometer implements a mechanical amplification mode of a quasi-zero stiffness system.By critically coupling the pendulum’s gravitational restoring moment with the stiffness of a flexure pivot, the system efficiently transforms minute tilt angles into measurable displacements. Theoretical modelling clarifies the mechanics of this angular amplification and guides our strategy for regulating the gravitational restoring moment.Experimental characterization demonstrates a resolution of 0.87 nrad over a 0–109 µrad range, the tunable amplification factor can be increased to exceeding 160 and the nonlinearity error as low as 1.18%. This compact and versatile design provides a strong motivation to deploy ultra-precision tilt measurement on advanced metrology and adaptive devices.