Areal measurement of vibration modes of a hemispherical shell resonator by deflectometry

The hemispherical shell resonator (HSR) is the core and sensitive part of a hemispherical resonator gyro. The geometrical accuracy and vibration properties of HSR determine the navigation performance of the system. A lack of areal measurement methods of vibration modes limits investigation of the kinetic mechanism and improvement in navigation performance. Consequently, an areal measurement method is developed based on deflectometry. The blurry spots on the image plane reflected from the vibrating HSR are extracted, and the blurring trajectories are obtained by the Wiener deconvolution method. The vibrating amplitude distribution of a standing wave mode is transformed into the swing angle distribution of normal vectors. The parameters of the vibration mode are fitted by the Levenberg-Marquardt method. This method can find widespread applications in the areal inspection of vibration modes.