Low-Frequency Vibration Measurement Based On The Concentric-Circle Grating Projection System

In low-frequency vibration measurement field, optical dynamic 3-D measurement based on camera-projector system is a novel approach. In this system, linear sinusoidal grating is the most common projection mode, which can meet the requirements of some vibration measurement. However, the dynamic measurement range of amplitude using the combination of linear grating and Fourier transform profilometry (FTP) is limited in some vibration measurement environments, because the linear fringe is periodic. To solve the problem, this article proposes a low-frequency vibration measurement method based on the concentric-circle grating camera-projector system and FTP. The center of the circle is traced dynamically and the coordinate system is transformed with the center of the circle as the origin. The phase distribution of concentric-circle grating is obtained by coordinate system transformation and FTP. By exploring the relationship between phase and relative height, the time-varying curve of the object surface height is recovered, which contains the vibration information. The experiments compare the measurement ability of the concentric-circle and linear grating. The results show that the linear grating and concentric-circle grating with the similar amplitude resolution have different amplitude measurement range. In this experiment, the maximum measurement range of linear grating is about 2.4 mm, while that of concentric-circle grating is more than about 3.9 mm. It means that the concentric-circle grating projection method can measure a large dynamic range of amplitude under the condition that the center of the circle can be traced, and solve the problem of amplitude limitation of linear grating in the use of FTP.