Temporally aliased video microscopy: an undersampling method for in-plane modal analysis of microelectromechanical systems

A simple optical method is proposed for performing in-plane experimental modal analysis of micromachined struc- tures with a conventional charge-coupled device (CCD) camera. The motion of a micromechanical device actuated by high- frequency sinusoidal forces (kilohertz range) is recorded at the fixed sampling rate of a camera (typically, 28 frames/s) which is configured with a short shutter aperture time (1/5000 s). Provided a CCD sensor with sufficient sensitivity, much information is contained in the video on the dynamics of the vibrating system despite the limited frame rate. Taking advantage of the theory of undersampling, we show that the dynamics of the systems with several-kilohertz bandwidth can be retrieved very easily. For demonstration purposes, we first study a push–pull electrostatic comb-drive actuator, which is a well-known damped harmonic os- cillator system. Then, we show that our measurement method also provides useful information on the behavior of nonlinear systems. In particular, we can characterize the systems’ superharmonic and subharmonic resonances in a straightforward way