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 structures with a conventional charge-coupled device (CCD) camera. The motion of a micromechanical device actuated by high frequency sinusoidal forces (kHz range) is recorded at the fixed sampling rate of a camera (typically 28 frames/sec.) which is configured with a short shutter aperture time (1/5000 s). Provided a CCD sensor with sufficient sensitivity, lots of information are 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 systems with several kHz 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 oscillator system. Then, we show that our measurement method also provides useful information on the behavior of nonlinear systems. In particular, we can characterize systems' superharmonic and subharmonic resonances in a straightforward way