Simultaneous mapping of phase and amplitude of MEMS vibrations by microscopic interferometry with stroboscopic illumination

Microscopic interferometry with monochromatic or white light stroboscopic illumination allows time-resolved measurements of out-of-plane MEMS vibration mode shapes with (sub)micron lateral resolution and a vertical resolution in the (sub)nanometer range. In this method, light pulses are synchronized with the sinusoidal excitation voltage to "freeze" microdevice vibrations, and automatic interferogram analysis techniques are used to get a 3D surface profile of the vibrating device. To obtain quantitative measurements of the vibration amplitudes, it is necessary to know in each point the phase delay between the light pulses and the microdevice vibrations. One way is first, to search manually for the phase delay tmax corresponding to an extremum of the vibration cycle, and then to perform two measurements at tmax and tmax+180°. The difference and the sum of these two measurements provide respectively the map of twice the vibration amplitudes and the map of twice the static deformations. Another way is to perform measurements while the phase delay is scanned in order to reconstitute the whole vibration cycle. We investigate herein an alternative method which enables, from only 3 measurements with different phase delays, a fully automatic mapping of the vibration phase, of the vibration amplitudes and of the static deformations. This method is illustrated by monochromatic and white light stroboscopic measurements on micromechanical devices. Factors affecting its accuracy such as the light pulse delay, the light pulse duty cycle and sample drift between acquisitions are analyzed from simulations and measurements.