Friday, March 20, 1998
4:00 - 5:00 pm
1200 EECS
In this paper, the most widely used mode of imaging where the cantilever is oscillated at its resonant frequency is studied. A nonlinear dynamic model for the cantilever-sample system is developed. Utilizing this model it is shown that the system exhibits periodic motion with period equal to that of the forcing. Using the Poincare map technique asymptotic orbital stability of the periodic motion is established. Furthermore, the sensitivity of the Poincare map's fixed point with respect to the cantilever-sample distance is obtained. The fixed point consists of the amplitude and the "phase" of the periodic orbit, which can be measured from the cantilever vibration. The sensitivity study of the fixed point has shown that the amplitude and the sine of the phase of the orbit vary linearly with respect to the cantilever-sample distance. Experiments conducted on a silicon cantilever have shown that the cantilever motion is indeed periodic with period equal to that of the forcing. Furthermore, the variation of the amplitude and sine of the phase were recorded as the sample was moved towards the cantilever. The experimental data confirms the theoretically predicted linear behavior of the quantities with respect to the cantilever-sample distance. This linear behavior provides an attractive and simple method for imaging with very high resolutions. Also, these results can be used to improve the performance of commercially available microscopes.
© UofM College of Engineering Control Research Group -
December 1997
bethi@umich.edu