Time delay q-control of the microcantilever in dynamic atomic force microscopy

Active control of the oscillatory behavior of the cantilever used in atomic force microscopy (AFM) allows one to tune the quality factor to purpose. For experiments requiring a high force sensitivity an enhancement of the quality factor may be desirable whereas in time critical experiments additional damping may be needed. In order to control the quality factor a feedback signal is used that approximately corresponds to the time derivative of the system state within the bandwidth of interest. A time delay force feedback with a delay corresponding to a phase shift of Δφ=-π/2 at the frequency of interest can easily be implemented using digital signal processing. However, the cantilever is a dynamic system with multiple degrees of freedom. Thus, also higher eigenmodes of the cantilever have to be considered in the design of a time-delay feedback.