Multi-Mode Q Control in Multifrequency Atomic Force Microscopy

Various Atomic Force Microscopy (AFM) modes have emerged which rely on the excitation and detection of multiple eigenmodes of the microcantilever. The conventional control loops employed in multifrequency AFM (MF-AFM) such as bimodal imaging where the fundamental mode is used to map the topography and a higher eigenmode is used to map sample material properties only focus on maintaining low bandwidth signals such as amplitude and/or frequency shift. However, the ability to perform additional high bandwidth control of the quality (Q) factor of the participating modes is believed to be imperative to unfolding the full potential of these methods. This can be achieved by employing a multi-mode Q control approach utilizing positive position feedback. The controller exhibits remarkable performance in arbitrarily modifying the Q factor of multiple eigenmodes as well as guaranteed stability properties when used on flexible structures with collocated actuators and sensors. A controller design method based on pole placement optimization is proposed for setting an arbitrary on-resonance Q factor of the participating eigenmodes. Experimental results using bimodal AFM imaging on a two component polymer sample are presented.