Transfer function analysis of a surface coupled atomic force microscope cantilever system

Current methods to study atomic force microscope (AFM) cantilever dynamics use model simplification, or are based on the non-trivial solutions of the equation of motion. As an alternative method, transfer function analysis gives a complete description of system dynamics. In this work, we derive the exact, analytical expression for the multivariable infinite dimensional transfer function of a surface coupled cantilever system. The inputs of the system are punctual force at the tip end and distributed force along the cantilever, whereas the outputs are the position and slope at the tip end. A linearization of the surface coupling force is considered. Free cantilever and pinned end are considered as limit cases of the surface coupling. Frequency response Bode plots are shown, and transfer function infinite product expansion are obtained, which allow to derive the exact location of poles and zeros of the system, as a function of the level of surface coupling. This is shown in a root locus kind of plot. Transfer function analysis gives insight into optimal input/output configurations of the system and enables the possibility of model-based AFM operation