Topography and force imaging in atomic force microscopy by state and parameter estimation

A novel imaging method for atomic force microscopy based on estimation of state and parameters is presented. The cantilever dynamics is modeled as a linear system augmented by the tip-sample interaction force. The states of this augmented system are observed. The tip-sample force function is based on the Lennard-Jones potential with a nonlinearly parameterized unknown topography parameter. By estimating this parameter together with the tip-sample force using a nonlinear observer approach, the topography of the sample can be found. The observer and parameter estimator is shown to be exponentially stable. Simulation results are presented and compared to a more conventional extended Kalman filter.