Dynamic Calibration of Higher Eigenmode Parameters of a Cantilever in   Atomic Force Microscopy Using Tip-Surface Interactions
  We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever responsivity) of a cantilever. The method is based on the tip-surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip-surface interaction. The calibration method proposed requires a single-point force measurement using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode. 
Stanislav S. Borysov, Daniel Forchheimer, David B. Haviland
physics.ins-det cond-mat.mes-hall