System modelling of a lateral force microscope

To quantitatively analyse lateral force microscope measurements one needs to develop a model able to relate the photodiode signal to the force acting on the tip apex. In this paper we focus on the modelling of the interaction between the cantilever and the optical chain. The laser beam is discretized by a set of rays which propagates in the system. The analytical equation of a single ray's position on the optical sensor is presented as a function of the reflection's state on top of the cantilever. We use a finite element analysis on the cantilever to connect the optical model with the force acting on the tip apex. A first-order approximation of the constitutive equations are derived along with a definition of the system's crosstalk. Finally, the model is used to analytically simulate the 'wedge method' in the presence of crosstalk in 2D. The analysis shows how the torsion loop and torsion offset signals are affected by the crosstalk.