Optimization of Measurement of the Interaction Force Vector in Atomic Force Microscopy

The optimization of measurements of three spatial components of the probe–sample interaction force and the corresponding “ideal cantilever” displacement vector is considered. To determine these components using an atomic force microscope with the optical beam deflection scheme, it is necessary to measure the bending angles at least at two points on the rectangular cantilever, as well as the torsion angle at any of these points. It is proved analytically that one of the optimal points is the intersection of the probe axis with the cantilever plane. A technique for calculating the optimal position of the other point is developed. An experiment concerning mapping of the force and displacement vector is performed, and satisfactory agreement with the theory is achieved.