Extracting Interaction Forces and Complementary Observables in Dynamic Probe Microscopy

We address the problem of interaction sensing in dynamic probe microscopy. An iterative method is presented for extracting the laws of interaction from dynamically measured observables. The method exploits the fact that in the limit of negligible anharmonicity of the tip motion, the observables are related to corresponding force laws via linear convolution operators involving weakly divergent kernels, which represent weighted monopole or dipole moments of the interaction probed by the tip.