Multimode and multitone analysis of the dynamic mode operation of the Atomic Force Microscope

This article investigates the multimode model of the cantilever beam during probe based imaging. It develops a framework to quantify the effects of different material properties like dissipativity and stiffness in a near tapping mode operation of Atomic Force Microscope (AFM), which is the primary mode of imaging soft matter, when excitation consists of more than one sinusoids. Averaging theory forms an important basis and provides the theoretical foundations. Effect of dissipative and stiffness properties of the sample on the forces experienced by probe is modeled as changes in parameters of an equivalent linear time invariant model, of the cantilever-sample system. It is shown that this model can be extended to the case when multiple modes of the cantilever participate in the nonlinear interaction with the sample forces.