Theory of phase spectroscopy in bimodal atomic force microscopy

We develop a theoretical formalism to describe bimodal atomic force microscopy (AFM) experiments. The theory relates observables such as amplitudes and phase shifts to physical properties of the tip-surface interaction. The theory is compatible with point-mass and continuous models of the cantilever-tip system. We explain the ability of the bimodal AFM to map compositional variations under the influence of very small conservative forces. This is achieved by representing the dependence of the phase shift or amplitude of one eigenmode with respect to the amplitude or phase shift of the other mode. The agreement obtained between the theory and the numerical simulations validates the theoretical formalism.