The atomic force microscope (AFM) is a high-resolution measurement tool for sample topography and material properties in nano-scale and micro-scale research. The dynamics of the cantilever probe in AFM is affected by the intrinsically nonlinear interaction between the probe tip and the sample. Previous works have shown that in off-resonance excited intermittent-contact AFM, a period-doubling bifurcation occurs as a result of the nonlinearity. The sub-harmonic amplitude of the response is used as the source of contrast to measure the effective modulus of the sample. This paper further investigates the performance of this proposed measurement method on more complicated 1-D samples and 2-D samples. The nonlinear relationship between the sub-harmonic amplitude and the tip-sample separation raises new challenges to the traditional PI controller. The design of the controller is revisited and modified in this paper to improve measurement accuracy.

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