Atomic force microscope (AFM) is an idealized tool to measure the physical and chemical properties of the sample surfaces by reconstructing the force curve, which is of great significance to materials science, biology, and medicine science. Frequency modulation atomic force microscope (FM-AFM) collects the frequency shift as feedback thus having high force sensitivity and it accomplishes a true noncontact mode, which means great potential in biological sample detection field. However, it is a challenge to establish the relationship between the cantilever properties observed in practice and the tip-sample interaction theoretically. Moreover, there is no existing method to reconstruct the force curve in FM-AFM combining the higher harmonics and the higher flexural modes. This paper proposes a novel method that a full force curve can be reconstructed by any order higher harmonics of the first two flexural modes under any vibration amplitude in FM-AFM. Moreover, in the small amplitude regime, short range forces are reconstructed more accurately by higher harmonics analysis compared with fundamental harmonics using the Sader-Jarvis formula.
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