Frequency Modulation Atomic Force Microscopy (FM-AFM) typically operates in non-contact mode by tracking frequency shifts of a resonator caused by distance-dependent variations in atomic force gradients between the tip and the sample. To enhance sensitivity, prior studies have investigated weak coupling between the primary AFM resonator and a secondary resonator—either physical or virtual—to detect stiffness perturbations through changes in the system’s eigenmodes, often evaluated using the amplitude ratio of the coupled resonators. This paper introduces a novel virtual resonator configuration that enhances stiffness perturbation sensitivity by several orders of magnitude. The proposed system weakly couples a single-degree-of-freedom (DOF) real resonator with a virtual two-DOF resonator, forming a composite three-DOF spring-mass-damper system. The system is self-excited at its highest (third) natural frequency using adaptive resonant feedback control, which maintains constant oscillation amplitude of the real resonator despite parameter perturbations. Stiffness changes are inferred by monitoring the amplitude ratio between the first and third masses. Numerical simulations in MATLAB Simulink demonstrate that this virtual resonator configuration significantly outperforms existing methods, enabling precise detection of both large and subtle stiffness variations. These results highlight the effectiveness and potential of the proposed approach in advancing AFM-based stiffness sensing.

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Ultra-Sensitive Measurement of Stiffness Variation of a Resonator Using Adaptive Feedback Self-Excitation

  • Prasanjit Kumar Kundu,
  • Shyamal Chatterjee

摘要

Frequency Modulation Atomic Force Microscopy (FM-AFM) typically operates in non-contact mode by tracking frequency shifts of a resonator caused by distance-dependent variations in atomic force gradients between the tip and the sample. To enhance sensitivity, prior studies have investigated weak coupling between the primary AFM resonator and a secondary resonator—either physical or virtual—to detect stiffness perturbations through changes in the system’s eigenmodes, often evaluated using the amplitude ratio of the coupled resonators. This paper introduces a novel virtual resonator configuration that enhances stiffness perturbation sensitivity by several orders of magnitude. The proposed system weakly couples a single-degree-of-freedom (DOF) real resonator with a virtual two-DOF resonator, forming a composite three-DOF spring-mass-damper system. The system is self-excited at its highest (third) natural frequency using adaptive resonant feedback control, which maintains constant oscillation amplitude of the real resonator despite parameter perturbations. Stiffness changes are inferred by monitoring the amplitude ratio between the first and third masses. Numerical simulations in MATLAB Simulink demonstrate that this virtual resonator configuration significantly outperforms existing methods, enabling precise detection of both large and subtle stiffness variations. These results highlight the effectiveness and potential of the proposed approach in advancing AFM-based stiffness sensing.