Sub-Nyquist sampling based amplitude demodulation for resonant-mode atomic force microscopy

In resonant modes of atomic force microscopy (AFM), such as tapping mode and multifrequency mode, the cantilever typically oscillates at its fundamental or higher-order resonance, with resonance frequencies reaching several hundred kilohertz. Among various amplitude demodulation methods, the lock-in amplifier is widely used in AFM due to its superior signal-to-noise ratio and strong immunity to interference. However, conventional lock-in amplifiers require high-speed, high-resolution analog-to-digital converters (ADCs) to oversample the high-frequency vibration signal, thereby imposing huge demands on fast data acquisition and real-time processing hardware. However, in most AFM applications, the effective bandwidth contained in the cantilever amplitude variations is much lower than the carrier vibration frequency, typically on the order of several kilohertz. To address this characteristic, a sub-Nyquist sampling-based amplitude demodulation method for resonant-mode AFM is proposed in this work. By exploiting the sub-Nyquist sampling principle, accurate demodulation of the cantilever amplitude is achieved at a sampling rate significantly lower than the Nyquist rate of the vibration signal. The reduced sampling rate provides additional computational time within each sampling period, enabling real-time amplitude demodulation without the need for high-speed ADCs and processing hardware. The proposed method is validated through force-distance curve measurements and imaging experiments. The extracted force-curve characteristics and image quality show good agreement with those obtained using a conventional lock-in amplifier. These results demonstrate that the method provides a practical and cost-effective approach for reducing hardware complexity in resonant-mode AFM systems.