Adaptive control of force microscope cantilever dynamics

Magnetic resonance force microscopy (MRFM) and other emerging scanning probe microscopies entail the detection of attonewton-scale forces. Requisite force sensitivities are achieved through the use of soft force microscope cantilevers as high resonant- Q micromechanical oscillators. In practice, the dynamics of these oscillators are greatly improved by the application of force feedback control computed in real time by a digital signal processor (DSP). Improvements include increased sensitive bandwidth, reduced oscillator ring up/down time, and reduced cantilever thermal vibration amplitude. However, when the cantilever tip and the sample are in close proximity, electrostatic and Casimir tip-sample force gradients can significantly alter the cantilever resonance frequency, foiling fixed-gain narrow-band control schemes. We report an improved, adaptive control algorithm that uses a Hilbert transform technique to continuously measure the vibration frequency of the thermally-excited cantilever and seamlessly adjust the DSP program coefficients. The closed-loop vibration amplitude is typically 0.05 nm. This adaptive algorithm enables narrow-band formally-optimal control over a wide range of resonance frequencies, and preserves the thermally-limited signal to noise ratio (SNR).