Direct design of closed-loop demodulators for amplitude modulation atomic force microscopy

A fundamental component of the z-axis feedback loop in amplitude modulation atomic force microscopy is the demodulator. It dictates both bandwidth and noise in the amplitude and phase estimate of the cantilever deflection signal. In this paper, we derive a linear time-invariant model of a closed-loop demodulator with user definable tracking bandwidth and sensitivity to other frequency components. A direct demodulator design method is proposed based on the reformulation of the Lyapunov filter as a modulated-demodulated controller in closed loop with a unity plant. Simulation and experimental results for a higher order Lyapunov filter as well as Butterworth and Chebyshev type demodulators are presented.