Operating a phase-locked loop controlling a high-Q tuning fork sensor for scanning force microscopy

TL;DR

This paper details the implementation and analysis of a phase-locked loop controlling a high-Q tuning fork sensor in a low-temperature scanning force microscope, emphasizing noise reduction and optimal feedback tuning.

Contribution

It introduces a linear control theory analysis of nested feedback in tuning fork sensors, enabling optimal feedback parameter determination from resonance data alone.

Findings

Nested feedback has a low pass response

Optimal feedback parameters can be derived from resonance data

System offers advantages over pure phase control

Abstract

The implementation of a tuning fork sensor in a scanning force microscope operational at 300 mK is described and the harmonic oscillator model of the sensor is motivated. These sensors exhibit very high quality factors at low temperatures. The nested feedback comprising the sensor, a phase locked loop and a conventional $z$-feedback is analyzed in terms of linear control theory and the dominant noise source of the system is identified. It is shown that the nested feedback has a low pass response and that the optimum feedback parameters for the phase-locked loop and the $z$-feedback can be determined from the knowledge of the tuning fork resonance alone regardless of the tip shape. The advantages of this system compared to pure phase control are discussed.