Calibration of oscillation amplitude in Dynamic Scanning Force Microscopy

TL;DR

This paper presents a method for precise calibration of oscillation amplitude in Dynamic Scanning Force Microscopy by relating thermal noise measurements to thermal energy, enabling accurate amplitude calibration.

Contribution

It introduces two novel procedures for calibrating oscillation amplitude based on thermal noise analysis and electronic signal processing in microscopy.

Findings

Thermal noise can be transferred to lower frequencies within electronics bandwidth.

Calibration methods accurately relate thermal noise to thermal energy $kT$.

Proposed procedures improve amplitude calibration precision in microscopy.

Abstract

A method to precisely calibrate the oscillation amplitude in Dynamic Scanning Force Microscopy is described. It is experimentally shown that a typical electronics used to process the dynamic motion of the cantilever can be adjusted to transfer the thermal noise of the cantilever motion from its resonance frequency to a much lower frequency within the typical bandwidth of the corresponding electronics. Therefore, the thermal noise measured in the in-phase ("phase") and out of phase ("amplitude") output of such an electronics can be related to the thermal energy $kT$. If the force constant of the cantilever is known then the oscillation amplitude can be precisely calibrated from the thermal power measured in these signals. Based on this concept, two procedures for the calibration of the oscillation amplitude are proposed. One is based on simple calculation of the Root Mean Square (RMS) measured at the outputs of the electronics used to process the dynamic motion of the cantilever, and the other one is based on analysis of the corresponding spectrum and the calculation of the quality factor, the resonance frequency and the signal strength.