Calibration of the oscillation amplitude of quartz tuning fork-based force sensors with astigmatic displacement microscopy.

Quartz tuning forks and qPlus-based force sensors offer an alternative approach to silicon cantilevers for investigating tip-sample interactions in scanning probe microscopy. The high-quality factor (Q) and stiffness of these sensors prevent the tip from jumping to the contact, even at sub-nanometer amplitude. The qPlus configuration enables simultaneous scanning tunneling microscopy and atomic force microscopy, achieving spatial resolution and spectroscopy at the subatomic level. However, to enable precise measurement of tip-sample interaction forces, confidence in these measurements is contingent upon the accurate calibration of the spring constant and oscillation amplitude of the sensor. Here, we have developed a method called astigmatic displacement microscopy with picometer sensitivity.