The tip-sample interaction force measurements in atomic force microscopy (AFM) provide information about materials' properties with nanoscale resolution. The T-shaped cantilevers used in Torsional-Harmonic AFM allow measuring the rapidly changing tip-sample interaction forces using the torsional (twisting) deflections of the cantilever due to the off-axis placement of the sharp tip. However, it has been difficult to calibrate these cantilevers using the commonly used thermal noise-based calibration method as the mechanical coupling between flexural and torsional deflections makes it challenging to determine the deflection sensitivities from force-distance curves. Here, we present thermal noise-based calibration of these T-shaped AFM cantilevers by simultaneously analyzing flexural and torsional thermal noise spectra, along with deflection signals during a force-distance curve measurement. The calibration steps remain identical to the conventional thermal noise method, but a computer performs additional calculations to account for mode coupling. We demonstrate the robustness of the calibration method by determining the sensitivity of calibration results to the laser spot position on the cantilever, to the orientation of the cantilever in the cantilever holder, and by repeated measurements. We validated the quantitative force measurements against the known unfolding force of a protein, the I91 domain of titin, which resulted in consistent unfolding force values among six independently calibrated cantilevers.

中文翻译：

---

使用热噪声法校准T形原子力显微镜悬臂梁

原子力显微镜 (AFM) 中的尖端与样品相互作用力测量以纳米级分辨率提供有关材料特性的信息。扭转谐波 AFM 中使用的 T 形悬臂允许使用由于尖锐尖端的离轴放置而产生的悬臂扭转（扭转）偏转来测量快速变化的尖端与样品相互作用力。然而，使用常用的基于热噪声的校准方法来校准这些悬臂很困难，因为弯曲和扭转偏转之间的机械耦合使得从力-距离曲线确定偏转灵敏度变得具有挑战性。在这里，我们通过同时分析弯曲和扭转热噪声谱以及力-距离曲线测量期间的偏转信号，对这些 T 形 AFM 悬臂进行基于热噪声的校准。校准步骤与传统的热噪声方法相同，但计算机执行额外的计算以考虑模式耦合。我们通过确定校准结果对悬臂上激光光斑位置、悬臂支架中悬臂方向的敏感性以及重复测量来证明校准方法的稳健性。我们根据已知的蛋白质（肌联蛋白 I91 结构域）的展开力验证了定量力测量结果，这导致六个独立校准的悬臂梁之间的展开力值一致。