Measuring Cantilever Bending Modes and Displacements with sub-pm Resolution

Problem

Traditional optical beam deflection (OBD) methods used in AFMs require complex calibration steps and make indirect measurements of displacement. They are prone to inaccuracies, especially for torsional motion or higher-order bending modes, and risk damaging the cantilever during calibration.

Solution

The PICOSCALE Vibrometer, a raster-scanning Michelson interferometer, enables direct, contactless measurement of true displacement at any point on the cantilever with sub-pm resolution. Its built-in closed-loop positioners and software-controlled scanning provide both spatial mode visualization and quantitative data.

Implementation

• Vibrational modes were excited using a linear chirp from 0.5 Hz to 2 MHz.

• Cantilever displacements were measured via lock-in detection and visualized in 3D for both flexural and torsional modes (up to F5 and T3).

• Thermal vibrations were measured at the free ends of four cantilevers of increasing stiffness.

• The thermal noise method was used to derive spring constants using mean squared displacement.

Results

• The system clearly resolved individual resonance peaks and corresponding mode shapes.

• Thermal vibration measurements showed noise floors well below 1 pm, allowing calibration even for very stiff cantilevers.

• The setup enabled precise localization of the measurement spot—critical for accurate stiffness calibration.

Conclusion

SmarAct’s PICOSCALE Vibrometer offers a superior alternative to OBD by delivering direct, calibration-free displacement measurements. It supports accurate analysis of both flexural and torsional behavior and is ideal for non-invasive, high-precision spring constant calibration in AFM applications—even when cantilevers remain unpackaged or on wafers.