Scan trajectories based on Lissajous curves have been studied previously in the field of medical imaging, such as in MRI devices. The key advantage of Lissajous scan trajectories is that they can be enabled using extremely narrow-band actuation signals, which do not excite any unwanted dynamics of the mechanical scanning device.

In a high-speed SPM, a pure single-tone frequency is used to actuate the SPM scanner in each of the two orthogonal in-plane axes. Owing to the interference between the two actuation frequencies, the scanner traces an elegant and smooth grid-like pattern. Also, with their narrow-band frequency spectrum, Lissajous trajectories can benefit from tailored scanner designs and control architectures with improved noise resiliency.

Multi-resolution effect

The curves possess a unique multi-resolution property (see image); they reveal the image area with a resolution that increases uniformly in time and space. This renders the Lissajous scan trajectories particularly attractive for modern high-speed interactive SPM applications.

Full details can be found in the journal Nanotechnology.