Design and control of a novel non-raster scan pattern for fast scanning probe microscopy

A significant difficulty associated with achieving high scan speeds in scanning probe microscopes is that the probe is required to scan the sample in a zig-zag (raster) pattern. The fast axis of the scanner is required to track a non-smooth signal that contains frequency components beyond its mechanical bandwidth. Therefore, fast raster scans lead to distortions in the obtained image. This paper proposes analysis and design methods for a nonlinear but smooth scan pattern, known as Lissajous pattern, which enables us to achieve high-quality images at very high scan speeds where raster scanning typically leads to significant image distortions. Criteria are also proposed and formulated for constructing Lissajous trajectory and calculating the parameters and resolution. Together with the implementation of an internal model controller for high precision tracking, the proposed method is successfully employed to scan images in high speeds using a low resonance frequency SPM platform of only 825 Hz.

I. INTRODUCTION

Since the invention of Scanning Probe Microscopy (SPM), rastering has been the standard method of scanning employed in these systems [1]. This is true about all variations of SPM, e.g. STM [2], AFM [3], SNONM [4], etc. Rastering has also been used in derivative technologies emerging from scanning probe microscopy. For example in probe storage systems, where sharp AFM-type probes are used to record digital information as tiny indentations on a storage medium, an array of probes is moved with respect to the storage medium in a raster pattern [5], [6]. One of the difficulties associated with rastering is the nature of the signals that must be tracked by the SPM's positioning mechanism. One axis is required to track a triangular waveform, while the orthogonal axis to that tracks either a ramp or a pseudo ramp signal. While this approach works well for slow scans, it fails to perform in a satisfactory manner during high-speed scans, which are becoming increasingly necessary in applications such as video-rate atomic force microscopy for investigation of biologically relevant samples with fast dynamics [7], [8]. The spectrum of a triangular signal consists of its fundamental frequency and all of its odd harmonics. Due to the finite mechanical bandwidth, and the highly resonant nature of SPM nanopositioners, tracking of such a signal is only possible at low frequencies. In an SPM the frequency of the raster signal is typically limited to 1% of its positioner's resonance frequency. This will ensure satisfactory tracking of high frequency components of the raster signal and will avoid exciting the mechanical resonance of the device. An immediate implication of this is the slow scan speed of SPMs, which results in a typical image taking a minute or longer to be developed. Fig. 1. Schematic of the Lissajous pattern at different time interval.