Video-Rate Lissajous-Scan Atomic Force Microscopy

Abstract

Abstract-Raster scanning is common in atomic force microscopy (AFM). The nonsmooth raster waveform contains highfrequency content that can excite mechanical resonances of an AFM nanopositioner during a fast scan, causing severe distortions in the resulting image. The mainstream approach to avoid scan-induced vibrations in video-rate AFM is to employ a highbandwidth nanopositioner with the first lateral resonance frequency above 20 kHz. In this paper, video-rate scanning on a nanopositioner with 11.3-kHz resonance frequency is reported using a smooth Lissajous scan pattern. The Lissajous trajectory is constructed by tracking two sinusoidal waveforms on the lateral axes of the nanopositioner. By combining an analog integral resonant controller (IRC) with an internal model controller, 1-and 2-kHz single tone set-points were successfully tracked. Highquality time lapsed AFM images of a calibration grating recorded at 9 and 18 frames/s without noticeable image distortions are reported.Index Terms-Atomic force microscopy, flexure-based, integral resonant control, internal model control, Lissajous-scan, nonraster scanning, video-rate.

High-stroke silicon-on-insulator MEMS nanopositioner: Control design for non-raster scan atomic force microscopy

“…However, the implementation of the Lissajous scanning method allows the scan speed to be increased significantly further above this value. 25,27 The Lissajous pattern is obtained in this case by driving the orthogonal axes of the nanopositioner with sinusoidal signals of different frequencies ( f x and f y ) and identical phase shifts (0 • ). In (2), the actuation signals V x and V y are presented for the X and Y axes, respectively.…”

“…However, there has been recent interest in the use of non-raster scan methods for AFM, which include the implementation of spiral, cycloid, and Lissajous scanning methods. [25][26][27][28][29] The Lissajous pattern is constructed through the use of two pure tone sinusoidal signals with slightly differing frequencies or phases as the reference signal for each axis. It has been shown that this scan method provides a number of distinct advantages compared with raster scanning including significantly increased scanning speeds, improved image quality, and a simpler control implementation.…”

Lissajous scan trajectory with internal model principle controller for fast AFM image scanning

“…To simplify the representation, define to be an unknown time-varying function of the system states, so that Eq. (9) can be simplified as: (10) Note that is a positive diagonal matrix since the piezoelectric coefficients and equivalent mass of the piezoelectric scanner are all positive values. Substituting Eq.…”

“…Therefore, selecting an appropriate scanning trajectory without inducing mechanical vibration is essential to achieving reasonable scanning speeds without sacrificing image quality. Several smooth scanning trajectories have been proposed to improve the scanning speeds in AFMs without any hardware modification, including spiral scanning [7] as well as sinusoidal [8], cycloid-like [9], and Lissajous scan paths [10]. In this research, in order to increase the scan rate of AFM, we design an internal model principle (IMP) advanced controller based on the dynamic characteristics of Lissajous trajectory to realize a fast AFM image scanning by reducing the mechanical vibration of the xy-piezoelectric canner.…”

A comparison of scanning methods and the vertical control implications for scanning probe microscopy

“…The primary advantages of raster scanning are the constant velocity and simple image reconstruction which is due to regularly sampled data appearing on a square grid. Similarly, the application of Lissajous scanning pattern in SPM can be found in [24][25][26]. Sinusoidal raster scanning involves driving the x-axis (fast axis) with a sinusoidal trajectory while shifting the sample in steps or continuously in the y-axis (slow axis) [14][15][16].…”