High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller

Abstract

This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM's piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.

Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

“…For example, a square lattice becomes rhombohedral and since this is a well-known structure one can draw the wrong conclusions [10]. To avoid this, spiral scanning approaches have been introduced in [17][18][19][20][21][22][23] for fast imaging using the AFM. In [24], a spiral scanning method is reported as a replacement for raster scanning and in this scanning method two challenges are mentioned: the first challenge is to achieve uniform distribution of sampling points in the 2-D plane and the second is to have a relatively constant linear speed.…”

“…2. A detail of spiral generation procedure can be found in [20,27]. The resultant spiral signal has a low-frequency content which moves slowly over time and regulates the tracking performance through continuous high-frequency imaging.…”

“…As a result, it limits the precision motion that can be obtained using the PTS [30]. In [20,21], an internal sinusoidal reference model-based optimal LQG controller is designed and implemented on an AFM to track a reference sinusoidal signal but it leads to a phase error due to the high frequency dynamics of the PTS. In this proposed scheme, a phase-locked loop (PLL)-based PI control is designed and implemented on the AFM to compensate for phase error between the X and Y positions.…”

Robust spiral positioning control of a piezoelectric tube scanner

“…PZM is widely used as a sole device in generating highprecision displacements and tracking systems such as AFMs, scanning tunneling microscopes (STMs), and diamond tunneling machine (DTM) [1]. The main features of the PZM are that it can generate a large force within a temperature range, repeats sub-nanometer motion without backlash, is generally free of wear and tear, has a fast response time, requires little maintenance, and is normally not affected by magnetic elds [2], [3]. Due to these properties PZMs are also widely used as sensors and actuators in noise and vibration control systems.…”

“…1. The details about generating the sinusoidal signal can be found in [2]. During spiral scanning two sine waves with relative phase shift of 90 degree are applied to the X-Y axes of the PTS to generate a spiral motion.…”