Spiral scanning: An alternative to conventional raster scanning in high-speed Scanning Probe Microscopes I. A. Mahmood and S. O. R. Moheimani Abstract— A spiral scanning method for high-speed Atomic Force Microscopy (AFM) is described in this paper. In this method, the sample is scanned in a spiral pattern instead of the conventional raster pattern. A spiral scan can be produced by applying single frequency cosine and sine signals with slowly varying amplitudes to the x axis and y axis of an AFM scanner respectively. The use of the single tone input signals allows the scanner to move at high speeds without exciting the mechanical resonance of the device and with relatively small control efforts. These scan methods can be incorporated into most modern AFMs with minimal effort since they can be implemented in software using the existing hardware. Experimental results ob- tained by implementing this scanning method on a commercial AFM indicate that the obtained images are of a good quality and the profile of the calibration grating is well captured up to scan frequency of 120 Hz with a scanner where the first resonance frequency is 580 Hz. I. I NTRODUCTION AFM was invented by Binnig et al. in 1986 [1] based on their design of the scanning tunneling microscopy (STM) [2], [3]. The main use of AFM is for imaging sample surface topography with a very high precision down to the atomic scale. Since its invention, it has emerged as a standard tool in nanotechnology research. This is because it can be used on any sample surfaces and in any environment including air, various gases, vacuum and fluid. Additionally, the AFM can also operate at high and low temperature. The basic components of the AFM include a micro-cantilever with a sharp tip on the free end, a scanner and a laser-photodetector sensor. During operation, the tip of the micro-cantilever is brought very close to the sample surface at a distance of the order of a few nanometers, or less. At such a distance, the interactive forces that exist between the tip and the sample surface change the deflections of the micro-cantilever. These changes in the micro-cantilever are measured using the laser- photodetector sensor [4]. AFM images can be generated by scanning the tip at a constant height over the area of inter- est on the sample surface. During scan, the measurements from the photodetector will vary according to the sample topographic features. These measurements are recorded and plotted as a function of the scanner’s lateral positions to produce an AFM image of the sample surface. Acquisition of the AFM image in this manner is called constant-height mode. Today, the majority of commercially available AFMs use raster scans to image a sample’s surface. A raster scan is I. A. Mahmood and S. O. R. Moheimani are with School of Electrical En- gineering and Computer Science, The University of Newcastle, Callaghan, NSW 2308, Australia. Reza.Moheimani@newcastle.edu.au performed by moving the scanner along the x axis (fast- axis) in forward and reversed directions (line scan), and then moving the piezoelectric tube along the y axis (slow-axis) in a small step to reach the next line scan. This movement is attained by applying a triangular wave signal to the x axis and a slowly increasing staircase signal to the y axis of the scanner. In order to scan the sample at high speed, a high frequency triangular waveform needs to be used. A drawback of a triangular waveform is that it contains all odd harmonics of the fundamental frequency whose amplitudes attenuate as 1/n 2 , with n being the harmonic number [5]. If a fast triangular waveform is applied to the scanner, the harmonics will inevitably excite the mechanical resonance of the scanner. Consequently, this causes the scanner to vibrate and trace a distorted triangular waveform along the x axis which can significantly distort the generated image. To avoid this complication, the scanning speed of AFMs is often limited to about 10 - 100 times lower then the scanner’s first resonance frequency [6]. Recently, there has been significant interest in utilizing feedback control to deal with resonant nature of AFM nanopositioners, e. g. see [7] for an exhaustive overview of the literature, and [8], [9], [10], [11], [12], [13] for further related results. In this approach, a feedback controller is used to flatten the frequency response of the scanner, thus allowing for faster scans. However, as the scan frequency is increased closer to the mechanical bandwidth of the scanner in order to realize high-speed AFM, the positioning precision of the scanner deteriorate considerably. The closed-loop tracking of the triangular waveform typically results in the corners of these waveform to be rounded off and distorted. This is mainly due to the presence of the high frequency harmonics that are outside of the bandwidth of the closed- loop system. Consequently, AFM images generated at high speeds often demonstrate significant distortions especially around the edges of the images. It should be noted that, recently a few prototype laboratory AFMs have been developed that are capable of imaging a sample at, or close to, video-rates, [14], [15], [16], [17]. Such functionality is particularly important for observing dynamic processes of nanoscale biological specimens, e.g. cells and biopolymers. In order to achieve video rates, using a raster scanned AFM; the scan frequency has to be very high, close to 5 kHz or higher. However to attain such a scan frequency calls for complicated scanner design in order to make the scanner’s first resonance frequency much higher than the scan frequency. Additionally, high scanner’s first resonance frequency also implies low scan range [18]. 2010 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02, 2010 FrB08.4 978-1-4244-7425-7/10/$26.00 ©2010 AACC 5757