Non-raster scanning in AFM
The atomic force microscope is one of the most versatile instruments for studying systems with nanometer-scale features. (For an introduction and background to AFM, see the atomic force microscopy lecture on nanohub.org. For a controls-oriented introduction, see the paper Abramovitch, Andersson, Pao, and Schitter, “A tutorial on the dynamics, control, and mechanisms of atomic force microscopes,” Proc. American Control Conference, pp. 3488-3502, 2007.)
The standard method for using an AFM to study dynamic phenomena is the use of time-lapse imaging. This approach is severely limited by the poor temporal resolution of ther device. Images are formed pixel-by-pixel and typically take on the order of seconds to minutes to acquire. This is far slower than the time scales of many systems of interest, particularly in molecular biology. As a result there is a broad interest in developing high-speed AFM (see, e.g., the 2008 review article of Schitter and Rost in Materials Today). Most ongoing efforts focus on novel actuator design, modern control-theoretic methods, or combinations of the two.
We take a completely different, and complementary, approach that centers on replacing the standard raster-scan pattern with more rational sampling schemes. As illustrated in the figure below, we seek to use the tip measurements to estimate an element of the sample and, based on this estimate, to steer the tip in a feedback fashion.
To date we are focusing on string-like samples and particularly on biopolymers such as DNA, actin, and microtubules. In addition to being interesting in their own right, there is a wealth of dynamic phenomena that occur along such samples, including the motion of molecular motors, of enzymes, and of proteins. The fundamental idea is to model the sample as a planar curve. The spatial evolution of such a curve is driven by the local value of tangent vector and of the curvature. By estimating these values based on the acquired measurements, the tip can be steered such that is stays in the vicinity of the sample. Nearly all the measurements, then, are of the sample itself rather than of the substrate. The raster-scan pattern is replaced by a local raster-scan in which the tip is dithered across the sample as illustrated below. The scheme provides for user-adjusted parameters: the amplitude (corresponding to the usual notion of image size) and the spatial frequency (corresponding to the usual notion of image resolution).
Below we show the results of these scheme when applied (in simulation) to a sample of DNA. The left image shows the tip trajectory (bright white) superimposed on a standard raster-scan image. Note the most of the standard image is of (completely uninteresting) substrate. The right image shows the data acquired along the tip trajectory.
Work to date has included theoretical development of the algorithm, including guarantees of complete imaging of the strand as well as early proof-of-concept experiments. We are currently implementing the scheme.
- P.I. Chang and S.B. Andersson, “A maximum-likelihood detection scheme for rapid imaging of string-like samples in atomic force microscopy,” IEEE Conference on Decision and Control, pp. 8290-8295, 2009. download
- P. Chang and S.B. Andersson, “Smooth trajectories for imaging string-like samples in AFM: A preliminary study,” in Proceedings of the American Control Conference, pp. 3207-3212, 2008.
- S.B. Andersson, “Curve tracking for rapid imaging in AFM,” IEEE Transactions on Nanobioscience, vol. 6, no. 4, pp. 354-361, 2007. link to journal