Image reconstruction for sub-sampled atomic force microscopy images using deep neural networks

Undersampling is a simple but efficient way to increase the imaging rate of atomic force microscopy (AFM). One major challenge in this approach is that of accurate image reconstruction from a limited number of measurements. In this work, we present a deep neural network (DNN) approach to reconstruct μ-path sub-sampled AFM images. Our network consists of two sub-networks, namely a RED-net and a U-net, in series, and is trained end-to-end from random images masked according to μ-path sub-sampling patterns. Using both simulation and experiments, the DNN is shown to yield better image quality than three existing optimization-based methods for reconstruction: basis pursuit, a variant of total variation minimization, and inpainting.

A review of demodulation techniques for multifrequency atomic force microscopy

This article compares the performance of traditional and recently proposed demodulators for multifrequency atomic force microscopy. The compared methods include the lock-in amplifier, coherent demodulator, Kalman filter, Lyapunov filter, and direct-design demodulator. Each method is implemented on a field-programmable gate array (FPGA) with a sampling rate of 1.5 MHz. The metrics for comparison include the sensitivity to other frequency components and the magnitude of demodulation artifacts for a range of demodulator bandwidths. Performance differences are demonstrated through higher harmonic atomic force microscopy imaging.

Resolution-Free Accurate DNA Contour Length Estimation from Atomic Force Microscopy Images

This research presented an accurate and efficient contour length estimation method developed for DNA digital curves acquired from Atomic Force Microscopy (AFM) images. This automation method is calibrated against different AFM resolutions and ideal to be extended to all different kinds of biopolymer samples, encompassing all different sample stiffnesses. The methodology considers the digital curve local geometric relationship, as these digital shape segments and pixel connections represent the actual morphology of the biopolymer sample as it is being imaged from the AFM scanning. In order to incorporate the true local geometry relationship that is embedded in the continuous form of the original sample, one needs to find this geometry counterpart in the digitized image. This counterpart is realized by taking the skeleton backbone of the sample contour and by using these digitized pixels' connection relationship to find its local shape representation. In this research, one uses the 8-connect Freeman Chain Code (CC) to describe the directional connection between DNA image pixels, in order to account for the local shapes of four connected pixels. The result is a novel shape number (SN) system derived from CC, which is a fully automated algorithm that can be applied to DNA samples of any length for accurate estimation, with efficient computational cost. This shape-wise consideration is weighted to modify the local length with great precision, accounting for all the different morphologies of the biopolymer sample, and resulted with accurate length estimation, as the error falls below 0.07%, an order of magnitude improvement compared to previous findings.

Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy

An important issue in the emerging field of multifrequency atomic force microscopy (MF-AFM) is the accurate and fast demodulation of the cantilever-tip deflection signal. As this signal consists of multiple frequency components and noise processes, a lock-in amplifier is typically employed for its narrowband response. However, this demodulator suffers inherent bandwidth limitations as high-frequency mixing products must be filtered out and several must be operated in parallel. Many MF-AFM methods require amplitude and phase demodulation at multiple frequencies of interest, enabling both z-axis feedback and phase contrast imaging to be achieved. This article proposes a model-based multifrequency Lyapunov filter implemented on a field-programmable gate array (FPGA) for high-speed MF-AFM demodulation. System descriptions and simulations are verified by experimental results demonstrating high tracking bandwidths, strong off-mode rejection and minor sensitivity to cross-coupling effects. Additionally, a five-frequency system operating at 3.5 MHz is implemented for higher harmonic amplitude and phase imaging up to 1 MHz.

Multi-actuation and PI control: a simple recipe for high-speed and large-range atomic force microscopy

High speed atomic force microscopy enables observation of dynamic nano-scale processes. However, maintaining a minimal interaction force between the sample and the probe is challenging at high speed specially when using conventional piezo-tubes. While rigid AFM scanners are operational at high speeds with the drawback of reduced tracking range, multi-actuation schemes have shown potential for high-speed and large-range imaging. Here we present a method to seamlessly incorporate additional actuators into conventional AFMs. The equivalent behavior of the resulting multi-actuated setup resembles that of a single high-speed and large-range actuator with maximally flat frequency response. To achieve this, the dynamics of the individual actuators and their couplings are treated through a simple control scheme. Upon the implementation of the proposed technique, commonly used PI controllers are able to meet the requirements of high-speed imaging. This forms an ideal platform for retroactive enhancement of existing AFMs with minimal cost and without compromise on the tracking range. A conventional AFM with tube scanner is retroactively enhanced through the proposed method and shows an order of magnitude improvement in closed loop bandwidth performance while maintaining large range. The effectiveness of the method is demonstrated on various types of samples imaged in contact and tapping modes, in air and in liquid.

Opportunities in high-speed atomic force microscopy

The atomic force microscope (AFM) has become integrated into standard characterisation procedures in many different areas of research. Nonetheless, typical imaging rates of commercial microscopes are still very slow, much to the frustration of the user. Developments in instrumentation for "high-speed AFM" (HSAFM) have been ongoing since the 1990s, and now nanometer resolution imaging at video rate is readily achievable. Despite thorough investigation of samples of a biological nature, use of HSAFM instruments to image samples of interest to materials scientists, or to carry out AFM lithography, has been minimal. This review gives a summary of different approaches to and advances in the development of high-speed AFMs, highlights important discoveries made with new instruments, and briefly discusses new possibilities for HSAFM in materials science.

High speed atomic force microscopy enabled by a sample profile estimator

In this paper, an estimation scheme for imaging in Atomic Force Microscopy (AFM) is presented which yields imaging rates well beyond the bandwidth of the vertical positioner and allows for high-speed AFM on a typical commercial instrument. The estimator can be applied to existing instruments with little to no hardware modification other than that needed to sample the cantilever signal. Experiments on a calibration sample as well as lambda DNA are performed to illustrate the effectiveness of this method. These show a greater than an order-of-magnitude improvement in the imaging rate.

High speed two-dimensional optical beam position detector

Disclosed is the design of a high speed two-dimensional optical beam position detector which outputs the X and Y displacement and total intensity linearly. The experimental detector measures the displacement from DC to 123 MHz and the intensity of an optical spot in a similar way as a conventional quadrant photodiode detector. The design uses four discrete photodiodes and simple dedicated optics for the position decomposition which enables higher spatial accuracy and faster electronic processing than conventional detectors. Measurements of the frequency response and the spatial sensitivity demonstrate high suitability for atomic force microscopy, scanning probe data storage applications, and wideband wavefront sensing. The operation principle allows for position measurements up to 20 GHz and more in bandwidth.

Local raster scanning for high-speed imaging of biopolymers in atomic force microscopy

A novel algorithm is described and illustrated for high speed imaging of biopolymers and other stringlike samples using atomic force microscopy. The method uses the measurements in real-time to steer the tip of the instrument to localize the scanning area over the sample of interest. Depending on the sample, the scan time can be reduced by an order of magnitude or more while maintaining image resolution. Images are generated by interpolating the non-raster data using a modified Kriging algorithm. The method is demonstrated using physical simulations that include actuator and cantilever dynamics, nonlinear tip-sample interactions, and measurement noise as well as through scanning experiments in which a two-axis nanopositioning stage is steered by the algorithm using simulated height data.

Reconstruction of a scanned topographic image distorted by the creep effect of a Z scanner in atomic force microscopy

We analyzed the illusory slopes of scanned images caused by the creep of a Z scanner in an atomic force microscope (AFM) operated in constant-force mode. A method to reconstruct a real topographic image using two scanned images was also developed. In atomic force microscopy, scanned images are distorted by undesirable effects such as creep, hysteresis of the Z scanner, and sample tilt. In contrast to other undesirable effects, the illusory slope that appears in the slow scanning direction of an AFM scan is highly related to the creep effect of the Z scanner. In the controller for a Z scanner, a position-sensitive detector is utilized to maintain a user-defined set-point or force between a tip and a sample surface. This serves to eliminate undesirable effects. The position-sensitive detector that detects the deflection of the cantilever is used to precisely measure the topography of a sample. In the conventional constant-force mode of an atomic force microscope, the amplitude of a control signal is used to construct a scanned image. However, the control signal contains not only the topography data of the sample, but also undesirable effects. Consequently, the scanned image includes the illusory slope due to the creep effect of the Z scanner. In an automatic scanning process, which requires fast scanning and high repeatability, an atomic force microscope must scan the sample surface immediately after a fast approach operation has been completed. As such, the scanned image is badly distorted by a rapid change in the early stages of the creep effect. In this paper, a new method to obtain the tilt angle of a sample and the creep factor of the Z scanner using only two scanned images with no special tools is proposed. The two scanned images can be obtained by scanning the same area of a sample in two different slow scanning directions. We can then reconstruct a real topographic image based on the scanned image, in which both the creep effect of the Z scanner and the slope effect of the sample have been eliminated. The slope effect of the sample should be eliminated so as to avoid further distortion after removal of the creep effect. The creep effect can be removed from the scanned image using the proposed method, and a real topographic image can subsequently be efficiently reconstructed.