Thanks to the ability to perform imaging and manipulation at the nanoscale, atomic force microscopy (AFM) has been widely used in biology, materials, chemistry, and other fields. However, as common error sources, vertical drift and illusory slope severely impair AFM imaging quality. To address this issue, this paper proposes a robust algorithm to synchronously correct the image distortion caused by vertical drift and slope, thus achieving accurate morphology characterization. Specifically, to eliminate the damage of abnormal points and feature areas on the correction accuracy, the laser spot voltage error acquired in the AFM scanning process is first utilized to preprocess the morphology height data of the sample, so as to obtain the refined alternative data suitable for line fitting. Subsequently, this paper proposes a novel line fitting algorithm based on sparse sample consensus, which accurately simulates vertical drift and slope in the cross-sectional profile of the topographic image, thereby achieving effective correction of the image distortion. In the experiments and applications, a nanoscale optical grating sample and a biological cell sample are adopted to perform topography imaging and distortion correction, so as to verify the ability of the proposed algorithm to promote AFM imaging quality.

In Part I of this diptych, we outline the parallel mode of differential phase contrast (TEM-DPC), which uses real-space distortion of Fresnel images arising from electrostatic or magnetostatic fields to quantify the phase gradient of samples with some degree of structural contrast. We present an analysis methodology and the associated software tools for the TEM-DPC method and, using them together with numerical simulations, compare the technique to the widely used method of phase recovery based on the transport-of-intensity equation (TIE), thereby highlighting the relative advantages and limitations of each. The TEM-DPC technique is particularly suitable for in situ studies of samples with significant structural contrast and, as such, complements the TIE method since structural contrast usually hinders the latter, but is an essential feature that enables the former. In Part II of this work, we apply the theory and methodology presented to the analysis of experimental data to gain insight into two-dimensional magnetic phase transitions.

In Part I of this diptych, we outlined the theory and an analysis methodology for quantitative phase recovery from real-space distortions of Fresnel images acquired in the parallel mode of transmission electron microscopy (TEM). In that work, the properties of the method, termed TEM-differential phase contrast (TEM-DPC), were highlighted through the use of simulated data. In this work, we explore the use of the TEM-DPC technique with experimental cryo-TEM images of a thin lamella of a low-temperature two-dimensional (2D) ferromagnetic material, K2CuF4, to perform two tasks. First, using images recorded below the ordering temperature, we compare the TEM-DPC method with the transport of intensity one for phase recovery and discuss the relative advantages the former has for experimental data. Second, by tracking the induction of the sample as it is driven through a phase transition by heating, we extract estimates for the critical temperature and critical exponent of the order parameter. The value of the latter is consistent with the 2D XY class, raising the prospect that a Kosterlitz–Thoules transition may have occurred.

Many approaches have been proposed in the literature to enhance the robustness of Convolutional Neural Network (CNN)-based architectures against image distortions. Attempts to combat various types of distortions can be made by combining multiple expert networks, each trained by a certain type of distorted images, which however lead to a large model with high complexity. In this paper, we propose a CNN-based architecture with a pre-processing unit in which only undistorted data are used for training. The pre-processing unit employs discrete cosine transform (DCT) and discrete wavelets transform (DWT) to remove high-frequency components while capturing prominent high-frequency features in the undistorted data by means of random selection. We further utilize the singular value decomposition (SVD) to extract features before feeding the preprocessed data into the CNN for training. During testing, distorted images directly enter the CNN for classification without having to go through the hybrid module. Five different types of distortions are produced in the SVHN dataset and the CIFAR-10/100 datasets. Experimental results show that the proposed DCT-DWT-SVD module built upon the CNN architecture provides a classifier robust to input image distortions, outperforming the state-of-the-art approaches in terms of accuracy under different types of distortions.

In this work, a new method to determine and correct the linear drift for any crystalline orientation in a single-column-resolved high-resolution scanning transmission electron microscopy (HR-STEM) image, which is based on angle measurements in the Fourier space, is presented. This proposal supposes a generalization and the improvement of a previous work that needs the presence of two symmetrical planes in the crystalline orientation to be applicable. Now, a mathematical derivation of the drift effect on two families of asymmetric planes in the reciprocal space is inferred. However, though it was not possible to find an analytical solution for all conditions, a simple formula was derived to calculate the drift effect that is exact for three specific rotation angles. Taking this into account, an iterative algorithm based on successive rotation/drift correction steps is devised to remove drift distortions in HR-STEM images. The procedure has been evaluated using a simulated micrograph of a monoclinic material in an orientation where all the reciprocal lattice vectors are different. The algorithm only needs four iterations to resolve a 15° drift angle in the image.

The aberration-corrected scanning transmission electron microscope has great sensitivity to environmental or instrumental disturbances such as acoustic, mechanical, or electromagnetic interference. This interference can introduce distortions to the images recorded and degrade both signal noise and resolution performance. In addition, sample or stage drift can cause the images to appear warped and leads to unreliable lattice parameters being exhibited. Here a detailed study of the sources, natures, and effects of imaging distortions is presented, and from this analysis a piece of image reconstruction code has been developed that can restore the majority of the effects of these detrimental image distortions for atomic-resolution data. Example data are presented, and the performance of the restored images is compared quantitatively against the as-recorded data. An improvement in apparent resolution of 16% and an improvement in signal-to-noise ratio of 30% were achieved, as well as correction of the drift up to the precision to which it can be measured.