High Precision STEM Imaging by Non-Rigid Alignment and Averaging of a Series of Short Exposures

B. Berkels, R. Sharpley, P. Binev, A. Yankovich, F. Shi, P. Voyles, W. Dahmen
2012 Microscopy and Microanalysis  
Precision in both high-resolution TEM and STEM imaging is fundamentally limited by signal to noise, but STEM encounters practical limits before the fundamental limit is reached. Because of the serial acquisition of the image, instabilities in the position of the probe or the sample introduce random and systematic errors in the positions of the atomic columns. As a result, 1 pm precision has been reported in TEM [1], but the best reported precision in STEM is 5 pm [2] . Instabilities that are
more » ... ilities that are fast compared to frame time and have zero mean can be removed by averaging over many frames. However, averaging with only a rigid translation between frames to account for sample drift often causes a loss of resolution and therefore does not reach the highest possible precision. We have developed a non-rigid registration scheme for series of STEM images. The registration of an image pair, R and T, is the task of transforming the two images into a common coordinate system. Taking R as reference image, the goal is to find a deformation  of the image domain such that the composition of T and , T , agrees with R. Here we use a pixelwise, nonparametric mapping  to model the deformation. To find this deformation we employ a general variational framework. The objective functional is defined by a distance measure between T and R, plus a penalty regularizer on the deformation  which favors smooth . In order to cope with low signal-to-noise ratio images we use the negative of the normalized cross correlation (i.e. the normalized covariance) of T  and R as the distance measure. As the penalty term we use the integrated squared deviation of the Jacobian of  from the identity matrix, which is called "Dirichlet energy" of the displacement. To numerically solve the minimization problem we employ a multilevel approach from a coarse downsampling of the original images to the single-pixel level. At each level of resolution we use a regularized gradient descent based on the H 1 scalar product [4] with explicit time discretization and step size control [5] . Finally, the registration framework connecting two images is extended to handle the registration of hundreds of consecutive images back to a single reference image. Due to the extended acquisition time of such long series, the frames typically exhibit large scale drift plus local deformations, which requires special care. Our iterative process adjusts the transforms of all images T j  j to R in an attempt to minimize the combined penalty of all  j together. Figure 1 shows the results of non-rigid averaging of a series of frames of Si [112]. The images were acquired on the a probe-corrected FEI Titan at 200 kV with a 24.5 mrad convergence angle, a 25 pA
doi:10.1017/s1431927612003352 fatcat:ycc7zu5eubcdrmebcijx4ju4wm