Microsc. Microanal. 23, 1121–1129, 2017 doi:10.1017/S1431927617012636


© MICROSCOPY SOCIETY OF AMERICA 2017


Improved Three-Dimensional (3D) Resolution of Electron Tomograms Using Robust Mathematical Data-Processing Techniques


Toby Sanders,1,* and Ilke Arslan2


1School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ 85287-1804, USA 2Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352, USA


Abstract: Electron tomography has become an essential tool for three-dimensional (3D) characterization of nanomaterials. In recent years, advances have been made in specimen preparation and mounting, acquisition geometries, and reconstruction algorithms. All of these components work together to optimize the resolution and clarity of an electron tomogram. However, one important component of the data-processing has received less attention: the 2D tilt series alignment. This is challenging for a number of reasons, namely because the nature of the data sets and the need to be coherently aligned over the full range of angles. An inaccurate alignment may be difficult to identify, yet can significantly limit the final 3Dresolution. In this work, we present an improved center- of-mass alignmentmodel that allows us to overcome discrepancies fromunwanted objects that enter the imaging area throughout the tilt series. In particular,we develop an approach to overcome changes in the totalmass upon rotation of the imaging area.We apply our approach to accurately recover small Pt nanoparticles embedded in a zeolite that may otherwise go undetected both in the 2D microscopy images and the 3D reconstruction. In addition to this, we highlight the particular effectiveness of the compressed sensing methods with this data set.


Key words: electron tomography, data processing, image alignment, image reconstruction, L1 regularization


INTRODUCTION Electron tomography is a nondestructive technique used to recover the three-dimensional (3D) morphology of nanoscale materials from a series of 2D projection images. These 3D tomograms provide a level of characterization and materials understanding that is not available with any other technique on this scale, and it is an integral part of the advancement of technology (Lui et al., 2005; Frank, 2006; Hayashida & Malac, 2016). Once the specimen has been prepared, electron tomo-


graphy can be separated into three components: (1) acquisition of a sequence of 2D projection images with an electron microscope; (2) alignment of the sequence of images using an image alignment technique; and (3) reconstruction of the 3D nanoscale imaging scene with a numerical algorithm. Although a great deal of well-founded research has been invested in reconstruction algorithmsin recent years (Batenburg et al., 2009; Goris et al., 2013; Leary et al., 2013), the resolution in the resultant electron tomogram is only as good as the weakest link of the three components. The alignment of the 2D projections is a critical component of the electron tomography process, and one that has been underdeveloped thus far. Traditionally the


alignment has been carried out by either cross-correlation or fiducial markers. With cross-correlation, each pair of neighboring projection images in the sequence are aligned relative to each


*Corresponding author. toby.sanders@asu.edu Received March 30, 2017; accepted September 25, 2017


other by selecting the shift where the cross-correlation peak is a maximum. This method is effective for producing an initial alignment for inspection of the tilt series, but is not rigorous enough to be effective in all cases. Although every set of neighboring images are likely to have only small alignment errors, a series of small cumulative errors can result in significant drift of the images over the entirety of the tilt series (Saxton et al., 1984), and therefore the cross- correlation approach has sometimes been regarded as unsuitable (Brandt et al., 2001). Optimal selection of the initial image in the tilt series for the cross-correlation has been proposed to reduce the destructive effect of this drift (Jones & Härting, 2013). Fiducial markers, on the other hand, generally


produce very accurate global alignments, which can be per- formed within the popularIMODsoftware package provided by the University of Colorado, Boulder (Kremer et al., 1996). This approach requires bright fiducial markers within the imaging area, which is often done artificially by introducing gold beads onto the sample (Masich et al., 2006). This approach is limited to cases where it is possible to deposit gold beads onto the specimen, and further when the gold beads will not interfere in the imaging of the nanostructure of interest. Other approaches have also been proposed for


alignment. One popular idea is alternating the reconstruc- tion and alignment (Houben & Bar Sadan, 2011), for instance by performing additional alignment by cross- correlation of the original projection images with projec- tion images of the reconstruction. The authors of this work


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