Improved 3D Resolution of Electron Tomograms 1127


electron tomography. Future work may include having these parameters variable and developing an automated adaptation.


ALIGNMENT ALGORITHMS APPLIED TO ELECTRON TOMOGRAPHY DATA


We demonstrate the advancementsmade in the resolution of the tomogram using our alignment methods through a tilt series of a zeolite. The zeolite sample is ZSM-5 (Si:Al=400) with nanosized Pt particles in the pores. The projection images were acquired on an FEI Tecnai scanning/transmis- sion electron microscope (S/TEM; FEI Company, Hillsboro, OR, USA) operated at 200 keV in STEM mode. The align- ment was performed using the methods reported in this paper. The reconstructions were performed over 512 ×512 ×1,016 mesh using simultaneous iterative recon- struction technique (SIRT) and TV regularization, with voxel sizes of 0.98× 0.98 ×0.47 nm, and the visualization was performed in TomViz (TomViz software, V. 1.2, tomviz.org). The projection images were acquired over a 138° angular


range at 2° angle increments for a total of 70 images, with a pixel size of 0.47nm. One projection image at a relative angle of −10° is shown in Figure 3a. A standard cross-correlation of the projection images was performed as an initial alignment. Then new shifts for the alignment were determined based on our model. These shifts were determined for all values 3≤‘≤70, where ‘ is the sequence length as described in


fourth section. The number of cross-sections selected for the alignment (or the size of Λj in the previous section) was taken to be 1% of the total number of cross-sections. Comparisons with conventional imaging techniques are


given in Figure 2. These cross-sectional images also give us a closer look at the accuracy of our approach. As indicated in the images, we compare our results with cross-correlation approach and the TV model with the classical least squares reconstruction approach, often referred to as the SIRT. Evident in these images, the cross-correlation alignment yields a roughly aligned data set which is sufficient to resolve the zeolite particle, but not sufficient to resolve the Pt parti- cles, which are about ~5nm in diameter. The correction shifts in our alignment approach, as a function of the chosen sequence length shown Figure 3i, indicate a total correction of up to 8–10nm. Thus, the Pt particles that the cross- correlation alignment did “recover,” as seen in the rightmost images are distorted and elongated. If the alignment were any worse, the Pt particles would likely be unresolved. The shift values for sequence lengths of less than about 10 are significantly different from the others, and in this case do not produce useful results. Generally speaking, the right sequence length can be determined by experimentation, as shown in the next section. Although the TV model has been shown superior to


SIRT in both electron tomography and many other applications (Binev et al., 2012; Chen et al., 2013; Leary et al., 2013), the particular effect that we observe here is quite


Figure 3. Three-dimensional imaging of zeolite nanoparticle from our center-of-mass alignment and total variation reconstruction model. a: Projection image at −10. b: Volume rendering of the reconstruction. c: Volume rendering of the Pt nanoparticles embedded in the zeolite. d: Projection image at 10° and magnified small patches in (e) and (g) give a closer look at the projected Pt particles. f,h: Show the approximate reconstruction of the particles visible in (e) and (g). i: Shows the shift values for each projection angle as a function of the sequence length.


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