Breaking the Crowther limit: Combining depth-sectioning and tilt tomography for high-resolution, wide-field 3D reconstructions

Abstract

To date, high-resolution (< 1 nm) imaging of extended objects in three-dimensions (3D) has not been possible. A restriction known as the Crowther criterion forces a tradeoff between object size and resolution for 3D reconstructions by tomography. Further, the sub-Angstrom resolution of aberrationcorrected electron microscopes is accompanied by a greatly diminished depth of field, causing regions of larger specimens (> 6 nm) to appear blurred or missing. Here we demonstrate a three-dimensional imaging method that overcomes both these limits by combining through-focal depth sectioning and traditional tilt-series tomography to reconstruct extended objects, with high-resolution, in all three dimensions. The large convergence angle in aberration corrected instruments now becomes a benefit and not a hindrance to higher quality reconstructions. A through-focal reconstruction over a 390 nm 3D carbon support containing over one hundred dealloyed and nanoporous PtCu catalyst particles revealed with sub-nanometer detail the extensive and connected interior pore structure that is created by the dealloying instability. IntroductionWith electron beams smaller than the bond length of hydrogen, aberration-corrected scanning transmission electron microscopes (STEM) can image materials with resolutions below the shortest bond lengths in nature 1 . However, these atomic resolution images are only 2D projections of a specimen. In order to determine the full 3D structure, one must acquire a series of STEM images over a range of specimen tilts 2,3 . Unfortunately, the resolution of a 3D STEM tomogram is degraded by missing information that is a consequence of the restricted specimen tilt range and finite tilt increments. While reconstructions of small objects have been reported at atomic resolution 4,5 , resolution places fundamental limitations to object-size. For larger objects (> 20 nm), the Crowther condition 1,6 discussed below typically limits volumetric resolutions of electron tomography to roughly 1 nm-twenty times worse than the best resolution in 2D projections. In addition, high-resolution (< 1 nm) tomography of general extended objects, to date, has not been possible with aberration-corrected instruments because the depth-of-field (5 -10 nm) of aberration-corrected STEMs is smaller than most objects of interest today 7 . High-resolution 3D reconstruction of extended objects, i.e. those larger than the depth-of-field, requires collecting information beyond a traditional tilt series. Here we present through-focal tomography that combines depth sectioning and traditional tilt-tomography to reconstruct extended objects, with highresolution, in three-dimensions. This combined approach fills in missing 3D information by acquiring a through-focal image series at each specimen tilt (Fig. 1)-decoupling the limiting Crowther relationship between 3D resolution and object size.For traditional (S)TEM tomography the images at every tilt-angle must correspond to a perfect projection of the original object to fulfill the "projection requ...

Electron Tomography: A Three‐Dimensional Analytic Tool for Hard and Soft Materials Research

“…The second option utilizes the full focal series at each tilt angle to combine both high-lateral-resolution information and depth information at every tilt angle. [82,83] The amount of information sampled about the object along the projection direction is directly related to the convergence semi-angle of the STEM (±3° for α = 30 mrad), which provides the additional advantage that fewer tilting angles are required to fully sample the object. The various tilt series are combined in Fourier space using bilinear extrapolation and per-pixel weighting of all spatial frequencies to compensate for over sampling.…”

“…The ability to determine the large-scale distribution of the nanoparticles and their internal porosity provides statistical information relevant to catalytic properties of the system from a single tomography data set using focus and tilt. [83] …”

Combined Tilt- and Focal-Series Tomography for HAADF-STEM

“…The method was evaluated on a whole-mount macrophage cell with gold nanoparticles coated with native low-density lipoprotein (LDL) taken up into vesicles [15][16][17][18][19][20][21][22] (Figure 2). The cell had a total thickness of about 1 µm.…”

Reverse Monte Carlo reconstruction algorithm for discrete electron tomography based on HAADF‐STEM atom counting

“…In order to limit the beam damage and the number of projections, electron tomography methods requiring a single specimen orientation without prior knowledge are under development (Jia et al, 2014), such as depth sectioning (van Benthem et al, 2006;Van den Broek et al, 2010;Hovden et al, 2014) and methods based on electron channelling (Van Aert et al, 2007;Jinschek et al, 2008;E et al, 2010;Van Dyck et al, 2012;Chen et al, 2015). However, these methods have not yet shown evidence of atomic-scale tomography experimentally.…”

“…Additionally, a method has been proposed that combines acquisition of a tilt series of images together with depth sectioning in order to increase resolution (Hovden et al, 2014). Nevertheless, although the quality of the reconstruction increases, we are still confronted with the problems of tilt limitation and beam damage of the specimen.…”