Atomic resolution tomography reconstruction of tilt series based on a GPU accelerated hybrid input–output algorithm using polar Fourier transform

Advances in diffraction and transmission electron microscopy (TEM) have greatly improved the prospect of three-dimensional (3D) structure reconstruction from two-dimensional (2D) images or diffraction patterns recorded in a tilt series at atomic resolution. Here, we report a new graphics processing unit (GPU) accelerated iterative transformation algorithm (ITA) based on polar fast Fourier transform for reconstructing 3D structure from 2D diffraction patterns. The algorithm also applies to image tilt series by calculating diffraction patterns from the recorded images using the projection-slice theorem. A gold icosahedral nanoparticle of 309 atoms is used as the model to test the feasibility, performance and robustness of the developed algorithm using simulations. Atomic resolution in 3D is achieved for the 309 atoms Au nanoparticle using 75 diffraction patterns covering 150° rotation. The capability demonstrated here provides an opportunity to uncover the 3D structure of small objects of nanometers in size by electron diffraction. - Highlights: • Three-dimensional atomic structural reconstruction demonstrated using simulated diffraction data in a tilt series. • Using diffraction patterns allows alignment free tomography reconstruction. • This method can be applied to general image based tomography by using the power spectra of the images as input. • Reconstruction is based on an iterative transformation algorithm (ITA) using polar fast Fourier transform. • The ITA algorithm is accelerated using graphics processing unit (GPU) for competitive high performance