Three-dimensional structure determination from a single view

Abstract

The ability to determine the structure of matter in three dimensions has profoundly advanced our understanding of nature. Traditionally, the most widely used schemes for 3D structure determination of an object are implemented by acquiring multiple measurements over various sample orientations, as in the case of crystallography and tomography (1,2), or by scanning a series of thin sections through the sample, as in confocal microscopy (3). Here we present a 3D imaging modality, termed ankylography (derived from the Greek words ankylos meaning 'curved' and graphein meaning 'writing'), which enables complete 3D structure determination from a single exposure using a monochromatic incident beam. We demonstrate that when the diffraction pattern of a finite object is sampled at a sufficiently fine scale on the Ewald sphere, the 3D structure of the object is determined by the 2D spherical pattern. We confirm the theoretical analysis by performing 3D numerical reconstructions of a sodium silicate glass structure at 2 Angstrom resolution and a single poliovirus at 2 - 3 nm resolution from 2D spherical diffraction patterns alone. Using diffraction data from a soft X-ray laser, we demonstrate that ankylography is experimentally feasible by obtaining a 3D image of a test object from a single 2D diffraction pattern. This approach of obtaining complete 3D structure information from a single view is anticipated to find broad applications in the physical and life sciences. As X-ray free electron lasers (X-FEL) and other coherent X-ray sources are under rapid development worldwide, ankylography potentially opens a door to determining the 3D structure of a biological specimen in a single pulse and allowing for time-resolved 3D structure determination of disordered materials.

30 pages

References in corpus (3)

• Femtosecond Diffractive Imaging with a Soft-X-ray Free-Electron Laser
• Quantitative Imaging of Single, Unstained Viruses with Coherent X-rays
• 2nd Response to "Feasibility of 3D reconstruction from a single 2D diffraction measurement"

Cited by in corpus (26)

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• Coherent diffractive imaging of single helium nanodroplets with a high harmonic generation source
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• Reconstruction of nanoscale particles from single-shot wide-angle FEL diffractions patterns with physics-informed neural networks
• Three-Dimensional Coherent Diffractive Imaging of Isolated Faceted Nanostructures
• The Scatman: an approximate method for fast wide-angle scattering simulations
• Melting, bubble-like expansion and explosion of superheated plasmonic nanoparticles
• Fast reconstruction of single-shot wide-angle diffraction images through deep learning
• 2nd Response to "Feasibility of 3D reconstruction from a single 2D diffraction measurement"
• An identity theorem for the Fourier transform of polytopes on rationally parameterisable hypersurfaces
• Using Convex Optimization of Autocorrelation with Constrained Support and Windowing for Improved Phase Retrieval Accuracy
• Phase retrieval methods applied to coherent imaging
• Potential and Challenge of Ankylography
• GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging
• Revealing domain wall stability during ultrafast demagnetization
• Reconstruction of polytopes from the modulus of the Fourier transform with small wave length
• Hard X-ray multi-projection imaging for single-shot approaches