Atomic resolution imaging of a carbon nanotube from diffraction intensities

Atomic imaging of three-dimensional structures has required a crystal in diffraction or a lens in electron imaging. Whereas diffraction achieves very high resolution by averaging over many cells, imaging gives localized structural information, such as the position of a single dopant atom. However, lens aberrations limit electron imaging resolution to about 1 angstrom. Resolution is reduced further by low contrast from weak scattering or from the limitations on electron dose for radiation-sensitive molecules. We show that both high resolution and high contrast can be achieved by imaging from diffraction with a nanometer-sized coherent electron beam. The phase problem is solved by oversampling and iterative phase retrieval. We apply this technique to image a double-wall carbon nanotube at 1-angstrom resolution, revealing the structure of two tubes of different helicities. Because the only requirement for imaging is a diffraction pattern sampled below the Nyquist frequency, our technique has the potential to image nonperiodic nanostructures, including biological macromolecules, at diffraction intensity-limited resolutions.