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 three-dimensional (3D) structure determination of an object are implemented by acquiring multiple measurements over various sample orientations, as in the case of crystallography and tomography1,2, or by scanning a series of thin sections through the sample, as in confocal microscopy3. Here we present a 3D imaging modality, termed ankylography (derived from the Greek words ankylos meaning ‘curved’ and graphein meaning ‘writing’), which under certain circumstances 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 in principle determined by the 2D spherical pattern. We confirm the theoretical analysis by performing 3D numerical reconstructions of a sodium silicate glass structure at 2 Å 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 also provide a preliminary demonstration that ankylography is experimentally feasible by obtaining a 3D image of a test object from a single 2D diffraction pattern. With further development, this approach of obtaining complete 3D structure information from a single view could find broad applications in the physical and life sciences.
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We thank P. Thibault for commenting on our manuscript, P. Thibault, M. M. Murnane, C.-C. Chen and R. Fung for discussions, C. Song for performing data analysis, Y. Mao for implementing an interpolation code, A. E. Sakdinawat for fabricating a test sample, P. Wachulak, M. Marconi, C. Menoni, J. J. Rocca and M. M. Murnane for help with data acquisition and T. Singh for parallelization of our phase retrieval codes. This work was supported by the US DOE, Office of Basic Energy Sciences, and the US NSF, Division of Materials Research and Engineering Research Center, an HHMI Gilliam fellowship for advanced studies and the UCLA MBI Whitcome fellowship. We used facilities supported by the NSF Center in EUV Science and Technology.
Author Contributions J.M. and K.S.R. conceived of ankylography. J.M. planned the project; K.S.R., S.S., H.J., J.A.R., J.D. and J.M. conducted the numerical experiments; S.S., K.S.R., R.L.S., H.J., H.C.K. and J.M. performed the analysis and image reconstruction of experimental data; J.M., K.S.R, S.S., J.D. and J.A.R. wrote the manuscript. All authors discussed the results and commented on the manuscript.
The authors declare no competing financial interests.
This file contains Supplementary Methods, Supplementary Figures S1-S7 with Legends, a Supplementary Discussion, Supplementary Data, Supplementary Tables S1-S2 and Supplementary References. (PDF 968 kb)
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Raines, K., Salha, S., Sandberg, R. et al. Three-dimensional structure determination from a single view. Nature 463, 214–217 (2010). https://doi.org/10.1038/nature08705
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