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.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Giacovazzo, C. et al. Fundamentals of Crystallography 2nd edn (Oxford Univ. Press, 2002)
Kak, A. C. & Slaney, M. Principles of Computerized Tomographic Imaging (SIAM, 2001)
Pawley, J. B. ed. Handbook of Biological Confocal Microscopy 3rd edn (Springer, 2006)
Sayre, D. in Imaging Processes and Coherence in Physics (eds Schlenker, M. et al.) 229–235 (Lecture Notes in Physics, Vol. 112, Springer, 1980)
Miao, J., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342 (1999)
Robinson, I. K., Vartanyants, I. A., Williams, G. J., Pfeifer, M. A. & Pitney, J. A. Reconstruction of the shapes of gold nanocrystals using coherent X-ray diffraction. Phys. Rev. Lett. 87, 195505 (2001)
Miao, J. et al. High resolution 3D X-ray diffraction microscopy. Phys. Rev. Lett. 89, 088303 (2002)
Miao, J. et al. Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction. Proc. Natl Acad. Sci. USA 100, 110–112 (2003)
Nugent, K. A., Peele, A. G., Chapman, H. N. & Mancuso, A. P. Unique phase recovery for nonperiodic objects. Phys. Rev. Lett. 91, 203902 (2003)
Shapiro, D. et al. Biological imaging by soft x-ray diffraction microscopy. Proc. Natl Acad. Sci. USA 102, 15343–15346 (2005)
Pfeifer, M. A., Williams, G. J., Vartanyants, I. A., Harder, R. & Robinson, I. K. Three-dimensional mapping of a deformation field inside a nanocrystal. Nature 442, 63–66 (2006)
Miao, J. et al. Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy. Phys. Rev. Lett. 97, 215503 (2006)
Chapman, H. N. et al. High resolution ab initio three-dimensional x-ray diffraction microscopy. J. Opt. Soc. Am. A 23, 1179–1200 (2006)
Williams, G. J. et al. Fresnel coherent diffractive imaging. Phys. Rev. Lett. 97, 025506 (2006)
Abbey, B. et al. Keyhole coherent diffractive imaging. Nature Phys. 4, 394–398 (2008)
Jiang, H. et al. Nanoscale imaging of mineral crystals inside biological composite materials using X-ray diffraction microscopy. Phys. Rev. Lett. 100, 038103 (2008)
Thibault, P. et al. High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008)
Song, C. et al. Quantitative imaging of single, unstained viruses with coherent X-rays. Phys. Rev. Lett. 101, 158101 (2008)
Nishino, Y., Takahashi, Y., Imamoto, N., Ishikawa, T. & Maeshima, K. Three-dimensional visualization of a human chromosome using coherent X-ray diffraction. Phys. Rev. Lett. 102, 018101 (2009)
Zuo, J. M., Vartanyants, I., Gao, M., Zhang, R. & Nagahara, L. A. Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300, 1419–1421 (2003)
Spence, J. C. H., Weierstall, U. & Howells, M. R. Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction. Phil. Trans. R. Soc. Lond. A 360, 875–895 (2002)
Sandberg, R. L. et al. Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams. Phys. Rev. Lett. 99, 098103 (2007)
Sandberg, R. L. et al. High numerical aperture tabletop soft X-ray diffraction microscopy with 70 nm resolution. Proc. Natl Acad. Sci. USA 105, 24–27 (2008)
Chapman, H. N. et al. Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nature Phys. 2, 839–843 (2006)
Barty, A. et al. Ultrafast single-shot diffraction imaging of nanoscale dynamics. Nature Photon. 2, 415–419 (2008)
Mancuso, A. P. et al. Coherent-pulse 2D crystallography using a free-electron laser X-ray source. Phys. Rev. Lett. 102, 035502 (2009)
Neutze, R., Wouts, R., Spoel, D., Weckert, E. & Hajdu, J. Potential for biomolecular imaging with femtosecond X-ray pulses. Nature 406, 752–757 (2000)
Miao, J., Sayre, D. & Chapman, H. N. Phase retrieval from the magnitude of the Fourier transforms of non-periodic objects. J. Opt. Soc. Am. A 15, 1662–1669 (1998)
Bubeck, D. et al. The structure of the poliovirus 135S cell entry intermediate at 10-Angstrom resolution reveals the location of an externalized polypeptide that binds to membranes. J. Virol. 79, 7745–7755 (2005)
Thibault, P. Feasibility of 3D reconstruction from a single 2D diffraction measurement. Preprint at 〈http://arXiv.org/abs/0909.1643v1〉 (2009)
Miao, J. Response to feasibility of 3D reconstruction from a single 2D diffraction measurement. Preprint at 〈http://arXiv.org/abs/0909.3500v1〉 (2009)
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)
About this article
Cite this article
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
Biophysical Reviews (2020)
Three-dimensional atomic scale electron density reconstruction of octahedral tilt epitaxy in functional perovskites
Nature Communications (2018)
Scientific Reports (2018)
Nature Communications (2017)
Nature Materials (2017)