Skip to main content
SpringerLink
Log in

Coherent Diffractive Imaging: From Nanometric Down to Picometric Resolution

  • Reference work entry
  • First Online:
Handbook of Coherent-Domain Optical Methods

Abstract

Coherent diffractive imaging (CDI) is a novel technique for inspecting (crystalline and non-crystalline) matter from nanometric down to picometric resolution. It was used originally with X-rays and, more recently, with electrons (so-called electron diffractive imaging, or EDI). This chapter introduces basic concepts concerning CDI and addresses the different types of X-ray CDI experiments that have been conducted, namely plane wave CDI from isolated objects in forward scattering, focused-beam Fresnel CDI from isolated objects in forward scattering, Bragg CDI from nanocrystals, and keyhole CDI and ptychography from extended objects. A CDI experiment with a transmission electron microscope, alternatively named an EDI experiment, is also introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 699.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. J.F. van der Veen, F. Pfeiffer, Coherent x-ray scattering. J. Phys.: Condens. Mat. 16, 5003–5030 (2004)

    Article  ADS  Google Scholar 

  2. D. Sayre, X-ray crystallography: the past and present of the phase problem. Struct. Chem. 13, 81–96 (2002) (and reference therein)

    Article  Google Scholar 

  3. D. Sayre, Some implications of a theorem due to Shannon. Acta Crystallogr. 5, 843 (1952)

    Article  Google Scholar 

  4. J. Miao, C. Charalambous, J. Kirz, D. Sayre, Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999)

    Article  ADS  Google Scholar 

  5. J. Miao, T. Ishikawa, B. Johnson, E.H. Anderson, B. Lai, K.O. Hodgson, High resolution 3D X-ray diffraction microscopy. Phys. Rev. Lett. 89, 088303 (2002)

    Article  ADS  Google Scholar 

  6. A. Barty, S. Marchesini, H.N. Chapman, C. Cui, M.R. Howells, D.A. Shapiro, A.M. Minor, J.C.H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S.P. Hau-Riege, A.B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, J.H. Kinney, Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms. Phys. Rev. Lett. 101, 055501 (2008)

    Article  ADS  Google Scholar 

  7. H.N. Chapman, A. Barty, M.J. Bogan, S. Boutet, M. Frank, S.P. Hau-Riege, S. Marchesini, B.W. Woods, S. Bajt, W.H. Benner et al., Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nat. Phys. 2, 839–843 (2006)

    Article  Google Scholar 

  8. M.J. Bogan, W.H. Benner, S. Boutet, U. Rohner, M. Frank, A. Barty, M.M. Seibert, F. Maia, S. Marchesini, S. Bajt, B. Woods, V. Riot, S.P. Hau-Riege, M. Svenda, E. Marklund, E. Spiller, J. Hajdu, H.N. Chapman, Single particle X-ray diffractive imaging. Nano Lett. 8(1), 310–316 (2008)

    Article  ADS  Google Scholar 

  9. J. Miao, K.O. Hodgson, T. Ishikawa, C.A. Larabell, M.A. LeGros, Y. Nishino, Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction. Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003)

    Article  ADS  Google Scholar 

  10. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A.M. Neiman, D. Sayre, Biological imaging by soft x-ray diffraction microscopy. Proc. Natl. Acad. Sci. U.S.A. 102, 15343–15346 (2005)

    Article  ADS  Google Scholar 

  11. C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S.S. Shah, Z.H. Zhou, T. Ishikawa, J. Miao, Quantitative imaging of single, unstained viruses with coherent X rays. Phys. Rev. Lett. 101, 158101 (2008)

    Article  ADS  Google Scholar 

  12. Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, K. Maeshima, Three-dimensional visualization of a human chromosome using coherent X-ray diffraction. Phys. Rev. Lett. 102, 018101 (2009)

    Article  ADS  Google Scholar 

  13. M.M. Seibert, T. Ekeberg, F.R.N.C. Maia, M. Svenda, J. Andreasson, O. Jönsson, D. Odić, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D.P. DePonte, A. Barty, J. Schulz, C.L.N. Gumprecht, A. Aquila, M. Liang, T.A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, J.-M. Claverie, C. Bostedt, J.D. Bozek, S. Boutet, A.A. Miahnahri, M. Messerschmidt, J. Krzywinski, G. Williams, K.O. Hodgson, M.J. Bogan, C.Y. Hampton, R.G. Sierra, D. Starodub, I. Andersson, S. Bajt, M. Barthelmess, J.C.H. Spence, P. Fromme, U. Weierstall, R. Kirian, M. Hunter, R.B. Doak, S. Marchesini, S.P. Hau-Riege, M. Frank, R.L. Shoeman, L. Lomb, S.W. Epp, R. Hartmann, D. Rolles, A. Rudenko, C. Schmidt, L. Foucar, N. Kimmel, P. Holl, B. Rudek, B. Erk, A. Hömke, C. Reich, D. Pietschner, G. Weidenspointner, L. Strüder, G. Hauser, H. Gorke, J. Ullrich, I. Schlichting, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.-U. Kühnel, R. Andritschke, C.-D. Schröter, F. Krasniqi, M. Bott, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, H.N. Chapman, J. Hajdu, Single mimivirus particles intercepted and imaged with an X-ray laser. Nature 470, 78–82 (2011)

    Article  ADS  Google Scholar 

  14. H.N. Chapman, P. Fromme, A. Barty, T.A. White, R.A. Kirian, A. Aquila, M.S. Hunter, J. Schulz, D.P. DePonte, U. Weierstall, R.B. Doak, F.R.N.C. Maia, A.V. Martin, I. Schlichting, L. Lomb, N. Coppola, R.L. Shoeman, S.W. Epp, R. Hartmann, D. Rolles, A. Rudenko, L. Foucar, N. Kimmel, G. Weidenspointner, P. Holl, M. Liang, M. Barthelmess, C. Caleman, S. Boutet, M.J. Bogan, J. Krzywinski, C. Bostedt, S. Bajt, L. Gumprecht, B. Rudek, B. Erk, C. Schmidt, A. Hömke, C. Reich, D. Pietschner, L. Strüder, G. Hauser, H. Gorke, J. Ullrich, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.-U. Kühnel, M. Messerschmidt, J.D. Bozek, S.P. Hau-Riege, M. Frank, C.Y. Hampton, R.G. Sierra, D. Starodub, G.J. Williams, J. Hajdu, N. Timneanu, M.M. Seibert, J. Andreasson, A. Rocker, O. Jönsson, M. Svenda, S. Stern, K. Nass, R. Andritschke, C.-D. Schröter, F. Krasniqi, M. Bott, K.E. Schmidt, X. Wang, I. Grotjohann, J.M. Holton, T.R.M. Barends, R. Neutze, S. Marchesini, R. Fromme, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, I. Andersson, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, J.C.H. Spence, Femtosecond X-ray protein nanocrystallography. Nature 470, 73–78 (2011)

    Article  ADS  Google Scholar 

  15. F. Mastropietro, D. Carbone, A. Diaz, J. Eymery, A. Sentenac, T.H. Metzger, V. Chamard, V. Favre-Nicolin, Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate. Opt. Express 19(20), 19223–19232 (2011)

    Article  ADS  Google Scholar 

  16. C.E. Shannon, Communication in the presence of noise. Proc. Inst. Radio Eng. 37(1), 10–21 (1949)

    MathSciNet  Google Scholar 

  17. L. De Caro, C. Giacovazzo, D. Siliqi, Confined structures: basic crystallographic aspects. Acta Cryst A 58, 415–423 (2002)

    Article  Google Scholar 

  18. J. Miao, D. Sayre, H.N. Chapman, Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects. J. Opt. Soc. Am. A 15, 1662–1669 (1998)

    Article  ADS  Google Scholar 

  19. R.W. Gerchberg, W.O. Saxton, A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237–246 (1972)

    Google Scholar 

  20. J.R. Fienup, Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982)

    Article  ADS  Google Scholar 

  21. S. Marchesini, A unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instrum. 78, 011301 (2007)

    Article  ADS  Google Scholar 

  22. H.N. Chapman, K.A. Nugent, Coherent lensless X-ray imaging. Nat. Photonics. 4, 833 (2010)

    Article  ADS  Google Scholar 

  23. K.A. Nugent, Coherent methods in the X-ray sciences. Adv. Phys. 59, 1–99 (2009)

    Article  ADS  Google Scholar 

  24. H.M. Quiney, A.G. Peele, Z. Cai, D. Paterson, K.A. Nugent, Diffractive imaging of highly focused X-ray fields. Nat. Phys. 2, 101–104 (2006)

    Article  Google Scholar 

  25. L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T.H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, S. Lagomarsino, In-line holography and coherent diffractive imaging with x-ray waveguides. Phys. Rev. B 77-R, 081408 (2008)

    Article  ADS  Google Scholar 

  26. C.G. Schroer, P. Boye, J.M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, C. Riekel, Coherent X-ray diffraction imaging with nanofocused illumination. Phys. Rev. Lett. 101, 090801 (2008)

    Article  ADS  Google Scholar 

  27. Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, K. Yamauchi, High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam. Phys. Rev. B 80, 054103 (2009)

    Article  ADS  Google Scholar 

  28. B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. De Jonge, I. Mcnulty, Keyhole coherent diffractive imaging. Nat. Phys. 4, 394–398 (2008)

    Article  Google Scholar 

  29. W. Hoppe, Diffraction in inhomogeneous primary wave fields: principle of phase determination from electron diffraction interference. Acta Crystallogr. A 25, 495–501 (1969)

    Article  ADS  Google Scholar 

  30. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008)

    Article  ADS  Google Scholar 

  31. H.M.L. Faulkner, J.M. Rodenburg, Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. Phys. Rev. Lett. 93, 023903 (2004)

    Article  ADS  Google Scholar 

  32. J.M. Rodenburg, H.M.L. Faulkner, A phase retrieval algorithm for shifting illumination. Appl. Phys. Lett. 85, 4795 (2004)

    Article  ADS  Google Scholar 

  33. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C.M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, Ptychographic X-ray computed tomography at the nanoscale. Nature 467, 436–439 (2010)

    Article  ADS  Google Scholar 

  34. M. Dierolf, P. Thibault, A. Menzel, C.M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, Ptychographic coherent diffractive imaging of weakly scattering specimens. New J. Phys. 12, 035017 (2010)

    Article  ADS  Google Scholar 

  35. I. Robinson, R. Harder, Coherent X-ray diffraction imaging of strain at the nanoscale. Nat. Mater. 8, 291–298 (2009)

    Article  ADS  Google Scholar 

  36. A. Biermanns, A. Davydok, H. Paetzelt, A. Diaz, V. Gottschalch, T.H. Metzger, U. Pietsch, Individual GaAs nanorods imaged by coherent X-ray diffraction. J. Synchrotron Rad. 16, 796–802 (2009)

    Article  Google Scholar 

  37. A. Diaz, C. Mocuta, J. Stangl, B. Mandl, C. David, J. Vila-Comamala, V. Chamard, T.H. Metzger, G. Bauer, Coherent diffraction imaging of a single epitaxial InAs nanowire using a focused x-ray beam. Phys. Rev. B 79, 125324 (2009)

    Article  ADS  Google Scholar 

  38. V. Favre-Nicolin, J. Eymery, R. Koester, P. Gentile, Coherent-diffraction imaging of single nanowires of diameter 95 nanometers. Phys. Rev. B 79, 195401 (2009)

    Article  ADS  Google Scholar 

  39. J.M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L.A. Nagahara, Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300, 1419–1421 (2003)

    Article  ADS  Google Scholar 

  40. W.J. Huang, R. Sun, J. Tao, L.D. Menard, R.G. Nuzzo, J.M. Zuo, Coordination-dependent surface atomic contraction in nanocrystals revealed by coherent diffraction. Nat. Mater. 7, 308–313 (2008)

    Article  ADS  Google Scholar 

  41. W.J. Huang, J.M. Zuo, B. Jiang, K.W. Kwon, M. Shim, Sub-ångström-resolution diffractive imaging of single nanocrystals. Nat. Phys. 5, 129–133 (2009)

    Article  Google Scholar 

  42. L. De Caro, E. Carlino, G. Caputo, D.P. Cozzoli, C. Giannini, Electron diffractive imaging of oxygen atoms in nanocrystals at sub-ängström resolution. Nat. Nanotechnol. 5, 360–365 (2010)

    Article  ADS  Google Scholar 

  43. P.W. Hawkes, Aberration correction past and present. Philos. Trans. R. Soc. A 367, 3637–3664 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. H.H. Rose, Optics of high-performance electron microscopes. Sci. Technol. Adv. Mater. 9, 014107 (2008) (30pp)

    Article  ADS  Google Scholar 

  45. N.D. Browning, S.J. Pennycook, Characterization of High Tc Materials and Devices by Electron Microscopy (Cambridge University Press, Cambridge, 2006). ISBN 052155490X

    Google Scholar 

  46. J.M. Cowley, Diffraction Physics, 2nd edn. (North-Holland, Amsterdam/Oxford/New York/Tokyo, 1990)

    Google Scholar 

  47. D. Sayre, H.N. Chapman, J. Miao, On the extendibility of X-ray crystallography to noncrystals. Acta Crystallogr. A54, 232–239 (1998)

    Google Scholar 

  48. J.M. Zuo, J. Zhang, W. Huang, K. Ran, B. Jiang, Combining real and reciprocal space information for aberration free coherent electron diffractive imaging. Ultramicroscopy (2010). doi:10.1016/j.ultramic.2010.10.013

    Google Scholar 

  49. K.W. Urban, Studying atomic structures by aberration-corrected transmission electron microscopy. Science 321, 506–510 (2008)

    Article  ADS  Google Scholar 

  50. L. Jiang, D. Georgieva, H.W. Zandbergen, J.P. Abrahams, Unit-cell determination from randomly oriented electron-diffraction patterns. Acta Crystallogr. D 65(7), 625–632 (2009)

    Article  Google Scholar 

  51. T.J. Cui, D.R. Smith, R. Liu (eds.), Metamaterials: Theory, Design, and Applications (Springer, New York, 2010)

    Google Scholar 

  52. H.M. Quiney, K.A. Nugent, Biomolecular imaging and electronic damage using X-ray free-electron lasers. Nat. Phys. 7, 142–146 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Cristallografia (IC-CNR), via Amendola 122/O, 70126, Bari, Italy

    Liberato De Caro, Dritan Siliqi & Cinzia Giannini

  2. IOM CNR Laboratorio TASC, Area Science Park – Basovizza, Bld MM SS 14, Km 163.5, 34149, Trieste, Italy

    Elvio Carlino

Authors
  1. Liberato De Caro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elvio Carlino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dritan Siliqi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cinzia Giannini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cinzia Giannini .

Editor information

Editors and Affiliations

  1. , Chair of Optics and Biophotonics, Saratov State University, Astrakhanskaya str. 83, Saratov, 410012, Russia

    Valery V. Tuchin

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this entry

Cite this entry

De Caro, L., Carlino, E., Siliqi, D., Giannini, C. (2013). Coherent Diffractive Imaging: From Nanometric Down to Picometric Resolution. In: Tuchin, V. (eds) Handbook of Coherent-Domain Optical Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5176-1_8

Download citation

Publish with us

Policies and ethics

Search

Navigation