OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 27 — Dec. 17, 2012
  • pp: 28871–28892

When holography meets coherent diffraction imaging

Tatiana Latychevskaia, Jean-Nicolas Longchamp, and Hans-Werner Fink  »View Author Affiliations

Optics Express, Vol. 20, Issue 27, pp. 28871-28892 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (2027 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The phase problem is inherent to crystallographic, astronomical and optical imaging where only the intensity of the scattered signal is detected and the phase information is lost and must somehow be recovered to reconstruct the object’s structure. Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, the reconstruction of the scattered complex-valued object wave is directly provided by a well-defined reference wave that must cover the entire detector area which often is an experimental challenge. CDI provides the highest possible, only wavelength limited, resolution, but the phase recovery is an iterative process which requires some pre-defined information about the object and whose outcome is not always uniquely-defined. Moreover, the diffraction patterns must be recorded under oversampling conditions, a pre-requisite to be able to solve the phase problem. Here, we report how holography and CDI can be merged into one superior technique: holographic coherent diffraction imaging (HCDI). An inline hologram can be recorded by employing a modified CDI experimental scheme. We demonstrate that the amplitude of the Fourier transform of an inline hologram is related to the complex-valued visibility, thus providing information on both, the amplitude and the phase of the scattered wave in the plane of the diffraction pattern. With the phase information available, the condition of oversampling the diffraction patterns can be relaxed, and the phase problem can be solved in a fast and unambiguous manner. We demonstrate the reconstruction of various diffraction patterns of objects recorded with visible light as well as with low-energy electrons. Although we have demonstrated our HCDI method using laser light and low-energy electrons, it can also be applied to any other coherent radiation such as X-rays or high-energy electrons.

© 2012 OSA

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(090.0090) Holography : Holography
(110.7440) Imaging systems : X-ray imaging
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Imaging Systems

Original Manuscript: October 3, 2012
Revised Manuscript: November 29, 2012
Manuscript Accepted: November 29, 2012
Published: December 12, 2012

Virtual Issues
Vol. 8, Iss. 1 Virtual Journal for Biomedical Optics

Tatiana Latychevskaia, Jean-Nicolas Longchamp, and Hans-Werner Fink, "When holography meets coherent diffraction imaging," Opt. Express 20, 28871-28892 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Gabor, “A new microscopic principle,” Nature161(4098), 777–778 (1948). [CrossRef] [PubMed]
  2. D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London, Ser. A197(1051), 454–487 (1949). [CrossRef]
  3. J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400(6742), 342–344 (1999). [CrossRef]
  4. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science300(5624), 1419–1421 (2003). [CrossRef] [PubMed]
  5. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982). [CrossRef] [PubMed]
  6. J. W. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A.100(1), 110–112 (2003). [CrossRef] [PubMed]
  7. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(43), 15343–15346 (2005). [CrossRef] [PubMed]
  8. C. Y. Song, H. D. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. W. Miao, “Quantitative imaging of single, unstained viruses with coherent x-rays,” Phys. Rev. Lett.101(15), 158101 (2008). [CrossRef] [PubMed]
  9. G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytometry, Part A73A(10), 949–957 (2008). [CrossRef] [PubMed]
  10. X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. M. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. J. Turner, and C. Jacobsen, “Soft X-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett.103(19), 198101 (2009). [CrossRef] [PubMed]
  11. Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent X-ray diffraction,” Phys. Rev. Lett.102(1), 018101 (2009). [CrossRef] [PubMed]
  12. J. Nelson, X. J. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A.107(16), 7235–7239 (2010). [CrossRef] [PubMed]
  13. R. N. Wilke, M. Priebe, M. Bartels, K. Giewekemeyer, A. Diaz, P. Karvinen, and T. Salditt, “Hard x-ray imaging of bacterial cells: nano-diffraction and ptychographic reconstruction,” Opt. Express20(17), 19232–19254 (2012). [CrossRef] [PubMed]
  14. 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, L. Gumprecht, N. Coppola, 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, and J. Hajdu, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature470(7332), 78–81 (2011). [CrossRef] [PubMed]
  15. S. Marchesini, H. N. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express11(19), 2344–2353 (2003). [CrossRef] [PubMed]
  16. J. C. H. Spence, U. Weierstall, and H. N. Chapman, “X-ray lasers for structural and dynamic biology,” Rep. Prog. Phys.75(10), 102601 (2012). [CrossRef] [PubMed]
  17. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr.5(6), 843–843 (1952). [CrossRef]
  18. D. Sayre, “X-ray crystallography: The past and present of the phase problem,” Struct. Chem.13(1), 81–96 (2002). [CrossRef]
  19. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).
  20. R. H. T. Bates, “On phase problems I,” Optik (Stuttg.)51, 161–170 (1978).
  21. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett.3(1), 27–29 (1978). [CrossRef] [PubMed]
  22. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B68(14), 140101 (2003). [CrossRef]
  23. T. Latychevskaia, J.-N. Longchamp, and H.-W. Fink, “Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging,” Opt. Express19(20), 19330–19339 (2011). [CrossRef] [PubMed]
  24. E. M. Hofstetter, “Construction of time-limited functions with specified auto-correlation functions,” IEEE Trans. Inf. Theory10(2), 119–126 (1964). [CrossRef]
  25. A. M. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, “On phase retrieval in electron-microscopy from image and diffraction pattern,” Optik (Stuttg.)45, 303–316 (1976).
  26. A. M. J. Huiser and H. A. Ferwerda, “On the problem of phase retrieval in electron microscopy from image and diffraction pattern. 2. Uniqueness and stability,” Optik (Stuttg.)46, 407–420 (1976).
  27. Y. M. Bruck and L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun.30(3), 304–308 (1979). [CrossRef]
  28. R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension 1. underlying theory,” Optik (Stuttg.)61, 247–262 (1982).
  29. R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vis. Graph. Image Process.25(2), 205–217 (1984). [CrossRef]
  30. R. P. Millane, “Multidimensional phase problems,” J. Opt. Soc. Am. A13(4), 725–734 (1996). [CrossRef]
  31. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A3(11), 1897–1907 (1986). [CrossRef]
  32. W. J. Huang, B. Jiang, R. S. Sun, and J. M. Zuo, “Towards sub-atomic resolution electron diffraction imaging of metallic nanoclusters: A simulation study of experimental parameters and reconstruction algorithms,” Ultramicroscopy107(12), 1159–1170 (2007). [CrossRef] [PubMed]
  33. P. Thibault and I. C. Rankenburg, “Optical diffraction microscopy in a teaching laboratory,” Am. J. Phys.75(9), 827–832 (2007). [CrossRef]
  34. K. S. Raines, S. Salha, R. L. Sandberg, H. D. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. C. Du, and J. W. Miao, “Three-dimensional structure determination from a single view,” Nature463(7278), 214–217 (2010). [CrossRef] [PubMed]
  35. R. Barakat and G. Newsam, “Necessary conditions for a unique solution to two-dimensional phase recovery,” J. Math. Phys.25(11), 3190–3193 (1984). [CrossRef]
  36. R. H. T. Bates and D. G. H. Tan, “Fourier phase retrieval when the image is complex,” Inverse Optics II, Proc. SPIE558, 54–59 (1985). [CrossRef]
  37. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier-transform using a support constraint,” J. Opt. Soc. Am. A4(1), 118–123 (1987). [CrossRef]
  38. U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy90(2-3), 171–195 (2002). [CrossRef] [PubMed]
  39. R. R. Nair, P. Blake, J. R. Blake, R. Zan, S. Anissimova, U. Bangert, A. P. Golovanov, S. V. Morozov, A. K. Geim, K. S. Novoselov, and T. Latychevskaia, “Graphene as a transparent conductive support for studying biological molecules by transmission electron microscopy,” Appl. Phys. Lett.97(15), 153102 (2010). [CrossRef]
  40. J.-N. Longchamp, T. Latychevskaia, C. Escher, and H.-W. Fink, “Low-energy electron transmission imaging of clusters on free-standing graphene,” Appl. Phys. Lett.101(11), 113117 (2012). [CrossRef]
  41. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett.97(2), 025506 (2006). [CrossRef] [PubMed]
  42. G. J. Williams, H. M. Quiney, B. B. Dahl, C. Q. Tran, A. G. Peele, K. A. Nugent, M. D. De Jonge, and D. Paterson, “Curved beam coherent diffractive imaging,” Thin Solid Films515(14), 5553–5556 (2007). [CrossRef]
  43. L. W. Whitehead, G. J. Williams, H. M. Quiney, K. A. Nugent, D. Paterson, M. D. de Jonge, and I. McNulty, “Fresnel diffractive imaging: Experimental study of coherence and curvature,” Phys. Rev. B77(10), 104112 (2008). [CrossRef]
  44. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys.12(3), 035020 (2010). [CrossRef]
  45. I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science256, 1009–1012 (1992). [CrossRef] [PubMed]
  46. S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature432(7019), 885–888 (2004). [CrossRef] [PubMed]
  47. S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel x-ray holography,” Nature Photon.2(9), 560–563 (2008). [CrossRef]
  48. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science321(5887), 379–382 (2008). [CrossRef] [PubMed]
  49. D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A80(6), 063823 (2009). [CrossRef]
  50. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009). [CrossRef] [PubMed]
  51. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy109(10), 1256–1262 (2009). [CrossRef] [PubMed]
  52. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature467(7314), 436–439 (2010). [CrossRef] [PubMed]
  53. R. H. T. Bates, “On phase problems II,” Optik (Stuttg.)51, 223–234 (1978).
  54. T. Latychevskaia and H.-W. Fink, “Simultaneous reconstruction of phase and amplitude contrast from a single holographic record,” Opt. Express17(13), 10697–10705 (2009). [CrossRef] [PubMed]
  55. T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett.98(23), 233901 (2007). [CrossRef] [PubMed]
  56. T. Latychevskaia, P. Formanek, C. T. Koch, and A. Lubk, “Off-axis and inline electron holography: Experimental comparison,” Ultramicroscopy110(5), 472–482 (2010). [CrossRef]
  57. E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy111(4), 282–284 (2011). [CrossRef] [PubMed]
  58. E. Steinwand, J. N. Longchamp, and H. W. Fink, “Fabrication and characterization of low aberration micrometer-sized electron lenses,” Ultramicroscopy110(9), 1148–1153 (2010). [CrossRef] [PubMed]
  59. J. C. H. Spence, X. Zhang, and W. Qian, “On the reconstruction of low voltage point projection holograms,” in Electron Holography, A. Tonomura, L. F. Allard, G. Pozzi, D. C. Joy, and Y. A. Ono, eds. (Elsevier Science, 1995), pp. 267–276.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited