Abstract

The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our recent experimental results, in which X-ray images were reconstructed from the diffraction pattern alone. A preliminary analysis of the radiation dose needed for CXDI imaging and the dose tolerance of frozen-hydrated life-science samples suggests that 3D tomography at a resolution of about 10 nm may be possible. In material science, where samples are less sensitive to radiation damage, we expect CXDI to be able to achieve 1 to 2 nm resolution using modern x-ray synchrotron sources. For higher resolution imaging of biological material, strategies based on fast-pulse illumination from proposed x-ray free-electron laser sources, can be considered as described in Neutze et al. Nature 406, 752–757 (2000).

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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  34. T. Beetz, C. Jacobsen, C. C. Cao, J. Kirz, O. Mentez, C. Sanches-Hanke, D. Sayre, D. Shapiro, "Development of a novel apparatus for experiments in soft x-ray diffraction imaging and diffraction tomography," J. de Phys. IV 104, 351-359 (2003).

Acad. Radiol.

H. He, S. Marchesini, M. Howells, U. Weierstall, H. Chapman, S. Hau-Riege, A. Noy, J. C. H. Spence, "Inversion of x-ray diffuse scattering to images using prepared objects," Phys. Rev. B 67, 174114 (2003).
[CrossRef]

Acta Cryst.

D. Sayre, "Some implications of a theory due to Shannon," Acta Cryst. 5, 843 (1952).
[CrossRef]

Acta. Cryst.

H. He, S. Marcesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, "Experimental lensless soft xray imaging using iterative algorithms: phasing diffuse scattering," Acta. Cryst. A59, 143-152 (2003).

Appl. Opt.

Chem. Phys. Lett.

A. Szoke, "Time resolved holographic diffraction with atomic resolution," Chem. Phys. Lett. 313, 777-788 (1999).
[CrossRef]

J. Appl. Phys.

B. L. Henke, J. W. M. DuMond, "Submicroscopic structure determination by long wavelength x-ray diffraction," J. Appl. Phys. 26, 903-917 (1955).
[CrossRef]

J. de Phys. IV

T. Beetz, C. Jacobsen, C. C. Cao, J. Kirz, O. Mentez, C. Sanches-Hanke, D. Sayre, D. Shapiro, "Development of a novel apparatus for experiments in soft x-ray diffraction imaging and diffraction tomography," J. de Phys. IV 104, 351-359 (2003).

J. Image. Sci. Technol.

A. Szöke, "Holographic microscopy with a complicated reference," J. Image. Sci. Technol. 41, 332-341 (1997).

J. Micros. Soc. Am.

H. N. Chapman, J. Fu, C. Jacobsen, S. Williams, "Dark-field X-ray microscopy of immunogold-labeled cells," J. Micros. Soc. Am. 2, 53-62 (1996).

J. Microsc.

W. Meyer-Ilse, D. Hamamoto, A. Nair, S. A. Lelievre, G. Denbeaux, L. Johnson, A. L. Pearson, D. Yager, M. A. Legros, C. A. Larabell, "High resolution protein localization using soft X-ray microscopy," J. Microsc. 201, 395-403 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Struct. Biol.

G. Huldt, A. Szoke, J. Hajdu, "Single Particle Diffraction Imaging: Image Classification," J. Struct. Biol. (to be published).
[PubMed]

S. P. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, "SPEDEN: Reconstructing single particles from their diffraction patterns," J. Struct. Biol. (submitted).

Nature

J. Miao, P. 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).
[CrossRef]

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, J. Hajdu, "Potential for biomolecular imaging with femtosecond x-ray pulses," Nature 406, 752-757 (2000).
[CrossRef] [PubMed]

Opt. Eng.

J. C. Solem, G. F. Chapline, "X-Ray Biomicroholography," Opt. Eng. 23, 193-202 (1984).

Phil. Trans. Roy. Soc. Lond. A

J. C. H. Spence, U. Weierstall, M. Howells, "Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction," Phil. Trans. Roy. Soc. Lond. A 360, 875-895 (2002).
[CrossRef]

Phys. Rev.

E. J. McGuire, "K-Shell Auger Transition Rates and Fluorescence Yields for Elements Be-Ar," Phys. Rev. 185, 1-6 (1969).
[CrossRef]

Phys. Rev. B

S. Marchesini, H. He, H. N. Chapman, A. Noy, S. P. Hau-Riege, M. R. Howells, U. Weierstall, J. C. H. Spence, "X-ray image reconstruciton from the diffraction pattern alone," Phys. Rev. B (to be published) arXiv:physics/0306174.

Phys. Rev. Lett.

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, 088303-1-4 (2002).
[CrossRef] [PubMed]

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, I. K. Robinson, "Three-Dimensional Imaging of Microstructure in Au Nanocrystals," Phys. Rev. Lett. 90, 175501-1-4 (2003).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci.

J. Miao, K. O. Hodgson, D. Sayre, "An approach to three-dimensional structures of biomolecules," Proc. Nat. Acad. Sci. 98, 6641-6645 (2001).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci. Am.

J. W. 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. Nat. Acad. Sci. Am. 100, 110-112 (2003).
[CrossRef]

Proc. SPIE

M. R. Howells, P. Charalambous, H. He, S. Marchesini, J. C. H. Spence, "An off-axis zone-plate monochromator for high-power undulator radiation," in Design and Microfabrication of Novel X-ray Optics, D. Mancini, ed. Vol. 4783, (SPIE, Bellingham, 2002).

Quart. Rev. Biophys.

M. v. Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, "Single-particle electron cryo-microscopy: towards atomic resolution," Quart. Rev. Biophys. 33, 269-307 (2000).

Science

J. C. Solem, G. C. Baldwin, "Microholography of Living Organisms," Science 218, 229-235 (1982).
[CrossRef] [PubMed]

Z. M. Zuo, I. Vartanyants, M. Gao, R. Zang, L. A. Nagahara, "Atomic resolution imaging of a carbon nanotube from diffraction intensities," Science 300, 1419-1421 (2003).
[CrossRef] [PubMed]

Ultramicrosc.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, R. R. Panepucci, "Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: theory and experiment," Ultramicrosc. 90, 171-195 (2002).
[CrossRef]

B. F. McEwen, K. H. Downing, R. M. Glaeser, "The relevance of dose-fractionation in tomography of radiation-sensitive specimens," Ultramicrosc. 60, 357-373 (1995).
[CrossRef]

Zeitschrift für Naturforschung

R. Hegerl, W. Hoppe, "Influence of electron noise on three-dimensional image reconstruction," Zeitschrift für Naturforschung 31a, 1717-1721 (1976).

Other

A. Rose, "Television pickup tubes and the problem of vision," in Advances in Electronics, L. Marton, ed. Vol. 1, (New York, 1948).

J. Franck, Three-Dimensional Electron Microscopy of Macromolecular Assemblies (Academic Press, San Diego, 1996).

I. F. Furguson, Auger Microprobe Analysis (Adam Hilger, New York, 1989).

TESLA Test Facility web page, <a href="http://www-hasylab.desy.de/facility/fel/vuv/main.htm">http://www-hasylab.desy.de/facility/fel/vuv/main.htm</a>

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Figures (4)

Fig. 1.
Fig. 1.

Experimental chamber layout (left) and rotation device for tomographic recordings (right).

Fig. 2.
Fig. 2.

Three-dimensional test objects fabricated for x-ray diffraction imaging. The left picture shows a SEM perspective image of a silicon nitride pyramid membrane, and the right picture shows a top view of a similar pyramid that has been decorated with 50 nm diameter gold spheres. The silicon nitride is 100 nm thick, and the pyramid is hollow. These objects are ideal for testing since they can be well characterized in the SEM, have extent in all three dimensions, and can be treated as an analogue to a molecule.

Fig. 3.
Fig. 3.

Comparison of reconstructed soft X-ray image (middle) and SEM images of gold ball clusters (left). Each ball has a diameter of 50 nm [He, H., S. Marchesini, M. Howells, U. Weierstall, H. Chapman, S. Hau-Riege, A. Noy, J. C. H. Spence, “Inversion of x-ray diffuse scattering to images using prepared objects,” Phys. Rev. B 67, 174114 (2003)]. Also shown (right) is a movie (1.1 MB) of the reconstruction as it iterates. Each frame of the movie displays the current estimate of the image intensity on the left and the image support on the right.

Fig. 4.
Fig. 4.

(top) Plot of dose against x-ray energy. (bottom) Plot of dose against resolution. The diamond and square shaped points are calculated for CXDI experiments on a single object using the formulas given in the text. They give the dose resulting from an x-ray illumination just sufficient for the voxel to be detectable according to the Rose criterion. The triangles represent estimates of the dose needed to destroy features based on spot-fading experiments in electron crystallography. The circles show x-ray damage experiments of two types. The two points at the far right show a damage limit due to mass loss as measured in an x-ray microscope. The other circles, at the far left, are derived from spot-fading experiments in x-ray crystallography. The CXDI experiments are only possible above the “required imaging dose” line and below the “feature-destroying dose” line, i.e. in the triangular region to the far right of the graph. The wide spread of the points indicates that only preliminary conclusions can be drawn at present. Generally the damage advantages of studying multiple copies of the same object (crystallography) compared to studying a single object (CXDI) are very obvious.

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