We demonstrate Fresnel Coherent Diffractive Imaging (FCDI) tomography in the X-ray regime. The method uses an incident X-ray illumination with known curvature in combination with ptychography to overcome existing problems in diffraction imaging. The resulting tomographic reconstruction represents a 3D map of the specimen’s complex refractive index at nano-scale resolution. We use this technique to image a lithographically fabricated glass capillary, in which features down to 70nm are clearly resolved.

© 2012 OSA

1. 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, 342–344 (1999). [CrossRef]
2. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys.59, 1–99 (2010). [CrossRef]
3. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. R. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A.23, 1179–1200 (2006). [CrossRef]
4. 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, and 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). [CrossRef] [PubMed]
5. 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, 018101 (2009). [CrossRef] [PubMed]
6. M. Dierolf, A. Menzel, T. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature467, 436–439 (2010). [CrossRef] [PubMed]
7. K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Crystallogr. A61, 373–381 (2005). [CrossRef] [PubMed]
8. 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, 025506 (2006). [CrossRef] [PubMed]
9. B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys.4, 394–398 (2008). [CrossRef]
10. B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett.93, 214101 (2008). [CrossRef]
11. G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. N. Clark, B. Abbey, G. A. 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,” Cytom. Part A73A, 949–957 (2008). [CrossRef]
12. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys.2, 101–104 (2006). [CrossRef]
13. L. W. Whitehead, G. J. Williams, H. M. Quiney, K. A. Nugent, A. G. Peele, D. Paterson, M.D. de Jonge, and I. McNulty, “Fresnel diffractive imaging: Experimental study of coherence and curvature,” Phys. Rev. B77, 104112 (2008). [CrossRef]
14. R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primarstrahlwellenfeld,” Ber. Bunsenges. Phys. Chem.74, 1148–1154 (1970).
15. J. M. Rodenburg and H. M. L Faulkner, “A phase retrieval algorithm for shifting illumination,” App. Phys. Lett.85, 4795–4797 (2004). [CrossRef]
16. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science321, 379–382 (2008). [CrossRef] [PubMed]
17. A. Schropp, R. Hoppe, J. Patommel, D. Samberg, F. Seiboth, S. Stephan, G. Wellenreuther, G. Falkenberg, and C. G. Schroer, “Hard x-ray scanning microscopy with coherent radiation: Beyond the resolution of conventional x-ray microscopes,” Applied Physics Letters100, 253112 –253112–3 (2012). [CrossRef]
18. 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, 063823 (2009). [CrossRef]
19. C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, H. M. Quiney, B. Abbey, K. A. Nugent, and I. McNulty, “Fresnel coherent diffraction tomography,” Opt. Express18, 11746–11753 (2010). [CrossRef] [PubMed]
20. C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett.106, 013903 (2011). [CrossRef] [PubMed]
21. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Optics21, 2758–2769 (1982). [CrossRef]
22. H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett.30, 1638–1640 (2005). [CrossRef] [PubMed]
23. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial Mathematics, 1988).
24. I. McNulty, A. Khounsary, Y. P. Feng, Y. Qian, J. Barraza, C. Benson, and D. Shu, “A beamline for 1–4 kev microscopy and coherence experiments at the advanced photon source,” Rev. Sci. Instrum.67, 3372 (1996). [CrossRef]
25. D. J. Vine, G. J. Williams, J. N. Clark, C. T. Putkunz, M. A. Pfeifer, D. Legnini, C. Roehrig, E. Wrobel, E. Huwald, G. van Riessen, B. Abbey, T. Beetz, J. Irwin, M. Feser, B. Hornberger, I. McNulty, K. A. Nugent, and A. G. Peele, “An in-vacuum x-ray diffraction microscope for use in the 0.7–2.9 kev range,” Rev. Sci. Instrum.83, 033703 (2012). [CrossRef] [PubMed]
26. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Edition) (Cambridge University Press, 1999). [PubMed]
27. 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. Nat. Acad. Sci. U.S.A.102, 15343–15346 (2005). [CrossRef]
28. J. N. Clark, C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, B. Chen, K. A. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express18, 1981 (2010).
29. R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and abberations by using phase diversity,” J. Opt. Soc. Am. A9, 1072–1085 (1992). [CrossRef]
30. L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett.103, 243902 (2009). [CrossRef]
31. B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Phot.5, 420–424 (2011). [CrossRef]

Acta Crystallogr. A

• K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Crystallogr. A61, 373–381 (2005). [CrossRef] [PubMed]

Adv. Phys.

• K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys.59, 1–99 (2010). [CrossRef]

App. Phys. Lett.

• B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett.93, 214101 (2008). [CrossRef]
• J. M. Rodenburg and H. M. L Faulkner, “A phase retrieval algorithm for shifting illumination,” App. Phys. Lett.85, 4795–4797 (2004). [CrossRef]

Appl. Optics

• J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Optics21, 2758–2769 (1982). [CrossRef]

Applied Physics Letters

• A. Schropp, R. Hoppe, J. Patommel, D. Samberg, F. Seiboth, S. Stephan, G. Wellenreuther, G. Falkenberg, and C. G. Schroer, “Hard x-ray scanning microscopy with coherent radiation: Beyond the resolution of conventional x-ray microscopes,” Applied Physics Letters100, 253112 –253112–3 (2012). [CrossRef]

Ber. Bunsenges. Phys. Chem.

• R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primarstrahlwellenfeld,” Ber. Bunsenges. Phys. Chem.74, 1148–1154 (1970).

Cytom. Part A

• G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. N. Clark, B. Abbey, G. A. 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,” Cytom. Part A73A, 949–957 (2008). [CrossRef]

J. Opt. Soc. Am. A

• R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and abberations by using phase diversity,” J. Opt. Soc. Am. A9, 1072–1085 (1992). [CrossRef]

J. Opt. Soc. Am. A.

• H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. R. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A.23, 1179–1200 (2006). [CrossRef]

Nat. Phot.

• B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Phot.5, 420–424 (2011). [CrossRef]

Nat. Phys.

• H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys.2, 101–104 (2006). [CrossRef]
• B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys.4, 394–398 (2008). [CrossRef]

Nature

• 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, 342–344 (1999). [CrossRef]
• M. Dierolf, A. Menzel, T. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature467, 436–439 (2010). [CrossRef] [PubMed]

Opt. Express

• J. N. Clark, C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, B. Chen, K. A. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express18, 1981 (2010).
• C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, H. M. Quiney, B. Abbey, K. A. Nugent, and I. McNulty, “Fresnel coherent diffraction tomography,” Opt. Express18, 11746–11753 (2010). [CrossRef] [PubMed]

Opt. Lett.

• H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett.30, 1638–1640 (2005). [CrossRef] [PubMed]

Phys. Rev. Lett.

• 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, and 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). [CrossRef] [PubMed]

Phys. Rev. A

• 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, 063823 (2009). [CrossRef]

Phys. Rev. B

• L. W. Whitehead, G. J. Williams, H. M. Quiney, K. A. Nugent, A. G. Peele, D. Paterson, M.D. de Jonge, and I. McNulty, “Fresnel diffractive imaging: Experimental study of coherence and curvature,” Phys. Rev. B77, 104112 (2008). [CrossRef]

Phys. Rev. Lett.

• 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, 018101 (2009). [CrossRef] [PubMed]
• 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, 025506 (2006). [CrossRef] [PubMed]
• C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett.106, 013903 (2011). [CrossRef] [PubMed]
• L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett.103, 243902 (2009). [CrossRef]

Proc. Nat. Acad. Sci. U.S.A.

• 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. Nat. Acad. Sci. U.S.A.102, 15343–15346 (2005). [CrossRef]

Rev. Sci. Instrum.

• I. McNulty, A. Khounsary, Y. P. Feng, Y. Qian, J. Barraza, C. Benson, and D. Shu, “A beamline for 1–4 kev microscopy and coherence experiments at the advanced photon source,” Rev. Sci. Instrum.67, 3372 (1996). [CrossRef]
• D. J. Vine, G. J. Williams, J. N. Clark, C. T. Putkunz, M. A. Pfeifer, D. Legnini, C. Roehrig, E. Wrobel, E. Huwald, G. van Riessen, B. Abbey, T. Beetz, J. Irwin, M. Feser, B. Hornberger, I. McNulty, K. A. Nugent, and A. G. Peele, “An in-vacuum x-ray diffraction microscope for use in the 0.7–2.9 kev range,” Rev. Sci. Instrum.83, 033703 (2012). [CrossRef] [PubMed]

Science

• P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science321, 379–382 (2008). [CrossRef] [PubMed]

Other

• M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Edition) (Cambridge University Press, 1999). [PubMed]
• A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial Mathematics, 1988).

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