Abstract

We have combined two high transmission planar x-ray waveguides glued onto each other in a crossed geometry to form an effective quasi-point source. From measurements of the far-field diffraction pattern, the phase and amplitude of the near-field distribution is retrieved using the error-reduction algorithm. In agreement with finite difference field simulations (forward calculation), the reconstructed exit wave intensity distribution (inverse calculation) exhibits a full width at half maximum (FWHM) below 15 nm in both dimensions. Finally, holographic imaging is successfully demonstrated for the crossed waveguide device by translation of a lithographic test structure through the waveguide beam.

© 2010 Optical Society of America

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  1. S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
    [CrossRef] [PubMed]
  2. S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
    [CrossRef] [PubMed]
  3. C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006).
    [CrossRef]
  4. 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]
  5. C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003).
    [CrossRef]
  6. A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
    [CrossRef]
  7. O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
    [CrossRef]
  8. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
    [CrossRef] [PubMed]
  9. H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
    [CrossRef]
  10. H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
    [CrossRef]
  11. W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, "Demonstration of 12 nm Resolution Fresnel Zone Plate Lens based Soft X-ray Microscopy," Opt. Express 17, 17669-17677 (2009).
    [CrossRef] [PubMed]
  12. C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
    [CrossRef]
  13. T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008).
    [CrossRef] [PubMed]
  14. F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
    [CrossRef] [PubMed]
  15. L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, "In-line holography and coherent diffractive imaging with x-ray waveguides," Phys. Rev. B 77, 081408 (2008).
    [CrossRef]
  16. I. A. Vartanyants and A. Singer, "Analysis of Coherence Properties of 3-rd Generation Synchrotron Sources and Free-Electron Lasers," (2009).
  17. Strictly speaking, only a mono-modal waveguide acts as a perfect coherence filter. However, numerical simulations of the coupling process show that even for a waveguide with three modes, coherence is already significantly filtered (M. Osterhoff et al., unpublished).
  18. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]
  19. C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005).
    [CrossRef]
  20. S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, "X-ray phasecontrast microscopy and microtomography," Opt. Express 11, 2289-2302 (2003).
    [CrossRef] [PubMed]
  21. C. Fuhse, "X-ray waveguides and waveguide-based lensless imaging," Ph.D. thesis, University of Gottingen (2006).
  22. A minor difference with respect to one of the four parameters was the following: The detector area used for the reconstruction shown in Fig. 4 was 256×241 pixels, for the simulation we have used a square area of 248×248 pixels with the same pixel size as in the experiment.
  23. L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
    [CrossRef]

2010 (2)

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
[CrossRef]

2009 (1)

2008 (3)

T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008).
[CrossRef] [PubMed]

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

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

2006 (2)

C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006).
[CrossRef]

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]

2005 (3)

C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005).
[CrossRef]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

2003 (3)

C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003).
[CrossRef]

O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
[CrossRef]

S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, "X-ray phasecontrast microscopy and microtomography," Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

2002 (1)

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
[CrossRef] [PubMed]

2000 (1)

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

1982 (2)

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
[CrossRef]

J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
[CrossRef] [PubMed]

Anderson, E. H.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, "Demonstration of 12 nm Resolution Fresnel Zone Plate Lens based Soft X-ray Microscopy," Opt. Express 17, 17669-17677 (2009).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Bahtz, C.

T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008).
[CrossRef] [PubMed]

Bergeman, C.

C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003).
[CrossRef]

Boye, P.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

Burghammer, M.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
[CrossRef] [PubMed]

Burkeeva, I.

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

Cai, Z.

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]

Cedola, A.

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

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
[CrossRef]

Chao, W.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, "Demonstration of 12 nm Resolution Fresnel Zone Plate Lens based Soft X-ray Microscopy," Opt. Express 17, 17669-17677 (2009).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Cloetens, P.

O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
[CrossRef]

Conley, R.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

David, C.

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
[CrossRef] [PubMed]

Davis, T.

De Caro, L.

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

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
[CrossRef]

Di Fonzo, S.

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

Eberhardt, W.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Eisebitt, S.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Feldkamp, J.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

Feldkamp, J. M.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Fienup, J. R.

Fischer, P.

Fuhse, C.

T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008).
[CrossRef] [PubMed]

C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006).
[CrossRef]

C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005).
[CrossRef]

Giannini, C.

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

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
[CrossRef]

Giewekemeyer, K.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Guagliardi, A.

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

Gulden, J.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Gureyev, T.

Handa, S.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
[CrossRef]

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Hellwig, O.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Hignette, O.

O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
[CrossRef]

Holt, M. V.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
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A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
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H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
[CrossRef]

Ishikawa, T.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
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S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

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H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

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C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003).
[CrossRef]

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Kimura, T.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
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T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008).
[CrossRef] [PubMed]

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C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

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C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
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Lagomarsino, S.

L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, "In-line holography and coherent diffractive imaging with x-ray waveguides," Phys. Rev. B 77, 081408 (2008).
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S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
[CrossRef]

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O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
[CrossRef]

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C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
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W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
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H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

Lorgen, M.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Ludwig, W.

O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
[CrossRef]

Luning, J.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Macrander, A. T.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

Mancuso, A. P.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Maser, J.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
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H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
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Metzger, T. H.

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

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
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L. De Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, "In-line holography and coherent diffractive imaging with x-ray waveguides," Phys. Rev. B 77, 081408 (2008).
[CrossRef]

Muller, M.

S. Di Fonzo, W. Jark, S. Lagomarsino, C. Giannini, L. De Caro, A. Cedola, and M. Muller, "Non-destructive determination of local strain with 100-nanometre spatial resolution," Nature 403, 638-640 (2000).
[CrossRef] [PubMed]

Nishino, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
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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).
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C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006).
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Paganin, D.

Paterson, D.

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).
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Patommel, J.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
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C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

Peele, A. G.

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]

Pelliccia, D.

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

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, "Phase retrieval in x-ray coherent Fresnel projection-geometry diffraction," Appl. Phys. Lett. 90, 041105 (1982).
[CrossRef]

Pfeiffer, F.

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
[CrossRef] [PubMed]

Pogany, A.

Quiney, H. M.

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]

Rekawa, S.

Riekel, C.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
[CrossRef] [PubMed]

Rostaing, G.

O. Hignette, P. Cloetens, W.-K. Lee, W. Ludwig, and G. Rostaing, "Hard X-ray microscopy with reflecting mirrors status and perspectives of the ESRF technology," J. Phys. IV France 104, 231-234 (2003).
[CrossRef]

Salditt, T.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

T. Salditt, S. P. Kruger, C. Fuhse, and C. Bahtz, "High-Transmission Planar X-RayWaveguides," Phys. Rev. Lett. 100, 184801-4 (2008).
[CrossRef] [PubMed]

C. Fuhse, C. Ollinger, and T. Salditt, "Waveguide-Based Off-Axis Holography with Hard X-Rays," Phys. Rev. Lett. 97, 254801 (2006).
[CrossRef]

C. Fuhse and T. Salditt, "Finite-difference field calculations for one-dimensionally confined X-ray waveguides," Physica B: Condensed Matter 357, 57-60 (2005).
[CrossRef]

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, "Two-Dimensional X-rayWaveguides and Point Sources," Science 297, 230 (2002).
[CrossRef] [PubMed]

Samberg, D.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Sano, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
[CrossRef]

Sch¨oder, S.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Schlotter, W. F.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Schroer, C. G.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

Schropp, A.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Stephan, S.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Stephenson, G. B.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

Stevenson, A.

Stohr, J.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef] [PubMed]

Tamasaku, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Breaking the 10 nm barrier in hard-X-ray focusing," Nat. Phys. 6, 122-125 (2010).
[CrossRef]

van der Hart, A.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

van der Veen, J. F.

C. Bergeman, H. Keymeulen, and J. F. van der Veen, "Focusing X-Ray Beams to Nanometer Dimensions," Phys. Rev. Lett. 91, 204801 (2003).
[CrossRef]

Vartanyants, I. A.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Vincze, L.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, "Hard x-ray nanoprobe based on refractive x-ray lenses," Appl. Phys. Lett. 87, 124103-3 (2005).
[CrossRef]

Vogt, S.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

Weckert, B.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Wilke, R. N.

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, B. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, "Hard x-ray nanobeam characterization by coherent diffraction microscopy," Appl. Phys. Lett. 96, 091102-3 (2010).
[CrossRef]

Wilkins, S.

Winarski, R. P.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, "Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens," Appl. Phys. Lett. 92, 221114 (2008).
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A minor difference with respect to one of the four parameters was the following: The detector area used for the reconstruction shown in Fig. 4 was 256×241 pixels, for the simulation we have used a square area of 248×248 pixels with the same pixel size as in the experiment.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the two crossed waveguide. (b) Profiles of the real and the imaginary parts of the index of refraction n = 1 − δ + , calculated for a photon energy E=17.5 keV. Transmission of the guided modes in the C guiding layer is enhanced by the high δ but relatively low β of Mo. (c) The scanning electron microscopy (SEM) image (magnification 52.85 kx) shows the Mo/C/Mo layers encompassed by highly absorbing Ge and a In52Sn48 alloy which acts as the bond material to an additional Ge cap wafer. (d) The thicknesses of the guiding layer and the interlayers are clearly identified in the high resolution SEM image (magnification 200 kx).

Fig. 2.
Fig. 2.

Experimental setup: A parallel hard x-ray wave front is focused by the KB mirror system onto the c2DWG. The NTT test pattern is illuminated at a distance z 1 and the in-line hologram is recorded by the Medipix detector at a distance z 1 + z 2.

Fig. 3.
Fig. 3.

(a) and (b) Measured and simulated far-field diffraction and pattern of the c2DWG, the intensity is encoded logarithmically in the colormap (I [cps] and I [arb. units]). (c) Simulated electromagnetic field intensity inside the 1DWG at 17.5 keV within a range of 221–261 µm in propagation direction z. (d) A Fourier transformation with respect to z of the simulated electromagnetic field in the 1DWG showing the guided modes. (e) Field intensities which correspond to the dashed lines in (c) illustrating 3-mode propagation. (f) FWHM of the simulated near-field distribution (top) and far-field distribution (bottom) as a function of the waveguide length l. (g) Autocorrelation of the measured far-field. (h) Reconstructed near-field intensity obtained from the error-reduction algorithm (see text). (i) and (j) Reconstructed intensity along with the simulated near-field intensity of the 1DWG-2 and 1DWG-1, respectively.

Fig. 4.
Fig. 4.

(left) Reconstructed phase in the object plane of the hologram of the test pattern after combination of 15×15 scan points. (right) Line scan through the phase distribution indicated by a red bar in the reconstructed image along with a fit of a Gaussian error function to a single phase step.

Fig. 5.
Fig. 5.

(a) Simulated normalized hologram of a lines-and-spaces (LS) pattern with the same scattering contrast as the sample used in the real experiment and a total photon count on the detector 104 times higher than collected in the experiment per one second. Further simulation parameters are given in the main text. (b) Holographic reconstruction corresponding to subfigure (a). The LS pattern has a half-period of 13.5 nm. (c) Holographic reconstruction corresponding to the hologram shown in subfigure (a), however now simulated with a total number of photons 104 times lower. Scale bars indicate 3 mm (a) and 50 nm (b/c). Colorbars indicate normalized intensity (a) and phase in rad (b/c).

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