Abstract

We propose a coherent x-ray zoom condenser lens composed of two-stage deformable Kirkpatrick-Baez mirrors. The lens delivers coherent x-rays with a controllable beam size, from one micrometer to a few tens of nanometers, at a fixed focal position. The lens is suitable for diffractive and scanning microscopy. We also propose non-scanning coherent diffraction microscopy for extended objects by using an apodized focused beam produced by the lens with a spatial filter. The proposed apodized-illumination method will be useful in highly efficient imaging with ultimate storage ring sources, and will also open the way to single-shot coherent diffraction microscopy of extended objects with x-ray free-electron lasers.

© 2013 OSA

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  1. A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
    [Crossref]
  2. G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to x-ray microbeam and nanobeam science,” Science 334(6060), 1234–1239 (2011).
    [Crossref] [PubMed]
  3. R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
    [Crossref]
  4. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
    [Crossref]
  5. I. K. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8(4), 291–298 (2009).
    [Crossref] [PubMed]
  6. J. Pérez and Y. Nishino, “Advances in X-ray scattering: from solution SAXS to achievements with coherent beams,” Curr. Opin. Struct. Biol. 22(5), 670–678 (2012).
    [Crossref] [PubMed]
  7. R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
    [Crossref]
  8. K. Shinohara, A. Ito, H. Nakano, I. Kodama, T. Honda, T. Matsumura, and K. Kinoshita, “X-ray holographic microscopy of biological specimens with an electronic zooming tube,” J. Synchrotron Radiat. 3(1), 35–40 (1996).
    [Crossref] [PubMed]
  9. I. K. Robinson, F. Pfeiffer, I. A. Vartanyants, Y. Sun, and Y. Xia, “Enhancement of coherent X-ray diffraction from nanocrystals by introduction of X-ray optics,” Opt. Express 11(19), 2329–2334 (2003).
    [Crossref] [PubMed]
  10. C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent X-Ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101(9), 090801 (2008).
    [Crossref] [PubMed]
  11. Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, and K. Yamauchi, “High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam,” Phys. Rev. B 80(5), 054103 (2009).
    [Crossref]
  12. 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(2), 122–125 (2010).
    [Crossref]
  13. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-Ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
    [Crossref] [PubMed]
  14. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
    [Crossref] [PubMed]
  15. 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,” Nature 467(7314), 436–439 (2010).
    [Crossref] [PubMed]
  16. 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]
  17. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406(6797), 752–757 (2000).
    [Crossref] [PubMed]
  18. R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
    [Crossref] [PubMed]
  19. J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum. 66(2), 2229 (1995).
    [Crossref]
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  21. T. Kimura, S. Handa, H. Mimura, H. Yumoto, D. Yamakawa, S. Matsuyama, K. Inagaki, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefront control system for phase compensation in hard x-ray optics,” Jpn. J. Appl. Phys. 48(7), 072503 (2009).
    [Crossref]
  22. H. Nakamori, S. Matsuyama, S. Imai, T. Kimura, Y. Sano, Y. Kohmura, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Experimental and simulation study of undesirable short-period deformation in piezoelectric deformable x-ray mirrors,” Rev. Sci. Instrum. 83(5), 053701 (2012).
    [Crossref] [PubMed]
  23. T. Kimura, H. Mimura, S. Handa, H. Yumoto, H. Yokoyama, S. Imai, S. Matsuyama, Y. Sano, K. Tamasaku, Y. Komura, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm,” Rev. Sci. Instrum. 81(12), 123704 (2010).
    [Crossref] [PubMed]
  24. S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20(22), 24977–24986 (2012).
    [Crossref] [PubMed]
  25. H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashil, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Phys. 7, 43–47 (2012).
  26. C. Song, R. Bergstrom, D. Ramunno-Johnson, H. Jiang, D. Paterson, M. D. de Jonge, I. McNulty, J. Lee, K. L. Wang, and J. Miao, “Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy,” Phys. Rev. Lett. 100(2), 025504 (2008).
    [Crossref] [PubMed]
  27. Y. Takahashi, H. Kubo, H. Furukawa, K. Yamauchi, E. Matsubara, T. Ishikawa, and Y. Nishino, “Element-specific hard x-ray diffraction microscopy,” Phys. Rev. B 78(9), 092105 (2008).
    [Crossref]
  28. M. Shimura, A. Saito, S. Matsuyama, T. Sakuma, Y. Terui, K. Ueno, H. Yumoto, K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, M. Yabashi, K. Tamasaku, K. Nishio, Y. Nishino, K. Endo, K. Hatake, Y. Mori, Y. Ishizaka, and T. Ishikawa, “Element array by scanning X-ray fluorescence microscopy after cis-diamminedichloro-platinum(II) treatment,” Cancer Res. 65(12), 4998–5002 (2005).
    [Crossref] [PubMed]
  29. S. Matsuyama, H. Mimura, H. Yumoto, Y. Sano, K. Yamamura, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Development of scanning x-ray fluorescence microscope with spatial resolution of 30,” Rev. Sci. Instrum. 77(10), 103102 (2006).
    [Crossref]
  30. S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, T. Ishikawa, M. Yabashi, and K. Yamauchi, “Diffraction-limited two-dimensional hard-x-ray focusing at the 100 nm level using a Kirkpatrick-Baez mirror arrangement,” Rev. Sci. Instrum. 76(8), 083114 (2005).
    [Crossref]
  31. 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(5), 394–398 (2008).
    [Crossref]
  32. S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, and N. Tanaka, “Diffractive imaging of the dumbbell structure in silicon by spherical-aberration-corrected electron diffraction,” Appl. Phys. Lett. 93(18), 183103 (2008).
    [Crossref]
  33. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
    [Crossref]
  34. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [Crossref] [PubMed]
  35. 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(2), 101–104 (2006).
    [Crossref]
  36. H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
    [Crossref]
  37. G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14(2), 474–486 (2006).
    [Crossref] [PubMed]

2012 (4)

J. Pérez and Y. Nishino, “Advances in X-ray scattering: from solution SAXS to achievements with coherent beams,” Curr. Opin. Struct. Biol. 22(5), 670–678 (2012).
[Crossref] [PubMed]

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20(22), 24977–24986 (2012).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashil, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Phys. 7, 43–47 (2012).

H. Nakamori, S. Matsuyama, S. Imai, T. Kimura, Y. Sano, Y. Kohmura, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Experimental and simulation study of undesirable short-period deformation in piezoelectric deformable x-ray mirrors,” Rev. Sci. Instrum. 83(5), 053701 (2012).
[Crossref] [PubMed]

2011 (2)

G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to x-ray microbeam and nanobeam science,” Science 334(6060), 1234–1239 (2011).
[Crossref] [PubMed]

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

2010 (4)

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (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(2), 122–125 (2010).
[Crossref]

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,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

T. Kimura, H. Mimura, S. Handa, H. Yumoto, H. Yokoyama, S. Imai, S. Matsuyama, Y. Sano, K. Tamasaku, Y. Komura, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm,” Rev. Sci. Instrum. 81(12), 123704 (2010).
[Crossref] [PubMed]

2009 (4)

T. Kimura, S. Handa, H. Mimura, H. Yumoto, D. Yamakawa, S. Matsuyama, K. Inagaki, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefront control system for phase compensation in hard x-ray optics,” Jpn. J. Appl. Phys. 48(7), 072503 (2009).
[Crossref]

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]

Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, and K. Yamauchi, “High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam,” Phys. Rev. B 80(5), 054103 (2009).
[Crossref]

I. K. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8(4), 291–298 (2009).
[Crossref] [PubMed]

2008 (6)

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent X-Ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101(9), 090801 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

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(5), 394–398 (2008).
[Crossref]

S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, and N. Tanaka, “Diffractive imaging of the dumbbell structure in silicon by spherical-aberration-corrected electron diffraction,” Appl. Phys. Lett. 93(18), 183103 (2008).
[Crossref]

C. Song, R. Bergstrom, D. Ramunno-Johnson, H. Jiang, D. Paterson, M. D. de Jonge, I. McNulty, J. Lee, K. L. Wang, and J. Miao, “Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy,” Phys. Rev. Lett. 100(2), 025504 (2008).
[Crossref] [PubMed]

Y. Takahashi, H. Kubo, H. Furukawa, K. Yamauchi, E. Matsubara, T. Ishikawa, and Y. Nishino, “Element-specific hard x-ray diffraction microscopy,” Phys. Rev. B 78(9), 092105 (2008).
[Crossref]

2007 (2)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-Ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

2006 (4)

S. Matsuyama, H. Mimura, H. Yumoto, Y. Sano, K. Yamamura, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Development of scanning x-ray fluorescence microscope with spatial resolution of 30,” Rev. Sci. Instrum. 77(10), 103102 (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(2), 101–104 (2006).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14(2), 474–486 (2006).
[Crossref] [PubMed]

2005 (2)

S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, T. Ishikawa, M. Yabashi, and K. Yamauchi, “Diffraction-limited two-dimensional hard-x-ray focusing at the 100 nm level using a Kirkpatrick-Baez mirror arrangement,” Rev. Sci. Instrum. 76(8), 083114 (2005).
[Crossref]

M. Shimura, A. Saito, S. Matsuyama, T. Sakuma, Y. Terui, K. Ueno, H. Yumoto, K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, M. Yabashi, K. Tamasaku, K. Nishio, Y. Nishino, K. Endo, K. Hatake, Y. Mori, Y. Ishizaka, and T. Ishikawa, “Element array by scanning X-ray fluorescence microscopy after cis-diamminedichloro-platinum(II) treatment,” Cancer Res. 65(12), 4998–5002 (2005).
[Crossref] [PubMed]

2003 (1)

2000 (1)

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406(6797), 752–757 (2000).
[Crossref] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

1998 (2)

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
[Crossref] [PubMed]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

1996 (1)

K. Shinohara, A. Ito, H. Nakano, I. Kodama, T. Honda, T. Matsumura, and K. Kinoshita, “X-ray holographic microscopy of biological specimens with an electronic zooming tube,” J. Synchrotron Radiat. 3(1), 35–40 (1996).
[Crossref] [PubMed]

1995 (1)

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum. 66(2), 2229 (1995).
[Crossref]

1982 (1)

1948 (1)

Abbey, B.

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(5), 394–398 (2008).
[Crossref]

Attwood, D.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[Crossref]

Baez, A. V.

Bergstrom, R.

C. Song, R. Bergstrom, D. Ramunno-Johnson, H. Jiang, D. Paterson, M. D. de Jonge, I. McNulty, J. Lee, K. L. Wang, and J. Miao, “Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy,” Phys. Rev. Lett. 100(2), 025504 (2008).
[Crossref] [PubMed]

Boye, P.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent X-Ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101(9), 090801 (2008).
[Crossref] [PubMed]

Brady, G. R.

Budai, J. D.

G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to x-ray microbeam and nanobeam science,” Science 334(6060), 1234–1239 (2011).
[Crossref] [PubMed]

Buffière, J.-Y.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

Bunk, O.

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,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-Ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Burghammer, M.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent X-Ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101(9), 090801 (2008).
[Crossref] [PubMed]

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(2), 101–104 (2006).
[Crossref]

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Clark, J. N.

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(5), 394–398 (2008).
[Crossref]

Cloetens, P.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

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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).
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S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, T. Ishikawa, M. Yabashi, and K. Yamauchi, “Diffraction-limited two-dimensional hard-x-ray focusing at the 100 nm level using a Kirkpatrick-Baez mirror arrangement,” Rev. Sci. Instrum. 76(8), 083114 (2005).
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S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, and N. Tanaka, “Diffractive imaging of the dumbbell structure in silicon by spherical-aberration-corrected electron diffraction,” Appl. Phys. Lett. 93(18), 183103 (2008).
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S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20(22), 24977–24986 (2012).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashil, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Phys. 7, 43–47 (2012).

H. Nakamori, S. Matsuyama, S. Imai, T. Kimura, Y. Sano, Y. Kohmura, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Experimental and simulation study of undesirable short-period deformation in piezoelectric deformable x-ray mirrors,” Rev. Sci. Instrum. 83(5), 053701 (2012).
[Crossref] [PubMed]

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(2), 122–125 (2010).
[Crossref]

T. Kimura, H. Mimura, S. Handa, H. Yumoto, H. Yokoyama, S. Imai, S. Matsuyama, Y. Sano, K. Tamasaku, Y. Komura, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm,” Rev. Sci. Instrum. 81(12), 123704 (2010).
[Crossref] [PubMed]

T. Kimura, S. Handa, H. Mimura, H. Yumoto, D. Yamakawa, S. Matsuyama, K. Inagaki, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefront control system for phase compensation in hard x-ray optics,” Jpn. J. Appl. Phys. 48(7), 072503 (2009).
[Crossref]

Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, and K. Yamauchi, “High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam,” Phys. Rev. B 80(5), 054103 (2009).
[Crossref]

Y. Takahashi, H. Kubo, H. Furukawa, K. Yamauchi, E. Matsubara, T. Ishikawa, and Y. Nishino, “Element-specific hard x-ray diffraction microscopy,” Phys. Rev. B 78(9), 092105 (2008).
[Crossref]

S. Matsuyama, H. Mimura, H. Yumoto, Y. Sano, K. Yamamura, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Development of scanning x-ray fluorescence microscope with spatial resolution of 30,” Rev. Sci. Instrum. 77(10), 103102 (2006).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, T. Ishikawa, M. Yabashi, and K. Yamauchi, “Diffraction-limited two-dimensional hard-x-ray focusing at the 100 nm level using a Kirkpatrick-Baez mirror arrangement,” Rev. Sci. Instrum. 76(8), 083114 (2005).
[Crossref]

M. Shimura, A. Saito, S. Matsuyama, T. Sakuma, Y. Terui, K. Ueno, H. Yumoto, K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, M. Yabashi, K. Tamasaku, K. Nishio, Y. Nishino, K. Endo, K. Hatake, Y. Mori, Y. Ishizaka, and T. Ishikawa, “Element array by scanning X-ray fluorescence microscopy after cis-diamminedichloro-platinum(II) treatment,” Cancer Res. 65(12), 4998–5002 (2005).
[Crossref] [PubMed]

Yashiro, W.

Yokoyama, H.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20(22), 24977–24986 (2012).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashil, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Phys. 7, 43–47 (2012).

T. Kimura, H. Mimura, S. Handa, H. Yumoto, H. Yokoyama, S. Imai, S. Matsuyama, Y. Sano, K. Tamasaku, Y. Komura, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm,” Rev. Sci. Instrum. 81(12), 123704 (2010).
[Crossref] [PubMed]

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(2), 122–125 (2010).
[Crossref]

Yumoto, H.

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashil, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Phys. 7, 43–47 (2012).

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(2), 122–125 (2010).
[Crossref]

T. Kimura, H. Mimura, S. Handa, H. Yumoto, H. Yokoyama, S. Imai, S. Matsuyama, Y. Sano, K. Tamasaku, Y. Komura, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm,” Rev. Sci. Instrum. 81(12), 123704 (2010).
[Crossref] [PubMed]

T. Kimura, S. Handa, H. Mimura, H. Yumoto, D. Yamakawa, S. Matsuyama, K. Inagaki, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefront control system for phase compensation in hard x-ray optics,” Jpn. J. Appl. Phys. 48(7), 072503 (2009).
[Crossref]

S. Matsuyama, H. Mimura, H. Yumoto, Y. Sano, K. Yamamura, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Development of scanning x-ray fluorescence microscope with spatial resolution of 30,” Rev. Sci. Instrum. 77(10), 103102 (2006).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, T. Ishikawa, M. Yabashi, and K. Yamauchi, “Diffraction-limited two-dimensional hard-x-ray focusing at the 100 nm level using a Kirkpatrick-Baez mirror arrangement,” Rev. Sci. Instrum. 76(8), 083114 (2005).
[Crossref]

M. Shimura, A. Saito, S. Matsuyama, T. Sakuma, Y. Terui, K. Ueno, H. Yumoto, K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, M. Yabashi, K. Tamasaku, K. Nishio, Y. Nishino, K. Endo, K. Hatake, Y. Mori, Y. Ishizaka, and T. Ishikawa, “Element array by scanning X-ray fluorescence microscopy after cis-diamminedichloro-platinum(II) treatment,” Cancer Res. 65(12), 4998–5002 (2005).
[Crossref] [PubMed]

Zettsu, N.

Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, and K. Yamauchi, “High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam,” Phys. Rev. B 80(5), 054103 (2009).
[Crossref]

Zhang, L.

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum. 66(2), 2229 (1995).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, and N. Tanaka, “Diffractive imaging of the dumbbell structure in silicon by spherical-aberration-corrected electron diffraction,” Appl. Phys. Lett. 93(18), 183103 (2008).
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R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
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Cancer Res. (1)

M. Shimura, A. Saito, S. Matsuyama, T. Sakuma, Y. Terui, K. Ueno, H. Yumoto, K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, M. Yabashi, K. Tamasaku, K. Nishio, Y. Nishino, K. Endo, K. Hatake, Y. Mori, Y. Ishizaka, and T. Ishikawa, “Element array by scanning X-ray fluorescence microscopy after cis-diamminedichloro-platinum(II) treatment,” Cancer Res. 65(12), 4998–5002 (2005).
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Contemp. Phys. (1)

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J. Pérez and Y. Nishino, “Advances in X-ray scattering: from solution SAXS to achievements with coherent beams,” Curr. Opin. Struct. Biol. 22(5), 670–678 (2012).
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Jpn. J. Appl. Phys. (1)

T. Kimura, S. Handa, H. Mimura, H. Yumoto, D. Yamakawa, S. Matsuyama, K. Inagaki, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefront control system for phase compensation in hard x-ray optics,” Jpn. J. Appl. Phys. 48(7), 072503 (2009).
[Crossref]

Nat. Mater. (1)

I. K. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8(4), 291–298 (2009).
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Nat. Photonics (1)

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[Crossref]

Nat. Phys. (4)

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(2), 122–125 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashil, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Phys. 7, 43–47 (2012).

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(2), 101–104 (2006).
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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(5), 394–398 (2008).
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Nature (3)

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,” Nature 467(7314), 436–439 (2010).
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Opt. Express (3)

Phys. Rev. B (2)

Y. Takahashi, H. Kubo, H. Furukawa, K. Yamauchi, E. Matsubara, T. Ishikawa, and Y. Nishino, “Element-specific hard x-ray diffraction microscopy,” Phys. Rev. B 78(9), 092105 (2008).
[Crossref]

Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, and K. Yamauchi, “High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam,” Phys. Rev. B 80(5), 054103 (2009).
[Crossref]

Phys. Rev. Lett. (4)

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).
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J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-Ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
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C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent X-Ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101(9), 090801 (2008).
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C. Song, R. Bergstrom, D. Ramunno-Johnson, H. Jiang, D. Paterson, M. D. de Jonge, I. McNulty, J. Lee, K. L. Wang, and J. Miao, “Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy,” Phys. Rev. Lett. 100(2), 025504 (2008).
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Rev. Sci. Instrum. (6)

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum. 66(2), 2229 (1995).
[Crossref]

H. Nakamori, S. Matsuyama, S. Imai, T. Kimura, Y. Sano, Y. Kohmura, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Experimental and simulation study of undesirable short-period deformation in piezoelectric deformable x-ray mirrors,” Rev. Sci. Instrum. 83(5), 053701 (2012).
[Crossref] [PubMed]

T. Kimura, H. Mimura, S. Handa, H. Yumoto, H. Yokoyama, S. Imai, S. Matsuyama, Y. Sano, K. Tamasaku, Y. Komura, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm,” Rev. Sci. Instrum. 81(12), 123704 (2010).
[Crossref] [PubMed]

S. Matsuyama, H. Mimura, H. Yumoto, Y. Sano, K. Yamamura, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Development of scanning x-ray fluorescence microscope with spatial resolution of 30,” Rev. Sci. Instrum. 77(10), 103102 (2006).
[Crossref]

S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, T. Ishikawa, M. Yabashi, and K. Yamauchi, “Diffraction-limited two-dimensional hard-x-ray focusing at the 100 nm level using a Kirkpatrick-Baez mirror arrangement,” Rev. Sci. Instrum. 76(8), 083114 (2005).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Science (2)

G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to x-ray microbeam and nanobeam science,” Science 334(6060), 1234–1239 (2011).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of coherent x-ray zoom condenser lens composed of two-stage deformable KB mirrors. The upstream and downstream KB mirrors share a single focus at the first focal point. The second focal spot size can be controlled at a fixed focal position by adjusting the first focal position.

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Fig. 2
Fig. 2

Schematic of the zooming mechanism. For simplicity, the figure is drawn to show one-dimensional focusing. (a) The positions of the second focus and the source are fixed, while the first focal position can be controlled on demand. (b) When the first focal position is closer to the second mirror, a larger focal spot size can be achieved with a smaller NA. (c) Conversely, when the first focal position is further away from the second mirror, a smaller focal spot size can be achieved with a larger NA.

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Fig. 3
Fig. 3

Dependence of the focal spot size on the first focal position. The curve is obtained by using Eqs. (1) and (3) with a = 350 µm, D = 1.5 m, and fb2 = 200 mm for 10 keV x-rays. The focal spot size can be controlled over a wide range, from one micrometer to a few tens of nanometers, with these realizable parameters.

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Fig. 4
Fig. 4

Example experimental setup for novel x-ray microscopy using the coherent x-ray zoom condenser lens. Coherent x-ray diffraction microscopy and various types of scanning x-ray microscopy can be combined in a single experimental setup.

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Fig. 5
Fig. 5

Intensity distributions at the two focal planes. Intensity distributions at the first focal plane are shown (a) with the spatial filter and (b) without the spatial filter. Intensity distributions at the second focal plane are shown (c) with the spatial filter and (d) without the spatial filter. (e) Intensity profiles are compared in the vertical direction through the second focus.

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Fig. 6
Fig. 6

Simulation of apodized-illumination coherent diffraction microscopy. (a) Spatially-extended sample image used for the simulation. The remaining parts of the figure show the results with and without the spatial filter, respectively: (b) and (c) are the amplitudes of the exit wave; (d) and (e) are the supports for the hybrid input-output algorithm; (f) and (g) are the simulated coherent diffraction patterns; and (h) and (i) are the reconstructed images.

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Tables (1)

Tables Icon

Table 1 Parameters used in the simulation of the two-stage deformable KB mirror optics

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Equations (6)

Equations on this page are rendered with MathJax. Learn more.

w≈ λ 2NA
NA≈ a 2 f b .
NA=N A 1 f f2 f b2 = a  f f2 2 f b1   f b2 = a  f f2 2(D− f f2 ) f b2 ,
δ< λ 8 sinθ .
θ c =λ n a r e f 1 ( λ ) π ≈λ n e r e π .
δ< 1 8 π n e r e .

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