Abstract

We describe a method for characterizing focused x-ray beams using phase retrieval, with diversity achieved by transversely translating a phase-shifting or absorbing structure close to the beam focus. The required measurements can be taken with an experimental setup that is similar to that already used for fluorescent scan testing. The far-field intensity pattern is measured for each position of the translating structure, and the collected measurements are jointly used to estimate the beam profile by using a nonlinear optimization gradient search algorithm. The capability to reconstruct 1D and 2D beam foci is demonstrated through numerical simulations.

© 2009 Optical Society of America

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  1. I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
    [CrossRef] [PubMed]
  2. W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics, 3rd Ed., (Roberts & Company, Englewood, 2005).
  4. 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]
  5. S. G. Podorov, K. M. Pavlov and D. M. Paganin, "A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging," Opt. Express 15, 9954-9962 (2007).
    [CrossRef] [PubMed]
  6. M. Guizar-Sicairos and J. R. Fienup, "Holography with extended reference by autocorrelation linear differential operation," Opt. Express 15, 17592-17612 (2007).
    [CrossRef] [PubMed]
  7. S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
    [CrossRef]
  8. M. Guizar-Sicairos and J. R. Fienup, "Direct image reconstruction from a Fourier intensity pattern using HERALDO," Opt. Lett. 33, 2668-2670 (2008).
    [CrossRef] [PubMed]
  9. J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3, 27-29 (1978).
    [CrossRef] [PubMed]
  10. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]
  11. J. R. Fienup, "Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint," J. Opt. Soc. Am. A 4, 118-123 (1987).
    [CrossRef]
  12. J. N. Cederquist, J. R. Fienup, J. C. Marron and R. G. Paxman, "Phase retrieval from experimental far-field speckle data," Opt. Lett. 13, 619-621 (1988).
    [CrossRef] [PubMed]
  13. 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, 342-344 (1999).
    [CrossRef]
  14. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
    [CrossRef]
  15. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
    [CrossRef] [PubMed]
  16. J. R. Fienup, "Lensless coherent imaging by phase retrieval with an illumination pattern constraint," Opt. Express 14, 498-508 (2006).
    [CrossRef] [PubMed]
  17. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
    [CrossRef]
  18. 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]
  19. M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with Fourier-weighted projections," J. Opt. Soc. Am. A 25, 701-709 (2008).
    [CrossRef]
  20. R. A. Gonsalves and R. Childlaw, "Wavefront sensing by phase retrieval," Proc. SPIE 207, 32-39 (1979).
  21. R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).
  22. R. G. Paxman, "Diversity imaging," in Signal Recovery and Synthesis, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper SWA1.
  23. G. R. Brady and J. R. Fienup, "Nonlinear optimization algorithm for retrieving the full complex pupil function," Opt. Express 14, 474-486 (2006).
    [CrossRef] [PubMed]
  24. H. M. L. Faulkner and J. M. Rodenburg, "Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm," Phys. Rev. Lett. 93, 023903 (2004).
    [CrossRef] [PubMed]
  25. J. M. Rodenburg and H. M. L. Faulkner, "A phase retrieval algorithm for shifting illumination," Appl. Phys. Lett. 85, 4795-4797 (2004).
    [CrossRef]
  26. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
    [CrossRef]
  27. M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with transverse translation diversity: a nonlinear optimization approach," Opt. Express 16, 7264-7278 (2008).
    [CrossRef] [PubMed]
  28. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
    [CrossRef] [PubMed]
  29. M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
    [CrossRef] [PubMed]
  30. H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).
  31. H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
    [CrossRef] [PubMed]
  32. A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
    [CrossRef]
  33. 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]
  34. Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun.  30, 304-308 (l979).
    [CrossRef]
  35. J. R. Fienup, "Invariant error metrics for image reconstruction," Appl. Opt. 36, 8352-8357 (1997).
    [CrossRef]
  36. M. Guizar-Sicairos, S. T. Thurman and J. R. Fienup, "Efficient subpixel image registration algorithms," Opt. Lett. 33, 156-158 (2008).
    [CrossRef] [PubMed]
  37. G. R. Brady, M. Guizar-Sicairos and J. R. Fienup, "Optical wavefront measurement using phase retrieval with transverse translation diversity," Opt. Express 17, 624-639 (2009).
    [CrossRef] [PubMed]
  38. S. T. Thurman, R. T. DeRosa and J. R. Fienup, "Amplitude metrics for field retrieval with hard-edge and uniformly-illuminated apertures," J. Opt. Soc. Am. A, doc. ID 101701 (posted 26 January 2009, in press).
    [CrossRef]
  39. M. Guizar-Sicairos and J. R. Fienup, "Focused x-ray beam characterization by phase retrieval with a moveable phase-shifting structure," in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2008), paper FWN3.

2009

2008

M. Guizar-Sicairos, S. T. Thurman and J. R. Fienup, "Efficient subpixel image registration algorithms," Opt. Lett. 33, 156-158 (2008).
[CrossRef] [PubMed]

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
[CrossRef]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with transverse translation diversity: a nonlinear optimization approach," Opt. Express 16, 7264-7278 (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, 379-382 (2008).
[CrossRef] [PubMed]

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, "Direct image reconstruction from a Fourier intensity pattern using HERALDO," Opt. Lett. 33, 2668-2670 (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, 394-398 (2008).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with Fourier-weighted projections," J. Opt. Soc. Am. A 25, 701-709 (2008).
[CrossRef]

2007

2006

2005

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

2004

H. M. L. Faulkner and J. M. Rodenburg, "Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm," Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, "A phase retrieval algorithm for shifting illumination," Appl. Phys. Lett. 85, 4795-4797 (2004).
[CrossRef]

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

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

2000

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

1999

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, 342-344 (1999).
[CrossRef]

1997

1992

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

1988

1987

1982

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

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

1979

R. A. Gonsalves and R. Childlaw, "Wavefront sensing by phase retrieval," Proc. SPIE 207, 32-39 (1979).

1978

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, 394-398 (2008).
[CrossRef]

Anderson, E. H.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Bajt, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Barty, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

Baumann, J.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

Beetz, T.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Bogan, M. J.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Boutet, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Bozovic, N.

A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
[CrossRef]

Brady, G. R.

Bunk, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

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

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[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, 101-104 (2006).
[CrossRef]

Cederquist, J. N.

Chapman, H. N.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

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, 342-344 (1999).
[CrossRef]

Childlaw, R.

R. A. Gonsalves and R. Childlaw, "Wavefront sensing by phase retrieval," Proc. SPIE 207, 32-39 (1979).

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, 394-398 (2008).
[CrossRef]

Conley, R.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

Cui, C.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

David, C.

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

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

de Jonge, M.

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]

Dierolf, M.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

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

Drakopoulos, M.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

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]

Elser, V.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Engelhardt, M.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

Evans-Lutterodt, K.

A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
[CrossRef]

Faulkner, H. M. L.

J. M. Rodenburg and H. M. L. Faulkner, "A phase retrieval algorithm for shifting illumination," Appl. Phys. Lett. 85, 4795-4797 (2004).
[CrossRef]

H. M. L. Faulkner and J. M. Rodenburg, "Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm," Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Fienup, J. R.

G. R. Brady, M. Guizar-Sicairos and J. R. Fienup, "Optical wavefront measurement using phase retrieval with transverse translation diversity," Opt. Express 17, 624-639 (2009).
[CrossRef] [PubMed]

M. Guizar-Sicairos, S. T. Thurman and J. R. Fienup, "Efficient subpixel image registration algorithms," Opt. Lett. 33, 156-158 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with Fourier-weighted projections," J. Opt. Soc. Am. A 25, 701-709 (2008).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with transverse translation diversity: a nonlinear optimization approach," Opt. Express 16, 7264-7278 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, "Direct image reconstruction from a Fourier intensity pattern using HERALDO," Opt. Lett. 33, 2668-2670 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, "Holography with extended reference by autocorrelation linear differential operation," Opt. Express 15, 17592-17612 (2007).
[CrossRef] [PubMed]

J. R. Fienup, "Lensless coherent imaging by phase retrieval with an illumination pattern constraint," Opt. Express 14, 498-508 (2006).
[CrossRef] [PubMed]

G. R. Brady and J. R. Fienup, "Nonlinear optimization algorithm for retrieving the full complex pupil function," Opt. Express 14, 474-486 (2006).
[CrossRef] [PubMed]

J. R. Fienup, "Invariant error metrics for image reconstruction," Appl. Opt. 36, 8352-8357 (1997).
[CrossRef]

J. N. Cederquist, J. R. Fienup, J. C. Marron and R. G. Paxman, "Phase retrieval from experimental far-field speckle data," Opt. Lett. 13, 619-621 (1988).
[CrossRef] [PubMed]

J. R. Fienup, "Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint," J. Opt. Soc. Am. A 4, 118-123 (1987).
[CrossRef]

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

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3, 27-29 (1978).
[CrossRef] [PubMed]

Frank, M.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

R. A. Gonsalves and R. Childlaw, "Wavefront sensing by phase retrieval," Proc. SPIE 207, 32-39 (1979).

Guizar-Sicairos, M.

Handa, S.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Hau-riege, S. P.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

He, H.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

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]

Howells, M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Howells, M. R.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Ishikawa, T.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Jacobsen, C.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

Kang, H. C.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

Kern, D. P.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Kimura, T.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Kirz, J.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

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, 342-344 (1999).
[CrossRef]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Kottler, C.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

Leitenberger, W.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

Lima, E.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Liu, C.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

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]

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, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

Marchesini, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

Marron, J. C.

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

Maser, J.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

Matsuyama, S.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

McNulty, I.

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]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Menzel, A.

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

Miao, H.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Miao, J.

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, 342-344 (1999).
[CrossRef]

Mimura, H.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Nishino, Y.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Noy, A.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

Nugent, K. A.

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]

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]

Paganin, D. M.

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).
[CrossRef]

Pavlov, K. M.

Paxman, R. G.

Peele, A. G.

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]

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]

Pfeifer, M. A.

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]

Pfeiffer, F.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

Podorov, S. G.

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]

Rodenburg, J. M.

H. M. L. Faulkner and J. M. Rodenburg, "Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm," Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, "A phase retrieval algorithm for shifting illumination," Appl. Phys. Lett. 85, 4795-4797 (2004).
[CrossRef]

Sakdinawat, A. E.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Sano, Y.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Sayre, D.

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, 342-344 (1999).
[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]

Schuster, M.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

Shapiro, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Snigirev, A.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

Snigireva, I.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

Spence, J. C. H.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

Stein, A.

A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
[CrossRef]

Stephenson, G. B.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

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]

Szoke, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Tamasaku, K.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Taylor, A.

A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
[CrossRef]

Thibault, P.

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

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Thurman, S. T.

Vogt, S.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

Weierstall, U.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

Weitkamp, T.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

Williams, G. J.

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]

Yabashi, M.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Yumoto, H.

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Appl. Opt.

Appl. Phys. Lett.

J. M. Rodenburg and H. M. L. Faulkner, "A phase retrieval algorithm for shifting illumination," Appl. Phys. Lett. 85, 4795-4797 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

A. Stein, K. Evans-Lutterodt, N. Bozovic and A. Taylor, "Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching," J. Vac. Sci. Technol. B 26, 122-127 (2008).
[CrossRef]

Nat. Photonics

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-riege, A. Szoke, C. Cui et al., "Massively parallel x-ray holography," Nat. Photonics 2, 560-563 (2008).
[CrossRef]

Nat. Phys.

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]

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]

Nature

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, 342-344 (1999).
[CrossRef]

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]

Opt. Commun.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva and A. Snigirev, "Microscopic imaging and holography with hard X-rays using Fresnel zone-plates," Opt. Commun. 180, 233-238 (2000).
[CrossRef]

Opt. Eng.

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Opt. Express

Opt. Lett.

Phys. Rev. A

H. Mimura, H. Yumoto, S. Matsuyama, S. Handa, T. Kimura, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa et al., "Direct determination of the wave field of an x-ray nanobeam," Phys. Rev. A 77, 015812 (2008).

Phys. Rev. B

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003).
[CrossRef]

Phys. Rev. Lett.

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander and S. Vogt, "Nanometer linear focusing of hard x rays by a multilayer Laue lens," Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, "Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm," Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005).
[CrossRef] [PubMed]

Proc. SPIE

R. A. Gonsalves and R. Childlaw, "Wavefront sensing by phase retrieval," Proc. SPIE 207, 32-39 (1979).

Rev. Sci. Instrum.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk and C. David, "Inspection of refractive x-ray lenses using high-resolution differential phase contrast imaging with a microfocus x-ray source," Rev. Sci. Instrum. 78, 093707 (2007).
[CrossRef] [PubMed]

Science

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

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

Ultramicroscopy

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, "Influence of the overlap parameter on the convergence of the ptychographical iterative engine," Ultramicroscopy 108, 481-487 (2008).
[CrossRef]

Other

R. G. Paxman, "Diversity imaging," in Signal Recovery and Synthesis, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper SWA1.

Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun.  30, 304-308 (l979).
[CrossRef]

S. T. Thurman, R. T. DeRosa and J. R. Fienup, "Amplitude metrics for field retrieval with hard-edge and uniformly-illuminated apertures," J. Opt. Soc. Am. A, doc. ID 101701 (posted 26 January 2009, in press).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, "Focused x-ray beam characterization by phase retrieval with a moveable phase-shifting structure," in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2008), paper FWN3.

J. W. Goodman, Introduction to Fourier Optics, 3rd Ed., (Roberts & Company, Englewood, 2005).

Supplementary Material (3)

» Media 1: MOV (2699 KB)     
» Media 2: MOV (2556 KB)     
» Media 3: MOV (3148 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setups for x-ray beam diagnostics for (a) 2D and (b) 1D beam foci. In both cases the far-field intensity patterns are measured for each position of the moveable translating structure.

Fig. 2.
Fig. 2.

(a) Amplitude transmissivity of the cylindrical lenses L 1 and L 2. Phase error (deviation from cylinder) for (b) L 1 and (c) L 2. Colorbar for phase in (b) and (c) is given in radians.

Fig. 3.
Fig. 3.

(a) Amplitude and (b) phase (deviation from sphere) of the field after L 2. (c) Square-root of the beam amplitude at the nominal focus. Line plots show cuts through amplitude of the focused beam through the origin. Colorbar in (b) is in radians.

Fig. 4.
Fig. 4.

(a) Square-root of x-ray beam amplitude at 1 mm downstream from focus. Line plots show vertical and horizontal cuts through the beam amplitude through the origin. (b) The 392 nm radius translating structure was moved to 16 positions along the transverse extent of the beam. (c) A second set of measurements with a 981 nm radius translating structure was used for an independent reconstruction.

Fig. 5.
Fig. 5.

X-ray beam intensity at the detector plane, 7.37 m from the translating structure. Square-root of the beam amplitude is shown for visualization purposes. (a) and (b) show far-field intensity patterns for the two positions of the 392 nm radius translating structure indicated by red circles in Fig. 4(b). (c) and (d) show the intensity patterns for the 981 nm radius structure for positions indicated by red circles in Fig. 4(c). (Media 1) and (Media 2), show the 16 intensity patterns for the 392 and 981 nm structures, respectively. Amplitude to the 0.75 power is shown in the multimedia files.

Fig. 6.
Fig. 6.

Square-root of the amplitude of the field reconstructed from detector measurements using (a) the 392 nm radius structure and (b) the 981 nm radius structure. (c) and (d) show cuts through the amplitude of the initial estimate (dashed curves), the true x-ray beam (solid curves) and the reconstructions with the 392 nm (circles) and the 981 nm radius structure (points).

Fig. 7.
Fig. 7.

Square-root of amplitude of the numerically refocused reconstructions obtained from measurements using the (a) 392 nm and (b) 981 nm structures. (c) Horizontal and (d) vertical cuts through the amplitude of the true x-ray beam at best focus (solid curves) and the numerically refocused reconstructions using the small (circles) and the large (points) structure.

Fig. 8.
Fig. 8.

Square-root of beam amplitude (a) at the nominal focus and (b) 1 mm downstream (plane of the translating structure). Line plots show horizontal and vertical cuts through the x-ray beam through the origin. (c) Phase of 1D binary phase-shifting structure, having unity transmissivity and phase values of 0 and π radians.

Fig. 9.
Fig. 9.

(a) Beam intensity at measurement plane. (b) After including the effect of integration due to finite pixel size (notice the very pronounced sampling effect along the y direction). (c) Result of integrating the intensity measurement in (b) along the undersampled direction. Multimedia file (Media 3) shows the 25 intensity patterns at the detector plane and the integrated measurements used for 1D phase retrieval. Amplitude to the 0.5 power is shown in (a) and (b) and to the 0.75 power in (Media 3).

Fig. 10.
Fig. 10.

(a) Initial estimate for reconstruction (dashed line). Projection of the true field at the position of the translating structure (solid curve) and 1D reconstruction (points). (b) Amplitude of the true beam projection at 2 μm downstream the nominal focus (solid curve) and the numerically refocused reconstruction (points).

Equations (10)

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u 1 ( x 1 , y 1 ) = t 1 ( x 1 , y 1 ) exp ( ik x 1 2 2 f ) ,
E 2 = min α , x , y x , y αû ( x x , y y ) u ( x , y ) 2 x , y u ( x , y ) 2 .
u out ( x , y ) d y = 𝓟 x , y { u in ; z } d y = 𝓟 x { u in ( x , y ) d y ; z } ,
u out ( x , y ) = 𝓟 x , y { u in ; z } = 1 iλz exp [ ik 2 z ( x 2 + y 2 ) ]
× u in ( x , y ) exp [ ik 2 z ( x 2 + y 2 ) ] exp [ i 2 π λz ( xx + yy ) ] d x d y
u out ( x , y ) = ( f x , f y ) ( x , y ) 1 { exp [ iπλz ( f x 2 + f y 2 ) ] ( x , y ) ( f x , f y ) { u in ( x , y ) } } ,
( x , y ) ( f x , f y ) { u ( x , y ) } = u ( x , y ) exp [ i 2 π ( x f x + y f y ) ] d x d y .
u in ( x , y ) = t ( x , y ) exp ( ik x 2 2 f ) ,
𝓟 x , y { u in ; z } = 1 iλz exp ( ik 2 z x 2 ) t ˜ ( x , y ) exp [ ik x 2 ( f z fz ) ] exp ( i 2 π λz xx ) d x ,
t ˜ ( x , y ) = f y y 1 { exp ( iπλz f y 2 ) y f y { t ( x , y ) } } ,

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