Abstract

We present the first experimental demonstration of the astigmatic phase retrieval technique, in which the diffracted wavefield is distorted by cylindrical curvature in two orthogonal directions. A charge-one vortex, a charge-two vortex, and a simple test image are all correctly reconstructed.

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2009 (3)

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

S. M. F. Raupach, “Cascaded adaptive-mask algorithm for twin-image removal and its application to digital holograms of ice crystals,” Appl. Opt. 48(2), 287–301 (2009).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17(4), 2670–2685 (2009).
[CrossRef]

2008 (6)

E. C. Cosgriff, A. J. D’Alfonso, L. J. Allen, S. D. Findlay, A. I. Kirkland, and P. D. Nellist, “Three-dimensional imaging in double aberration-corrected scanning confocal electron microscopy, part I: elastic scattering,” Ultramicroscopy 108(12), 1558–1566 (2008).
[CrossRef]

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

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]

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]

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. 93(21), 214101 (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]

K. A. Nugent, “X-ray noninterferometric phase imaging: a unified picture,” J. Opt. Soc. Am. A 24, 536–547 (2007).
[CrossRef]

2006 (2)

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442(7098), 63–66 (2006).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef]

2005 (3)

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61(Pt 3), 321–324 (2005).
[CrossRef]

H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30(13), 1638–1640 (2005).
[CrossRef]

2003 (3)

B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20(8), 1490–1504 (2003).
[CrossRef]

T. A. Pitts and J. F. Greenleaf, “Fresnel transform phase retrieval from magnitude,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50(8), 1035–1045 (2003).
[CrossRef]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91(20), 203902 (2003).
[CrossRef]

2001 (3)

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(3 Pt 2), 037602 (2001).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, “Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy,” Ultramicroscopy 88(2), 85–97 (2001).
[CrossRef]

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]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

1995 (2)

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12(9), 1942–1946 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef]

1994 (1)

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef]

1993 (1)

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

W. Coene, G. Janssen, M. O. Debeeck, and D. Vandyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69(26), 3743–3746 (1992).
[CrossRef]

1982 (3)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Abbey, B.

B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. 93(21), 214101 (2008).
[CrossRef]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[CrossRef]

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

Allen, L. J.

E. C. Cosgriff, A. J. D’Alfonso, L. J. Allen, S. D. Findlay, A. I. Kirkland, and P. D. Nellist, “Three-dimensional imaging in double aberration-corrected scanning confocal electron microscopy, part I: elastic scattering,” Ultramicroscopy 108(12), 1558–1566 (2008).
[CrossRef]

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61(Pt 3), 321–324 (2005).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, “Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy,” Ultramicroscopy 88(2), 85–97 (2001).
[CrossRef]

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(3 Pt 2), 037602 (2001).
[CrossRef]

Artyukhin, A. B.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Barth, R.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Barty, A.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Bates, R. H. T.

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. 1. Underlying theory,” Optik (Stuttg.) 61, 247–262 (1982).

Baumann, T.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef]

Beetz, T.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Bowers, C. W.

Bunk, O.

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]

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]

Cadenazzi, G.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

Chapman, H. N.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91(20), 203902 (2003).
[CrossRef]

Clark, J.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

Clark, J. N.

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A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Schreiber, S.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Schropp, A.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Schulz, T. J.

Seldin, J. H.

Shapiro, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Shapiro, D. A.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Singer, A.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

Spence, J. C. H.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Stadler, L. M.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Staier, F.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Stickler, D.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Stillrich, H.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Stolken, J.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Streit-Nierobisch, S.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Teague, M. R.

Thibault, P.

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]

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Tilley, L.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

Torrance, A.

B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. 93(21), 214101 (2008).
[CrossRef]

Tran, C. Q.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef]

Treusch, R.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

van Buuren, T.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

van der Spoel, D.

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]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
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Vandyck, D.

W. Coene, G. Janssen, M. O. Debeeck, and D. Vandyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69(26), 3743–3746 (1992).
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Vartanyants, I. A.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442(7098), 63–66 (2006).
[CrossRef]

Vogt, S.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

Weckert, E.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

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]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

Weierstall, U.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Wilhein, T.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Willey, T.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms,” Phys. Rev. Lett. 101(5), 055501 (2008).
[CrossRef]

Williams, G. J.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. 93(21), 214101 (2008).
[CrossRef]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442(7098), 63–66 (2006).
[CrossRef]

Wouts, R.

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]

Yurkov, M. V.

A. P. Mancuso, A. Schropp, B. Reime, L. M. Stadler, A. Singer, J. Gulden, S. Streit-Nierobisch, C. Gutt, G. Grübel, J. Feldhaus, F. Staier, R. Barth, A. Rosenhahn, M. Grunze, T. Nisius, T. Wilhein, D. Stickler, H. Stillrich, R. Frömter, H. P. Oepen, M. Martins, B. Pfau, C. M. Günther, R. Könnecke, S. Eisebitt, B. Faatz, N. Guerassimova, K. Honkavaara, V. Kocharyan, R. Treusch, E. Saldin, S. Schreiber, E. A. Schneidmiller, M. V. Yurkov, E. Weckert, and I. A. Vartanyants, “Coherent-pulse 2D crystallography using a free-electron laser x-ray source,” Phys. Rev. Lett. 102(3), 035502 (2009).
[CrossRef]

Acta Crystallogr. A (1)

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61(Pt 3), 321–324 (2005).
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Appl. Opt. (3)

Appl. Phys. Lett. (2)

B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. 93(21), 214101 (2008).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
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IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

T. A. Pitts and J. F. Greenleaf, “Fresnel transform phase retrieval from magnitude,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50(8), 1035–1045 (2003).
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J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nat. Phys. (1)

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]

Nature (2)

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]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442(7098), 63–66 (2006).
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Opt. Commun. (1)

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
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Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
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Part A (1)

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytom,” Part A 73A, 949–957 (2008).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(3 Pt 2), 037602 (2001).
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Supplementary Material (4)

» Media 1: MOV (2362 KB)     
» Media 2: MOV (2807 KB)     
» Media 3: MOV (3831 KB)     
» Media 4: MOV (1206 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

The steps of the algorithm. The wavefunctions at the lens plane (L) and at the detector plane (D) are modified by the functions between, which are explained in the accompanying text. Arrows indicate the order of the functions.

Fig. 2.
Fig. 2.

(a-c) Generated diffractive intensities on a 256×256 pixel array with: (a) horizontal curvature, (b) no curvature, and (c) vertical curvature; (d) the 100×100 pixel test sample used to generate the diffractive data, and (e) reconstruction at the 3000th iteration of the algorithm (Media 1), using a 110×110 pixel square pupil function as a support.

Fig. 3.
Fig. 3.

The set-up for the experiments; where l is the distance between the hologram or sample and the lens, and z is the distance between the exit surface of the lens and the CCD chip in the camera, and f is the focal length of the lens.

Fig. 4.
Fig. 4.

(a) Image printed onto hologram used to create the charge-two vortex; (b) Simulation for testing the quality of the reconstructed charge-two vortex.

Fig. 5.
Fig. 5.

Experimental diffraction data of a charge-one optical vortex. Where: (a), (b) and (c) are the recorded intensities of the three propagated wavefunctions.

Fig. 6.
Fig. 6.

Reconstructed charge-one vortex from a start function of random numbers. Displayed is the phase of the averaged reconstructed wavefunction, at the lens plane (Media 2).

Fig. 7.
Fig. 7.

Experimental diffraction data of a charge-two optical vortex. Where: (a), (b) and (c) are the recorded intensities of the three propagated wavefunctions.

Fig. 8.
Fig. 8.

Reconstructed charge-two vortex from a start function of random numbers. Displayed is the phase of the averaged reconstructed wavefunction, at the lens plane (Media 3).

Fig. 9.
Fig. 9.

Experimental diffraction data from an array of apertures. Where: (a), (b) and (c) are the recorded intensities of the three propagated wavefunctions. (d) Microscope image of the sample and (e) with it blurred to have a resolution comparable to the expected best resolution possible from the diffraction data. (e) Intensity of the reconstructed wavefunction at the lens plane (Media 4).

Equations (3)

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k0RxΔIx(ρ)=ρx[I(ρ)ρxΦ(ρ)],
Φ=πx2λf,
ε(p)=1N2i(IiIip)2,

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