Abstract

Previously, we have proposed a lensless coherent imaging using a nonholographic and noniterative phase-retrieval method that allows the reconstruction of a complex-valued object from a single diffraction intensity measured with an aperture-array filter. The proof-of-concept experiment of this method has been demonstrated under the Fresnel diffraction approximation. In applications to microscopy, however, the measurement of the diffraction intensity with high numerical aperture beyond the Fresnel approximation is required to obtain the object information at high spatial resolution. Thus we have also presented an extension procedure to apply the method to the cases beyond the Fresnel approximation by means of computer simulations. Here the effectiveness of the procedure is demonstrated by the experiments, in which the reconstruction with about 10 times the resolution of our previous experiment has been achieved and the object information in depth direction has been retrieved.

© 2013 Optical Society of America

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2012 (1)

2011 (2)

2010 (3)

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

2009 (1)

2008 (2)

N. Nakajima, “Lensless coherent imaging by a deterministic phase retrieval method with an aperture-array filter,” J. Opt. Soc. Am. A 25, 742–750 (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, 394–398 (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, 034801 (2007).
[CrossRef]

N. Nakajima, “Noniterative phase retrieval from a single diffraction intensity pattern by use of an aperture array,” Phys. Rev. Lett. 98, 223901 (2007).
[CrossRef]

2006 (3)

2004 (1)

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

2003 (1)

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

1999 (2)

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

Y. Takaki and H. Ohzu, “Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy,” Appl. Opt. 38, 2204–2211 (1999).
[CrossRef]

1996 (1)

1987 (1)

1982 (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, 394–398 (2008).
[CrossRef]

Acremann, Y.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Barth, R.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Barty, A.

Beetz, T.

Bunk, O.

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, 034801 (2007).
[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 speciments,” Nature 400, 342–344 (1999).
[CrossRef]

Christophis, C.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[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, 394–398 (2008).
[CrossRef]

Cui, C.

Cullis, A. G.

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, 034801 (2007).
[CrossRef]

David, C.

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, 034801 (2007).
[CrossRef]

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]

Dobson, B. R.

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, 034801 (2007).
[CrossRef]

Du, J.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Eberhardt, W.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Eisebitt, S.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Fahimian, B. P.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Farle, M.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Feldhaus, J.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Fienup, J. R.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

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]

Fischer, P.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Friedenberger, N.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Garcia-Sucerquia, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gorniak, Th.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Graulig, C.

Grübel, G.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Grunze, M.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Guerassimova, N.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Guizar-Sicairos, M.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Gulden, J.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Gutt, C.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Hau-Riege, S. P.

He, H.

Hellwig, O.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Howells, M. R.

Hurst, A. C.

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, 034801 (2007).
[CrossRef]

Jacobsen, C.

Jefimovs, K.

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, 034801 (2007).
[CrossRef]

Jericho, M. H.

Jericho, S. K.

Jiang, H.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Johnson, I.

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, 034801 (2007).
[CrossRef]

Kanka, M.

Kapteyn, H. C.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Kirz, 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 speciments,” Nature 400, 342–344 (1999).
[CrossRef]

Klages, P.

Kreuzer, H. J.

Lörgen, M.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Lüning, J.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Mancuso, A. P.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

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

Marchesini, S.

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]

Miao, J.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

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

Nakajima, N.

Nisius, Th.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Noy, A.

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]

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

Ohzu, H.

Ollefs, K.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

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]

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

Petruck, P.

Pettit, M. E.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[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.

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, 034801 (2007).
[CrossRef]

Raines, K. S.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Reime, B.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Riesenberg, R.

Rodenburg, J. M.

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, 034801 (2007).
[CrossRef]

Rodriguez, J. A.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Rosen, R.

Rosenhahn, A.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Saleh, B. E. A.

Salha, S.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

Sandberg, R. L.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

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 speciments,” Nature 400, 342–344 (1999).
[CrossRef]

Scherz, A.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Schlotter, W. F.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Shapiro, D.

Singer, A.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Spence, J. C. H.

Staier, F.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Stöhr, J.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

Takaki, Y.

Treusch, R.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Tylisztzak, T.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Vartanyants, I. A.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Weckert, E.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Weierstall, U.

Wilhein, Th.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[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]

Wu, B.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Xu, W.

Yefanov, O. M.

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Zhu, D.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

Appl. Opt. (6)

J. Opt. Soc. Am. A (4)

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, 394–398 (2008).
[CrossRef]

Nature (3)

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

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodriguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463, 214–217 (2010).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef]

New J. Phys. (1)

A. P. Mancuso, Th. Gorniak, F. Staier, O. M. Yefanov, R. Barth, C. Christophis, B. Reime, J. Gulden, A. Singer, M. E. Pettit, Th. Nisius, Th. Wilhein, C. Gutt, G. Grübel, N. Guerassimova, R. Treusch, J. Feldhaus, S. Eisebitt, E. Weckert, M. Grunze, A. Rosenhahn, and I. A. Vartanyants, “Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH,” New J. Phys. 12, 035003 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (4)

N. Nakajima, “Noniterative phase retrieval from a single diffraction intensity pattern by use of an aperture array,” Phys. Rev. Lett. 98, 223901 (2007).
[CrossRef]

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution x-ray lensless imaging by differential holographic encoding,” Phys. Rev. Lett. 105, 043901 (2010).
[CrossRef]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[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, 034801 (2007).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental system. An object with a finite extent is illuminated by a diode laser beam. The object function is reconstructed from a single intensity pattern consisting of isolated diffraction intensities of the aperture-array filter by using the deterministic phase-retrieval method.

Fig. 2.
Fig. 2.

Reconstruction of an object consisting of lines in the portion (group 7, elements 1 and 2) of a negative USAF 1951 target with a circular pinhole of 50 μm. (a) Modulus of the object imaged by a microscope objective lens with the NA of 0.4. (b) Measured intensity in the detector plane through the array filter, which is represented on the base-10 logarithmic grayscale of a normalized intensity distribution by its peak value with a cutoff at 104 for display purposes. (c) and (d) are moduli of the reconstructed objects from the same complex amplitude, consisting of the measured modulus and the retrieved phase in the diffraction plane, by using the inverse RS integral and the inverse Fresnel integral, respectively.

Fig. 3.
Fig. 3.

Experimental data for an object having a depth structure in which an aluminum sheet with a circular pinhole of 50 μm is sandwiched between two positive USAF targets. (a) and (b) are moduli at two focal planes of the object imaged by the microscope objective lens with the NA of 0.4. The spacing between the two planes is about 140 μm. In (a) the lines at the upper part correspond to the portion (group 6, element 6) of one positive USAF target. In (b) the wide line at the lower part is equal to one of the lines in the portion (group 4, element 6) of the other positive USAF target. (c) Measured intensity pattern through the array filter in the diffraction plane for the object, which is represented in the same way as in Fig. 2(b).

Fig. 4.
Fig. 4.

Reconstruction of the object having the depth structure shown in Figs. 3(a) and 3(b). (a),(b) Show the moduli of reconstructed complex amplitudes in the object plane from the same complex amplitude, consisting of the measured modulus and the retrieved phase in the diffraction plane, by using the inverse RS integral and the inverse Fresnel integral, respectively. (c),(e) [or (d),(f)] Show the moduli of the backpropagated complex amplitudes at the positions of 30 and 155 μm, respectively, in front of the object plane from the reconstructed complex amplitude in the object plane, which was calculated by the inverse RS integral (or the inverse Fresnel integral). (c),(e) Correspond to the moduli in Figs. 3(a) and 3(b), respectively.

Equations (21)

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F(x,y)=1iλσf(u,v)exp(ikr)rcosθdudv,
r=[z2+(xu)2+(yv)2]1/2,
F(x,y)=ziλσf(u,v)exp(ikr)r2dudv.
K(ξ,η)=eikliλln=N/2N/21m=M/2M/21F(x,y)R(xxn,yym)exp{iπλl[(ξx)2+(ηy)2]}dxdy,
K(αxn,αym)eiρexp[iπλz(x2+y2)]F(x,y)R(xxn,yym)dxdy,
R(x,y)=R(x,y)exp[iπαλl(x2+y2)],
NF=(w/2)2λl(1+lz).
I1[K(αxn,αym)]=exp[iπλz(u2+v2)]fb(u,v)r(u,v),
fb(u,v)=F(xn,ym)exp{iπλz[(uxn)2+(vym)2]}dxndym.
I{exp[iπλz(u2+v2)]fb(u,v)}=exp[iπλz(xn2+ym2)]F(xn,ym),
f(u,v)=F(xn,ym)exp(ikr)r2dxndym,
r=[z2+(xnu)2+(ymv)2]1/2,
NAlimit=(2λπz+2λ)1/2.
|K(αxn±τ,αym)||exp[iπλz(x2+y2)]F(x,y)R(xxn,yym)exp(i2πλlxτ)dxdy|,
|K(αxn±τ,αym)|p|exp[iπλz(x2+y2)]F(x,y)G[x(xn±sic),yym]dxdy|,
|K(αxn±τ,αym)|p|M(xn±sic,ym)exp[iϕ(xn±sic,ym)]|.
ϕ(xn±sic,ym)=ϕR(xn±s,ym)iϕI(xn±s,ym),
|K(αxn±τ,αym)|p|M(xn±sic,ym)|exp[±ϕI(xn±s,ym)].
D(xn,ym;τ)2ϕI(xn,ym),
D(xn,ym;τ)=ln[|K[α(xns)+τ,αym]||K[α(xn+s)τ,αym]|],
ϕ(xn,ym)I1[Γ(X,ym)j=1J2isinh(2πcjX)]+Γ(0,ym)2j=1Jcjxn,

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